diff --git a/CHANGELOG.md b/CHANGELOG.md
index ce136bd..7c05f16 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,28 @@ and this project adheres to [Semantic Versioning](https://semver.org/).
 This file is maintained using the shared changelog workflow in
 [`docs/ai/changelog.md`](docs/ai/changelog.md).
 
+## [Unreleased]
+
+### Changed
+
+- **Breaking: IRF convolution is now a quadrature-weighted kernel-matrix operator** (`conv_matrix_operator` / `conv_matrix_apply` in `utils/arrays.py`), replacing the sampled-1D-kernel convolution (`my_conv` + per-theta kernel support) on both the mcp and compiled (GIR) evaluation paths. Consequences:
+  - **Non-uniform time axes are convolved correctly.** The axis enters through the time-difference matrix and trapezoid quadrature weights, so measured fine-around-t0 + coarse-tail delay axes no longer produce silently biased fits (the old sample-index convolution deviated by up to ~7% of the trace maximum on example 21's stepped axis). Uniform axes agree with the previous path within its documented kernel-truncation tolerance.
+  - **Exact edge handling for any kernel width**: kernel mass beyond the time window contributes through the edge samples (edge-value padding semantics), computed analytically per kernel via edge-mass companions (`functions/time.py::CONV_EDGE_MASS`, cancellation-safe erfc/exp/clip tail forms). No support truncation at any width or axis spacing; a kernel without a registered companion is rejected at model validation (mcp) and scheduling (GIR).
+  - **Kernel parameters must be strictly positive**: widths/timescales with a non-positive initial value or lower bound — or varying without an explicit lower bound — are rejected at model load with a clear error (previously a fit could propose width = 0 and fail mid-fit). The edge-mass companions additionally reject nonpositive/non-finite parameter values at evaluation time, as a backstop for expression-driven kernel parameters (`boxCONV` with width 0 would otherwise silently become the identity operator). Example/test model YAMLs updated from `0` to `1.0E-6` lower bounds.
+  - **Non-monotonic time axes are rejected** at model construction with a clear error (previously accepted and silently misconvolved).
+  - **A kernel far narrower than the local step now degrades to identity** instead of raising a zero-sum-kernel error (the dt=0 diagonal keeps every row sum positive).
+  - **Static array shapes per evaluation**: the theta-independent operator — interior-only `(n_t, n_t)` deduplicated dt matrix, true trapezoid weights, edge-mass abscissae — is precomputed once per axis (`ScheduledPlan2D.conv_operator`, numeric kernel ids only; cached on the mcp `Component`), removing the theta-dependent kernel-shape blocker for the JAX track and the SciPy convolution utilities from the lowered conv path (the Gaussian edge masses still use `scipy.special.erfc`, which has a `jax.scipy.special` equivalent).
+  - **API removals**: `conv_kernel_support`, `Component.create_t_kernel`, and the `*_kernel_width` registry helpers are gone; kernel functions must be elementwise in their first argument and ship a `CONV_EDGE_MASS` companion. Conv components keep the model time axis instead of a private kernel-support axis.
+  - Example 21's data was regenerated through the new operator (the old operator's artifact was baked into the CSVs).
+
+### Fixed
+
+- Function-name discovery (`config/functions.py`) now only accepts functions defined in the `functions/` modules themselves. Imported helpers (`erf`, `erfc`, `wofz`, `Callable`) no longer leak into `all_functions()` / `time_functions()`, so a malformed YAML component naming one of them fails function-name validation upfront instead of erroring mid-evaluation.
+
+### Removed
+
+- **Breaking: `voigtCONV` and `lorentzCONV` convolution kernels.** Neither has a physical basis as a *time-domain* instrument response (Voigt and Lorentzian are energy-domain lineshape profiles, which the energy layer provides); no example used them. Voigt additionally has no closed-form CDF, which blocked the exact analytic edge handling above, and its removal retires `scipy.special.wofz` from `functions/time.py`. Remaining kernels: `gaussCONV`, `expSymCONV`, `expDecayCONV`, `expRiseCONV`, `boxCONV`. Model YAMLs referencing the removed kernels fail validation with an unknown-function error.
+
 ## [0.10.2] - 2026-07-10
 
 ### Added
diff --git a/TODO.md b/TODO.md
index 192e5c0..b025118 100644
--- a/TODO.md
+++ b/TODO.md
@@ -3,8 +3,6 @@
 ## Fitting
 
 - [ ] **Enable 1D time-trace fitting (post-SbS kinetics)**: wire standalone `TIME_1D` dynamics models (already evaluable on the mcp path per `docs/design/supported_models.md`, but connected to no fit method) to a fit entry point, so parameter-vs-time traces extracted from SbS results can be fit to `functions/time.py` dynamics (`expFun` sums, IRF convolution) inside the package instead of in external scripts. Frame it as the diagnostic/initialization rung before `fit_2d`, not a statistical equivalent (per-slice correlations and unpropagated SbS uncertainties make two-step inferior). Design direction: promote SbS results into a time-axis `File` — the promoted object inherits limits/CI/MCMC/save/export machinery, and trace fits land in a `SavedFitSlot` like every other fit type (no parallel fitting pipeline). Requires `File` to support time as the primary axis, which today it assumes is energy. Weighting traces by per-slice stderr ties into the `sigma_type` expansion item below.
-- [ ] **Kernel-matrix convolution (non-uniform time axes)**: replace the 1D-kernel convolution (`my_conv` + per-theta `conv_kernel_support`) with a quadrature-weighted kernel-matrix operator on both the mcp and GIR paths (one branch — parity tests couple them). Fixes silently wrong IRF convolution on non-uniform time axes (measured 2026-07-10 on example 21's 0.5→2.0 step axis: deviations up to ~7% of trace max vs the exact continuous convolution, worst just past the step change; the shipped example round-trips only because its data was generated through the same operator) and removes the theta-dependent kernel-shape jit blocker for the JAX track. One shared helper serves standalone 1D time traces and dynamics traces inside 2D models (single mcp conv site in `Model._combine_component`, plus two GIR sites), so it also enables the 1D time-trace fitting item above on measured delay axes. Requires regenerating example 21's data and one golden-value update. Plan: [docs/design/kernel-matrix-convolution.md](docs/design/kernel-matrix-convolution.md). Sequencing: after `fix-conv-kernels` merges, before the JAX backend item below.
-
 
 ## Noise and simulation
 
diff --git a/docs/ai/add-function.md b/docs/ai/add-function.md
index 30520f6..b7c755d 100644
--- a/docs/ai/add-function.md
+++ b/docs/ai/add-function.md
@@ -13,7 +13,7 @@ This guide covers both:
 
 - Format: `<function_name> <module>`
 - `function_name`: the Python function name
-  (e.g. `GLP`, `expFun`, `pGauss`, `lorentzCONV`)
+  (e.g. `GLP`, `expFun`, `pGauss`, `gaussCONV`)
 - `module`: one of `energy`, `time`, `profile`
 
 ## Module mapping
@@ -53,8 +53,22 @@ Read the source file and find the function. Verify:
 - [ ] `#\n` before function definition
 - [ ] No underscores in function name (enforced by guard test)
 - [ ] Profile functions start with `p` prefix
-- [ ] Convolution kernels end with `CONV` suffix and have a companion
-      `<name>_kernel_width()` function returning an int
+- [ ] Convolution kernels end with `CONV` suffix and are elementwise in
+      their first argument (they are evaluated on the 2D dt matrix of
+      the kernel-matrix convolution operator)
+- [ ] Convolution kernels have a private edge-mass companion
+      `_<name>_edge_mass(dt_left, dt_right, *params)` registered in
+      `CONV_EDGE_MASS` (in `functions/time.py`). It must return the
+      exact analytic integrals of the kernel body — *including its
+      normalization* — over `(-inf, t[0]]` and `[t[-1], inf)`, using
+      cancellation-safe tail forms (erfc / direct exp / clip, never
+      `G(inf) - G(x)` CDF differences). Companions must validate their
+      parameters via `_validate_kernel_par` (strictly positive, finite)
+      — they are the runtime backstop for expression-driven kernel
+      parameters that bypass model-load bound checks. A kernel without
+      a companion fails model validation (mcp) and scheduling (GIR).
+      Kernels whose body has no closed-form antiderivative do not fit
+      this contract (this is why `voigtCONV` was removed).
 
 Note: these functions do NOT use `*` for keyword-only args because the
 framework calls them via `self.fct(x, **parameters)`.
@@ -73,7 +87,12 @@ Registration notes:
 - Background functions are manually listed in
   `src/trspecfit/config/functions.py::background_functions()`.
 - Convolution kernels are discovered dynamically by their `CONV` suffix in
-  `config/functions.py`; they do not require a separate manual registry there.
+  `config/functions.py` (no manual registry there), but additionally
+  require two manual entries: the `CONV_EDGE_MASS` companion registry in
+  `functions/time.py` (mcp path; missing entry fails model validation)
+  and, for GIR support, `CONV_EDGE_MASS_DISPATCH` in `eval_2d.py`
+  alongside `CONV_KERNEL_DISPATCH` (missing entry fails scheduling).
+  A completeness test asserts kernels and companions stay in lockstep.
 
 Module-specific guidance:
 
@@ -140,12 +159,17 @@ Convolution kernels:
 - [ ] Add the kernel to the convolution enum/name mapping in
       `src/trspecfit/graph_ir.py`.
 - [ ] Add runtime dispatch in `src/trspecfit/eval_2d.py`
-      (`CONV_KERNEL_DISPATCH`).
-- [ ] Verify kernel-width handling still works with the new kernel.
+      (`CONV_KERNEL_DISPATCH` **and** `CONV_EDGE_MASS_DISPATCH` — the
+      edge-mass companion, keyed by the same enum; scheduling fails
+      without it).
+- [ ] Verify the kernel is elementwise in its first argument (it is
+      evaluated on the deduplicated dt values; no shape assumptions, no
+      normalization requirements — the operator row-normalizes; the
+      edge-mass companion must match the body's normalization though).
 - [ ] Verify unsupported kernels still fall back cleanly to MCP.
 - [ ] If lowering fails, recommend a kernel signature and behavior compatible
-      with the current compiled path (pure kernel function, explicit parameter
-      list, companion `<name>_kernel_width(...)`, no hidden state).
+      with the current compiled path (pure elementwise kernel function,
+      explicit parameter list, no hidden state).
 
 Profile functions:
 
@@ -245,9 +269,15 @@ test_half_max_at_half_width -- FWHM check using independent property, NOT formul
 test_zero_for_negative_x    -- (causal kernels only: expDecayCONV)
 test_zero_for_positive_x    -- (anti-causal kernels only: expRiseCONV)
 test_decays_monotonically   -- monotonic decay away from peak
-test_kernel_width_positive  -- companion kernel_width() > 0
 ```
 
+Additionally, register the kernel in `_KERNEL_TEST_PARAMS` in
+`tests/test_functions_convolution.py`: the parametrized
+`TestConvEdgeMassCompanions` suite iterates `CONV_EDGE_MASS` and checks
+every companion against `scipy.integrate.quad` of the kernel body, plus
+registry/dispatch completeness — verify the new kernel is picked up
+(the sync test fails until the params entry exists).
+
 **Profile functions**:
 
 ```text
diff --git a/docs/design/archive/kernel-matrix-convolution.md b/docs/design/archive/kernel-matrix-convolution.md
new file mode 100644
index 0000000..9d03acd
--- /dev/null
+++ b/docs/design/archive/kernel-matrix-convolution.md
@@ -0,0 +1,290 @@
+---
+orphan: true
+---
+
+# Kernel-Matrix Convolution
+
+> **Status: implemented** (2026-07, `conv-kernel-matrix` branch). The
+> operator lives in `utils/arrays.py` (`conv_matrix_operator` /
+> `conv_matrix_apply`, bundled as the `ConvOperator` NamedTuple:
+> `dt_unique`, `gather_idx`, `quad_weights`, `dt_left`, `dt_right`);
+> the mcp path consumes it via `Component.conv_operator()` /
+> `Component.convolve()` (cached per `Component.time` identity) and the
+> GIR path via the `ScheduledPlan2D.conv_operator` plan field (numeric
+> kernel ids only — companions resolve via enum-keyed dispatch, so the
+> plan stays serializable).
+>
+> **Edge handling (revised 2026-07-11):** the note below proposed edge
+> policy (b) via a ghost-point extension of the quadrature grid. That
+> was implemented first, then replaced: its coverage (`n_t` ghost
+> samples per side continuing the boundary step) silently truncated
+> kernels broader than `n_t x boundary_step`, and row normalization hid
+> the loss — worst exactly on fine-boundary axes (user-reported). The
+> final implementation computes the exterior masses **analytically**:
+> each kernel registers a private edge-mass companion in
+> `functions/time.py::CONV_EDGE_MASS` returning the exact integrals of
+> the kernel body over `(-inf, t[0]]` and `[t[-1], inf)`
+> (cancellation-safe tail forms: erfc / exp / clip). No ghost points,
+> no coverage limit, no truncation for any theta; the dt matrix is
+> interior-only `(n_t, n_t)` with true trapezoid weights (half-cells at
+> the window edges). This is what made dropping `voigtCONV` (no
+> closed-form CDF) and `lorentzCONV` (no time-domain physical basis)
+> part of this change; it also retired `wofz` from `functions/time.py`.
+> Kernels without a companion are rejected at model validation (mcp)
+> and scheduling (GIR); kernel parameters must be strictly positive
+> with positive lower bounds, enforced at model load.
+>
+> Other deviations from the plan below:
+>
+> 1. a kernel far narrower than the local step now degrades to identity
+>    (the dt=0 diagonal keeps row sums positive) instead of raising the
+>    old zero-sum-kernel error;
+> 2. the kernel is evaluated only on the **unique** dt values
+>    (`dt_unique` + `gather_idx` reconstruction) rather than the full
+>    matrix — a naive elementwise evaluation was a 2.6x GIR regression;
+>    the dedup makes the new path faster than the old 1D convolution.
+>
+> **Measured results** (2026-07-11, ghost-scheme state; see changelog
+> for the final edge-mass numbers):
+>
+> - *Accuracy on example 21's non-uniform axis* (steps 0.5 → 2.0, truth
+>   parameters): worst-case deviation from the exact continuous
+>   convolution dropped from ~7% of trace max (old sample-index
+>   convolution) to ~4% (residual O(h) sampling at the ``expFun`` jump).
+> - *Performance, example 01* (the conv GIR path, 481x400 grid,
+>   `benchmark_gir.py --example 1 --calls 200`): 2.95 ms/call GIR
+>   (interior-only matrix + analytic edge masses; was 8.4 ms/call with
+>   the ghost scheme, ~11 ms/call with the original 1D kernel); 6.5x vs
+>   the interpreter per-call.
+> - *Parity*: mcp and GIR paths agree to 4.4e-14 (max |diff|).
+>
+> The next section records the final design decisions (folded from the
+> implementation plan when it was cleared); the rest of this note is
+> the original planning note, kept for the rationale and the measured
+> defect it fixed.
+
+## Final design decisions (2026-07-11)
+
+- **Kernel drop rationale.** `voigtCONV` and `lorentzCONV` were removed
+  on physics grounds: neither has a basis as a *time-domain* IRF (Voigt
+  and Lorentzian are energy-domain lineshape stories, already covered by
+  the energy layer), and no example used them; pre-1.0 is the time to
+  remove names. Voigt's missing closed-form CDF is what blocked the
+  exact-edge design; Lorentz has an elementary CDF
+  (`(W/2)(atan(2x/W) + pi/2)` for our body), so its removal was the
+  physics/API call, not a technical necessity.
+- **Companions return masses, not CDFs.**
+  `_<name>CONV_edge_mass(dt_left, dt_right, *params) -> (M_L, M_R)`,
+  where `M_L(i)` is the integral of the kernel body over `(-inf, t[0]]`
+  (upper tail at `dt_left[i] = t_i - t[0]`) and `M_R(i)` the integral
+  over `[t[-1], inf)` (lower tail at `dt_right[i] = t_i - t[-1]`).
+  Returning masses lets each kernel use its natural well-conditioned
+  form — `erfc` for gauss, direct `exp` for the exponentials, `clip`
+  for box — and removes any `G(inf)`/`np.inf`-evaluation convention.
+  (Plain `G(inf) - G(x)` subtraction would already be fine in
+  *absolute* terms — masses join O(1) row sums — but the direct forms
+  are cleaner and free.) Companions must integrate the body with its
+  exact normalization: the gauss body is peak-1, so
+  `M = SD*sqrt(pi/2)*erfc(x/(sqrt(2)*SD))`; expDecay/expRise are
+  `tau`-scaled one-sided exponentials with one of the two masses
+  identically 0; expSym is piecewise; box uses the `clip` form.
+- **Quadrature weights are true trapezoid** — half-cells at both window
+  ends, NOT `np.gradient`, whose endpoint weights are full cells and
+  would double-count against the analytic edge masses.
+- **Layering.** `utils/arrays.py` stays kernel-agnostic:
+  `conv_matrix_apply(operator, kernel_values, edge_mass_left,
+  edge_mass_right, y)`; callers compute the masses via the registry.
+- **Companions are private** (`_gaussCONV_edge_mass`, ...), exposed
+  through the single public registry dict `CONV_EDGE_MASS` — one source
+  of truth for both evaluation paths, and the private names keep them
+  out of registry introspection (no INTERNAL_SUFFIXES resurrection in
+  the guard tests).
+- **No callables on the plan.** `ScheduledPlan2D` keeps numeric
+  kernel-kind ids; the evaluator resolves companions via
+  `CONV_EDGE_MASS_DISPATCH`, keyed by the same `ConvKernelKind` enum as
+  `CONV_KERNEL_DISPATCH`; `schedule_2d` only validates the entry
+  exists. This keeps the plan serializable / JAX-friendly. A missing
+  companion is a loud validation error at `add_components` /
+  `schedule_2d` time, not a silent fallback.
+- **Validation split per the two-layer design.** Authoring layer: conv
+  kernel parameters must be strictly positive, and varying parameters
+  must carry an explicit positive lower bound (the unbound
+  `[value, True]` form would give lmfit `min=-inf`), enforced at model
+  load with a clear error. The edge-mass companions validate their
+  parameters (strictly positive, finite) on every evaluation as the
+  backstop for expression-driven kernel parameters (`boxCONV` with
+  width 0 would otherwise silently become the identity operator). Hot
+  path: cheap O(n) finite/nonnegative checks on `kernel_values`, both
+  mass vectors, and all input shapes in `conv_matrix_apply` (a row-sum
+  check alone lets signed errors cancel). All of these are host-side
+  checks, outside any future jit boundary.
+- **Related registry cleanup** in the same change: function discovery
+  in `config/functions.py` was restricted to functions defined in the
+  `functions/` modules, so imported helpers (`erf`, `erfc`, `wofz`,
+  `Callable`) no longer leak into the function registry.
+- **Released as 0.11.0, not 0.10.3**: public names were removed (two
+  kernels, `conv_kernel_support`, the `*_kernel_width` helpers) and the
+  convolution semantics changed.
+
+## Summary
+
+Replace the 1D-kernel-array convolution
+([`my_conv`](../../../src/trspecfit/utils/arrays.py) plus the per-theta
+`conv_kernel_support` rebuild) with a quadrature-weighted kernel-matrix
+operator, on both the mcp and GIR paths, in one branch. Two motivations:
+
+1. **Correctness.** Sample-index convolution is silently wrong on
+   non-uniform time axes. Measured on example 21's axis
+   (steps 0.5 → 2.0) with its truth parameters (2026-07-10): up to ~7% of
+   the trace maximum versus the exact continuous convolution, worst just
+   past the step change.
+2. **Architecture.** It removes theta-dependent kernel array shapes — the
+   main jit blocker for the JAX track
+   ([jax-planning.md](../jax-planning.md)) — and retires the SciPy
+   convolution dependency in the lowered path.
+
+The mcp and GIR changes cannot be split across branches: parity tests
+assert the two paths agree to 1e-10, so the convolution semantics must
+change everywhere at once.
+
+
+## The defect today
+
+- Kernels are sampled at `t_step = time[1] - time[0]`
+  ([`Component.create_t_kernel`](../../../src/trspecfit/mcp.py),
+  `resolve_param_traces` in
+  [`eval_2d.py`](../../../src/trspecfit/eval_2d.py), and the schedule-time
+  trace init in [`graph_ir.py`](../../../src/trspecfit/graph_ir.py)).
+- `my_conv` convolves by sample index; the axis itself never enters the
+  computation. On a non-uniform axis the effective IRF width scales with
+  the local step (4x wider in example 21's coarse region), and points
+  near the step change see a blend of both regimes.
+- Nothing guards against this: a non-uniform time axis flows into the
+  convolution path silently.
+- The shipped example is self-consistent — its data was generated through
+  the same operator, so parameter recovery round-trips. Real measured
+  data on a fine-around-t0 + coarse-tail axis would produce biased fits,
+  concentrated in the IRF width and everything near the step change.
+
+
+## The operator
+
+For a monotonic time axis `t` (length `n_t`) and kernel function `g`
+with fitted parameters `theta_k`:
+
+- `dt[i, j] = t_i - t_j` — theta-independent, built once.
+- `w_j` = trapezoid quadrature weights (`np.gradient(t)`) —
+  theta-independent, built once.
+- Per evaluation: `K[i, j] = g(dt[i, j]; theta_k) * w_j`, rows
+  normalized to sum to 1; then `y_conv = K @ y`.
+
+Properties:
+
+- Exact on any monotonic axis; on a uniform axis the weights cancel in
+  the row normalization and the result matches the current path up to
+  the (small) truncation of the current finite support.
+- Static shapes, no support truncation at all — this supersedes the
+  dynamic-support machinery from the `fix-conv-kernels` branch rather
+  than layering on top of it.
+- Differentiable and jit-friendly: per-theta work is an elementwise
+  kernel evaluation plus a matmul.
+- O(n_t^2) per convolution node per evaluation. At the current
+  n_t ~ hundreds this is sub-millisecond; see the benchmark gate below.
+
+
+## Generality: one operator for 1D and 2D
+
+Call-site inventory — every convolution in the package acts on a 1D
+trace sampled on the time axis:
+
+- **mcp (single site).** `Model._combine_component` in
+  [`mcp.py`](../../../src/trspecfit/mcp.py) handles `comp_type == "conv"`
+  for standalone `TIME_1D` models and for dynamics traces inside 2D
+  models alike — parameter time dependence evaluates via
+  `par.t_model.create_value_1d()`, i.e. the 2D case reuses the 1D
+  time-trace evaluator. Replacing this one site covers both.
+- **GIR (two sites).** The `kind == 2` branch of
+  `resolve_param_traces` in
+  [`eval_2d.py`](../../../src/trspecfit/eval_2d.py), and the schedule-time
+  trace initialization in
+  [`graph_ir.py`](../../../src/trspecfit/graph_ir.py). The plan gains the
+  precomputed `dt` matrix and weights; the per-theta support recompute
+  disappears.
+- **Future.** The 1D time-trace fitting item in `TODO.md` inherits
+  correct convolution on measured (typically non-uniform) delay axes
+  automatically — the matrix operator is an enabler for that feature,
+  not just compatible with it.
+- Energy-domain convolution remains undefined (explicitly rejected in
+  `_combine_component`); out of scope here, though the same helper
+  would apply if it is ever defined.
+
+
+## Design decisions
+
+1. **Edge policy.** `my_conv` pads the signal with edge values
+   (`mode="edge"`), convolves, and crops. Matrix equivalents:
+   (a) row normalization only — kernel mass falling outside the window
+   is renormalized over interior samples; or (b) edge-mass
+   accumulation — kernel mass beyond each end of the axis is added to
+   the first/last column, reproducing edge-padding semantics.
+   Recommendation: (b). It matches current behavior on uniform axes
+   (signal assumed constant beyond the window — the right assumption
+   for saturating or decaying traces) and minimizes golden-value churn.
+   Decide before implementation and test both edge rows explicitly.
+2. **Kernel bodies evaluate on `dt` directly.** Registry kernel
+   functions (`gaussCONV`, …) are elementwise in their first argument,
+   so they apply to the `dt` matrix unchanged; no new numeric bodies.
+   The `*_kernel_width` helpers and `conv_kernel_support` existed only
+   to size the 1D support and are removed together with the
+   dynamic-support recompute and its tests.
+3. **Normalization.** Per-row, generalizing the current
+   kernel-divided-by-sum normalization to non-uniform sampling.
+4. **Validation.** Keep a monotonic-axis check at the authoring layer;
+   non-uniform spacing stops being a (silent) error condition and
+   becomes supported.
+
+
+## Implementation order and blast radius
+
+1. `utils/arrays.py`: matrix-convolution helper (theta-independent
+   builder + per-theta apply), unit-tested against an analytic
+   Gaussian-times-exponential reference, uniform-axis agreement with
+   the current path within truncation tolerance, and a dense
+   continuous-convolution reference on a non-uniform axis.
+2. mcp path: `_combine_component` and the `Component` kernel handling
+   (`create_t_kernel` path).
+3. GIR: plan fields (`dt`, weights; kernel function ids stay), the
+   `kind == 2` branch of `resolve_param_traces`, and the schedule-time
+   init convolution.
+4. Parity: mcp vs GIR tests keep asserting 1e-10 — both paths must
+   consume the same helper.
+5. Regenerate example 21's data (`generate_data.ipynb`; the old
+   operator's artifact is baked into the CSVs) and re-run affected
+   examples per `docs/ai/check-example.md`. Update roundtrip/golden
+   values once.
+6. Benchmark before/after per `docs/ai/benchmark.md`. The O(n_t^2)
+   cost is expected to be noise at current sizes; if long time axes
+   ever make it matter, the escape hatch is a banded matrix with a
+   static support cap derived from parameter bounds (shapes stay
+   static).
+
+
+## Relationship to the JAX track
+
+Land this before Phase B/C of [jax-planning.md](../jax-planning.md). It
+removes two blockers listed there: the SciPy convolution utilities in
+the lowered path, and the theta-dependent kernel shapes introduced by
+the dynamic-support fix. After this change, porting convolution to JAX
+is an elementwise kernel evaluation plus a matmul.
+
+
+## Success criteria
+
+- Non-uniform-axis convolution matches a dense continuous-convolution
+  reference to floating-point tolerance.
+- Uniform-axis results match the previous path within the documented
+  truncation tolerance; examples and golden values updated exactly once.
+- mcp/GIR parity retained at 1e-10.
+- No per-theta array shapes remain anywhere in the convolution path.
+- Benchmarks show no regression beyond noise, or document the banded
+  fallback and its trigger.
diff --git a/docs/design/jax-planning.md b/docs/design/jax-planning.md
index 53993ab..aeca284 100644
--- a/docs/design/jax-planning.md
+++ b/docs/design/jax-planning.md
@@ -73,13 +73,12 @@ useful cleanup before or during a JAX port:
   `evaluate(plan, theta)` is already the right API. New work should protect
   that contract rather than pushing JAX concerns back into model objects or
   fit-time parsing.
-- **Land kernel-matrix convolution first.** The lowered convolution path
-  builds a theta-dependent 1D kernel whose support length tracks the fitted
-  width — silently wrong on non-uniform time axes and a jit blocker
-  (theta-dependent array shapes). Replacing it with the quadrature-weighted
-  kernel-matrix operator
-  ([kernel-matrix-convolution.md](kernel-matrix-convolution.md)) on the
-  NumPy paths removes that blocker before the port begins.
+- **Kernel-matrix convolution has landed** (2026-07): the lowered
+  convolution path now evaluates registry kernels elementwise on a
+  precomputed dt matrix and applies a quadrature-weighted matmul
+  ([kernel-matrix-convolution.md](archive/kernel-matrix-convolution.md)). All
+  array shapes in the convolution path are theta-independent, so the
+  former jit blocker (per-theta kernel support lengths) is gone.
 
 Of these, expression flattening is the one prep item most worth doing even if
 the eventual backend choice changes again.
@@ -99,11 +98,15 @@ The main technical work is in the evaluator itself:
 - **Host-side checks must stay outside the jitted region.** Shape checks and
   Python exceptions are fine at the outer boundary, but should not live inside
   the compiled path.
-- **SciPy-dependent kernels need JAX-compatible replacements.** The current
-  code still depends on SciPy for Voigt/Faddeeva (`wofz`) and for convolution
-  utilities used by the lowered convolution path. The kernel-matrix change
-  ([kernel-matrix-convolution.md](kernel-matrix-convolution.md)) retires the
-  convolution dependency, leaving Voigt/`wofz` as the remaining gap.
+- **SciPy-dependent kernels need JAX-compatible replacements.** The
+  kernel-matrix change
+  ([kernel-matrix-convolution.md](archive/kernel-matrix-convolution.md)) retired
+  the SciPy convolution utilities from the lowered path, and the removal
+  of `voigtCONV`/`lorentzCONV` (2026-07) retired `wofz` from
+  `functions/time.py` entirely — the conv path is now JAX-expressible
+  (`erfc` for the Gaussian edge masses exists in `jax.scipy.special`).
+  The energy-domain `Voigt` profile still uses `wofz` and remains the
+  one special-function gap.
 
 ### 3. Jacobian and optimizer work
 
@@ -183,7 +186,7 @@ Add the remaining lowered features incrementally:
 - profile-varying parameters,
 - subcycle-aware dynamics,
 - resolved-trace convolution (kernel-matrix form; see
-  [kernel-matrix-convolution.md](kernel-matrix-convolution.md)),
+  [kernel-matrix-convolution.md](archive/kernel-matrix-convolution.md)),
 - Voigt / special-function support.
 
 Each widening step should ship with direct parity tests against the existing
diff --git a/docs/design/kernel-matrix-convolution.md b/docs/design/kernel-matrix-convolution.md
deleted file mode 100644
index a287324..0000000
--- a/docs/design/kernel-matrix-convolution.md
+++ /dev/null
@@ -1,168 +0,0 @@
----
-orphan: true
----
-
-# Planning Note: Kernel-Matrix Convolution
-
-## Summary
-
-Replace the 1D-kernel-array convolution
-([`my_conv`](../../src/trspecfit/utils/arrays.py) plus the per-theta
-`conv_kernel_support` rebuild) with a quadrature-weighted kernel-matrix
-operator, on both the mcp and GIR paths, in one branch. Two motivations:
-
-1. **Correctness.** Sample-index convolution is silently wrong on
-   non-uniform time axes. Measured on example 21's axis
-   (steps 0.5 → 2.0) with its truth parameters (2026-07-10): up to ~7% of
-   the trace maximum versus the exact continuous convolution, worst just
-   past the step change.
-2. **Architecture.** It removes theta-dependent kernel array shapes — the
-   main jit blocker for the JAX track
-   ([jax-planning.md](jax-planning.md)) — and retires the SciPy
-   convolution dependency in the lowered path.
-
-The mcp and GIR changes cannot be split across branches: parity tests
-assert the two paths agree to 1e-10, so the convolution semantics must
-change everywhere at once.
-
-
-## The defect today
-
-- Kernels are sampled at `t_step = time[1] - time[0]`
-  ([`Component.create_t_kernel`](../../src/trspecfit/mcp.py),
-  `resolve_param_traces` in
-  [`eval_2d.py`](../../src/trspecfit/eval_2d.py), and the schedule-time
-  trace init in [`graph_ir.py`](../../src/trspecfit/graph_ir.py)).
-- `my_conv` convolves by sample index; the axis itself never enters the
-  computation. On a non-uniform axis the effective IRF width scales with
-  the local step (4x wider in example 21's coarse region), and points
-  near the step change see a blend of both regimes.
-- Nothing guards against this: a non-uniform time axis flows into the
-  convolution path silently.
-- The shipped example is self-consistent — its data was generated through
-  the same operator, so parameter recovery round-trips. Real measured
-  data on a fine-around-t0 + coarse-tail axis would produce biased fits,
-  concentrated in the IRF width and everything near the step change.
-
-
-## The operator
-
-For a monotonic time axis `t` (length `n_t`) and kernel function `g`
-with fitted parameters `theta_k`:
-
-- `dt[i, j] = t_i - t_j` — theta-independent, built once.
-- `w_j` = trapezoid quadrature weights (`np.gradient(t)`) —
-  theta-independent, built once.
-- Per evaluation: `K[i, j] = g(dt[i, j]; theta_k) * w_j`, rows
-  normalized to sum to 1; then `y_conv = K @ y`.
-
-Properties:
-
-- Exact on any monotonic axis; on a uniform axis the weights cancel in
-  the row normalization and the result matches the current path up to
-  the (small) truncation of the current finite support.
-- Static shapes, no support truncation at all — this supersedes the
-  dynamic-support machinery from the `fix-conv-kernels` branch rather
-  than layering on top of it.
-- Differentiable and jit-friendly: per-theta work is an elementwise
-  kernel evaluation plus a matmul.
-- O(n_t^2) per convolution node per evaluation. At the current
-  n_t ~ hundreds this is sub-millisecond; see the benchmark gate below.
-
-
-## Generality: one operator for 1D and 2D
-
-Call-site inventory — every convolution in the package acts on a 1D
-trace sampled on the time axis:
-
-- **mcp (single site).** `Model._combine_component` in
-  [`mcp.py`](../../src/trspecfit/mcp.py) handles `comp_type == "conv"`
-  for standalone `TIME_1D` models and for dynamics traces inside 2D
-  models alike — parameter time dependence evaluates via
-  `par.t_model.create_value_1d()`, i.e. the 2D case reuses the 1D
-  time-trace evaluator. Replacing this one site covers both.
-- **GIR (two sites).** The `kind == 2` branch of
-  `resolve_param_traces` in
-  [`eval_2d.py`](../../src/trspecfit/eval_2d.py), and the schedule-time
-  trace initialization in
-  [`graph_ir.py`](../../src/trspecfit/graph_ir.py). The plan gains the
-  precomputed `dt` matrix and weights; the per-theta support recompute
-  disappears.
-- **Future.** The 1D time-trace fitting item in `TODO.md` inherits
-  correct convolution on measured (typically non-uniform) delay axes
-  automatically — the matrix operator is an enabler for that feature,
-  not just compatible with it.
-- Energy-domain convolution remains undefined (explicitly rejected in
-  `_combine_component`); out of scope here, though the same helper
-  would apply if it is ever defined.
-
-
-## Design decisions
-
-1. **Edge policy.** `my_conv` pads the signal with edge values
-   (`mode="edge"`), convolves, and crops. Matrix equivalents:
-   (a) row normalization only — kernel mass falling outside the window
-   is renormalized over interior samples; or (b) edge-mass
-   accumulation — kernel mass beyond each end of the axis is added to
-   the first/last column, reproducing edge-padding semantics.
-   Recommendation: (b). It matches current behavior on uniform axes
-   (signal assumed constant beyond the window — the right assumption
-   for saturating or decaying traces) and minimizes golden-value churn.
-   Decide before implementation and test both edge rows explicitly.
-2. **Kernel bodies evaluate on `dt` directly.** Registry kernel
-   functions (`gaussCONV`, …) are elementwise in their first argument,
-   so they apply to the `dt` matrix unchanged; no new numeric bodies.
-   The `*_kernel_width` helpers and `conv_kernel_support` existed only
-   to size the 1D support and are removed together with the
-   dynamic-support recompute and its tests.
-3. **Normalization.** Per-row, generalizing the current
-   kernel-divided-by-sum normalization to non-uniform sampling.
-4. **Validation.** Keep a monotonic-axis check at the authoring layer;
-   non-uniform spacing stops being a (silent) error condition and
-   becomes supported.
-
-
-## Implementation order and blast radius
-
-1. `utils/arrays.py`: matrix-convolution helper (theta-independent
-   builder + per-theta apply), unit-tested against an analytic
-   Gaussian-times-exponential reference, uniform-axis agreement with
-   the current path within truncation tolerance, and a dense
-   continuous-convolution reference on a non-uniform axis.
-2. mcp path: `_combine_component` and the `Component` kernel handling
-   (`create_t_kernel` path).
-3. GIR: plan fields (`dt`, weights; kernel function ids stay), the
-   `kind == 2` branch of `resolve_param_traces`, and the schedule-time
-   init convolution.
-4. Parity: mcp vs GIR tests keep asserting 1e-10 — both paths must
-   consume the same helper.
-5. Regenerate example 21's data (`generate_data.ipynb`; the old
-   operator's artifact is baked into the CSVs) and re-run affected
-   examples per `docs/ai/check-example.md`. Update roundtrip/golden
-   values once.
-6. Benchmark before/after per `docs/ai/benchmark.md`. The O(n_t^2)
-   cost is expected to be noise at current sizes; if long time axes
-   ever make it matter, the escape hatch is a banded matrix with a
-   static support cap derived from parameter bounds (shapes stay
-   static).
-
-
-## Relationship to the JAX track
-
-Land this before Phase B/C of [jax-planning.md](jax-planning.md). It
-removes two blockers listed there: the SciPy convolution utilities in
-the lowered path, and the theta-dependent kernel shapes introduced by
-the dynamic-support fix. After this change, porting convolution to JAX
-is an elementwise kernel evaluation plus a matmul.
-
-
-## Success criteria
-
-- Non-uniform-axis convolution matches a dense continuous-convolution
-  reference to floating-point tolerance.
-- Uniform-axis results match the previous path within the documented
-  truncation tolerance; examples and golden values updated exactly once.
-- mcp/GIR parity retained at 1e-10.
-- No per-theta array shapes remain anywhere in the convolution path.
-- Benchmarks show no regression beyond noise, or document the banded
-  fallback and its trigger.
diff --git a/docs/design/repo_architecture.md b/docs/design/repo_architecture.md
index d325f43..5759bc0 100644
--- a/docs/design/repo_architecture.md
+++ b/docs/design/repo_architecture.md
@@ -216,9 +216,15 @@ Dynamics and convolution kernels. Dynamics functions (e.g. `expFun`,
 `func(t, par1, ..., t0)` with the invariant `f(t < t0) = 0`; constant
 offsets are their own additive component (`stepFun`, or `erfFun` for a
 broadened onset) rather than a `y0` parameter on every function.
-Convolution kernels are named `funcCONV` (e.g. `gaussCONV`) with a
-companion `funcCONV_kernel_width(...)` returning the kernel-width multiplier.
-Add new time-domain behavior or IRF kernels here.
+Convolution kernels are named `funcCONV` (e.g. `gaussCONV`) and must be
+elementwise in their first argument: the kernel-matrix convolution
+evaluates them on a 2D matrix of time differences
+(`utils.arrays.conv_matrix_operator`). Every kernel additionally
+registers a private edge-mass companion in `CONV_EDGE_MASS` (exact
+analytic exterior masses of the kernel body, for edge-value padding);
+kernels without one are rejected at model validation and scheduling.
+Add new time-domain behavior or IRF kernels here (see
+`docs/ai/add-function.md` for the full checklist).
 
 ### `functions/profile.py`
 
@@ -233,11 +239,15 @@ shapes here.
 
 ### `utils/arrays.py`
 
-Array/numeric helpers. Notably `my_conv` (used by the 2D evaluator for
-IRF convolution), `format_float_scientific` (fixed-width scientific
-notation), `oom` (order-of-magnitude), running averages, sign-change
-detection, angular normalization. Use `my_conv` rather than rolling your
-own `scipy.signal.convolve` wrapper.
+Array/numeric helpers. Notably the kernel-matrix convolution pair
+`conv_matrix_operator` / `conv_matrix_apply` (used by both the mcp and
+GIR evaluators for IRF convolution — exact on non-uniform time axes,
+static shapes per theta, exterior kernel mass handled analytically via
+per-kernel edge-mass companions), `my_conv` (padded 1D convolution, now only
+backing `running_mean`), `format_float_scientific` (fixed-width
+scientific notation), `oom` (order-of-magnitude), running averages,
+sign-change detection, angular normalization. Use these rather than
+rolling your own `scipy.signal.convolve` wrapper.
 
 ### `utils/hdf5.py`
 
diff --git a/docs/quickstart.md b/docs/quickstart.md
index 5fc340c..503bc12 100644
--- a/docs/quickstart.md
+++ b/docs/quickstart.md
@@ -79,7 +79,7 @@ model_name:
 - **Peaks**: `Gauss`, `GaussAsym`, `Lorentz`, `Voigt`, `GLP`, `GLS`, `DS`
 - **Backgrounds**: `LinBack`, `Shirley`, `Offset`
 - **Time dynamics**: `linFun`, `expFun`, `sinFun`, `sinDivX`, `erfFun`, `sqrtFun`
-- **Convolution kernels**: `gaussCONV`, `lorentzCONV`, `expDecayCONV`, `expRiseCONV`
+- **Convolution kernels**: `gaussCONV`, `expSymCONV`, `expDecayCONV`, `expRiseCONV`, `boxCONV`
 - **Profile functions**: `pExpDecay`, `pLinear`, `pGauss`
 
 See the [API Reference](api/index.rst) for all function signatures and
diff --git a/examples/fitting_workflows/01_basic_fitting/data/models_time_truth.yaml b/examples/fitting_workflows/01_basic_fitting/data/models_time_truth.yaml
index 360be80..adabef8 100644
--- a/examples/fitting_workflows/01_basic_fitting/data/models_time_truth.yaml
+++ b/examples/fitting_workflows/01_basic_fitting/data/models_time_truth.yaml
@@ -3,7 +3,7 @@
 
 MonoExpIRF:
     gaussCONV:
-        SD: [3, True]
+        SD: [3, True, 1.0E-6, 10]
     expFun:
         A: [5, True]
         tau: [50, True]
diff --git a/examples/fitting_workflows/01_basic_fitting/models_time.yaml b/examples/fitting_workflows/01_basic_fitting/models_time.yaml
index 640f464..b3b64ff 100644
--- a/examples/fitting_workflows/01_basic_fitting/models_time.yaml
+++ b/examples/fitting_workflows/01_basic_fitting/models_time.yaml
@@ -3,7 +3,7 @@
 
 MonoExpIRF:
     gaussCONV:
-        SD: [5, True, 0, 10]
+        SD: [5, True, 1.0E-6, 10]
     expFun:
         A: [5, True, 0, 15]
         tau: [10, True, 1, 100]
diff --git a/examples/fitting_workflows/03_multi_cycle_dynamics/data/models_time_truth.yaml b/examples/fitting_workflows/03_multi_cycle_dynamics/data/models_time_truth.yaml
index c6a84cf..3eb7210 100644
--- a/examples/fitting_workflows/03_multi_cycle_dynamics/data/models_time_truth.yaml
+++ b/examples/fitting_workflows/03_multi_cycle_dynamics/data/models_time_truth.yaml
@@ -5,7 +5,7 @@
 # global element 0: Gaussian instrument response, convolves all time traces
 IRF:
     gaussCONV:
-        SD: [0.15, True]
+        SD: [0.15, True, 1.0E-6, 1]
 
 # subcycle 1: negative shift, decays back to 0 on its local clock
 MonoExpNeg:
diff --git a/examples/fitting_workflows/03_multi_cycle_dynamics/models_time.yaml b/examples/fitting_workflows/03_multi_cycle_dynamics/models_time.yaml
index 5076e97..15ecce5 100644
--- a/examples/fitting_workflows/03_multi_cycle_dynamics/models_time.yaml
+++ b/examples/fitting_workflows/03_multi_cycle_dynamics/models_time.yaml
@@ -9,7 +9,7 @@
 # (Use a model containing only `none: {}` here if no global effect is needed.)
 IRF:
     gaussCONV:
-        SD: [0.1, True, 0, 1]
+        SD: [0.1, True, 1.0E-6, 1]
 
 # Subcycle 1: negative exponential shift, relaxing back to 0.
 # t0 is on the subcycle's local clock, which resets at each subcycle start.
diff --git a/examples/fitting_workflows/04_parameter_profiles/data/models_time_truth.yaml b/examples/fitting_workflows/04_parameter_profiles/data/models_time_truth.yaml
index 6435757..321f4b1 100644
--- a/examples/fitting_workflows/04_parameter_profiles/data/models_time_truth.yaml
+++ b/examples/fitting_workflows/04_parameter_profiles/data/models_time_truth.yaml
@@ -9,7 +9,7 @@
 # the bands are driven all the way to flat-band condition (SPV saturation).
 BandBendingRecovery:
     gaussCONV:
-        SD: [10, True]
+        SD: [10, True, 1.0E-6, 100]
     expFun:
         A: [0.5, True]
         tau: [100, True]
diff --git a/examples/fitting_workflows/10_model_comparison/models_time.yaml b/examples/fitting_workflows/10_model_comparison/models_time.yaml
index 48469f4..94e5f62 100644
--- a/examples/fitting_workflows/10_model_comparison/models_time.yaml
+++ b/examples/fitting_workflows/10_model_comparison/models_time.yaml
@@ -5,7 +5,7 @@
 # Matches the simulated ground truth in this notebook (IRF σ ≈ 3, τ ≈ 30).
 MonoExpPosIRF:
     gaussCONV:
-        SD: [3, True, 0, 10]
+        SD: [3, True, 1.0E-6, 10]
     expFun:
         A: [2, True, 0, 10]
         tau: [30, True, 1, 100]
diff --git a/examples/fitting_workflows/20_multi_file_independent_fit/models_time.yaml b/examples/fitting_workflows/20_multi_file_independent_fit/models_time.yaml
index 1bed166..32a1e6c 100644
--- a/examples/fitting_workflows/20_multi_file_independent_fit/models_time.yaml
+++ b/examples/fitting_workflows/20_multi_file_independent_fit/models_time.yaml
@@ -3,7 +3,7 @@
 
 MonoExpPosIRF:
     gaussCONV:
-        SD: [5, project, 0, 10]
+        SD: [5, project, 1.0E-6, 10]
     expFun:
         A: [5, file, 0, 15]
         tau: [10, project, 1, 100]
diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_1.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_1.csv
index 1b89c32..c87f2be 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_1.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_1.csv
@@ -16,7 +16,7 @@
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diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_2.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_2.csv
index c2a7994..a8e6079 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_2.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_2.csv
@@ -30,69 +30,69 @@
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diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_3.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_3.csv
index f72aa16..372b63a 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_3.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_3.csv
@@ -29,70 +29,70 @@
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diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_4.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_4.csv
index 0360e2e..405f00b 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_4.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_4.csv
@@ -1,98 +1,98 @@
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diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_5.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_5.csv
index 85b0c5b..a3983f7 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_5.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_5.csv
@@ -34,65 +34,65 @@
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diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_6.csv b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_6.csv
index 21a2766..865f281 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/data_6.csv
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/data_6.csv
@@ -35,64 +35,64 @@
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
diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/data/models_time_truth.yaml b/examples/fitting_workflows/21_multi_file_shared_fit/data/models_time_truth.yaml
index 9a48413..481178f 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/data/models_time_truth.yaml
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/data/models_time_truth.yaml
@@ -2,7 +2,7 @@
 
 MonoExpPosIRF:
     gaussCONV:
-        SD: [3, True, 0, 10]
+        SD: [3, True, 1.0E-6, 10]
     expFun:
         A: [5, True, 0, 15]
         tau: [50, True, 1, 100]
diff --git a/examples/fitting_workflows/21_multi_file_shared_fit/models_time.yaml b/examples/fitting_workflows/21_multi_file_shared_fit/models_time.yaml
index 1bed166..32a1e6c 100644
--- a/examples/fitting_workflows/21_multi_file_shared_fit/models_time.yaml
+++ b/examples/fitting_workflows/21_multi_file_shared_fit/models_time.yaml
@@ -3,7 +3,7 @@
 
 MonoExpPosIRF:
     gaussCONV:
-        SD: [5, project, 0, 10]
+        SD: [5, project, 1.0E-6, 10]
     expFun:
         A: [5, file, 0, 15]
         tau: [10, project, 1, 100]
diff --git a/examples/synthetic_data/01_simulator/models_time.yaml b/examples/synthetic_data/01_simulator/models_time.yaml
index fbad753..cec6377 100644
--- a/examples/synthetic_data/01_simulator/models_time.yaml
+++ b/examples/synthetic_data/01_simulator/models_time.yaml
@@ -5,7 +5,7 @@ IRF:
     # define Gauss to convolve everything with 
     # (instrument response function)
     gaussCONV:
-        SD: [5.0E-2, True, 0, 1]
+        SD: [5.0E-2, True, 1.0E-6, 1]
              
 MonoExpPos:
     # expFun(t, A, tau, t0)
@@ -23,7 +23,7 @@ MonoExpNeg:
 
 MonoExpPosIRF:
     gaussCONV:
-        SD: [3, True, 0, 10]
+        SD: [3, True, 1.0E-6, 10]
     expFun:
         A: [5, True, 0, 15]
         tau: [50, True, 1, 100]
diff --git a/examples/synthetic_data/02_ml_training_data/models_time.yaml b/examples/synthetic_data/02_ml_training_data/models_time.yaml
index 9af37f8..0b08183 100644
--- a/examples/synthetic_data/02_ml_training_data/models_time.yaml
+++ b/examples/synthetic_data/02_ml_training_data/models_time.yaml
@@ -5,7 +5,7 @@ IRF:
     # define Gauss to convolve everything with 
     # (instrument response function)
     gaussCONV:
-        SD: [5.0E-2, True, 0, 1]
+        SD: [5.0E-2, True, 1.0E-6, 1]
              
 MonoExpPos:
     # expFun(t, A, tau, t0)
@@ -23,7 +23,7 @@ MonoExpNeg:
 
 MonoExpPosIRF:
     gaussCONV:
-        SD: [3, True, 0, 10]
+        SD: [3, True, 1.0E-6, 10]
     expFun:
         A: [5, True, 0, 15]
         tau: [50, True, 1, 100]
diff --git a/pyproject.toml b/pyproject.toml
index 596a68c..2466263 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "trspecfit"
-version = "0.10.2"
+version = "0.11.0"
 authors = [
     {name = "Johannes Mahl", email = "infinitymonkeyatwork@gmail.com"},
 ]
diff --git a/src/trspecfit/config/functions.py b/src/trspecfit/config/functions.py
index 522b50c..a05521a 100644
--- a/src/trspecfit/config/functions.py
+++ b/src/trspecfit/config/functions.py
@@ -18,22 +18,36 @@
 from trspecfit.functions import time as fcts_time
 
 
+#
+def _module_functions(module) -> tuple[str, ...]:
+    """
+    Get public function names defined in a functions module.
+
+    Only plain functions whose ``__module__`` is the module itself are
+    discovered: imported names (scipy/numpy helpers, typing constructs)
+    would otherwise leak into the registry and let malformed YAML pass
+    function-name validation only to fail during evaluation.
+    """
+
+    return tuple(
+        name
+        for name in dir(module)
+        if not name.startswith("_")
+        and inspect.isfunction(getattr(module, name))
+        and getattr(module, name).__module__ == module.__name__
+    )
+
+
 #
 def all_functions() -> tuple[str, ...]:
     """
     Dynamically discover all available function names from the functions modules.
-    Returns a set of all function names that can be used as components.
+    Returns a tuple of all function names that can be used as components.
     """
 
-    function_names = set()
-
-    # Get all function names from each module
+    function_names: set[str] = set()
     for module in [fcts_energy, fcts_time, fcts_profile]:
-        for name in dir(module):
-            # Only include callable functions (not constants or classes)
-            if callable(getattr(module, name)) and not name.startswith("_"):
-                function_names.add(name)
-
+        function_names.update(_module_functions(module))
     return tuple(function_names)
 
 
@@ -90,11 +104,7 @@ def energy_functions() -> tuple[str, ...]:
         All public function names from energy module
     """
 
-    return tuple(
-        name
-        for name in dir(fcts_energy)
-        if callable(getattr(fcts_energy, name)) and not name.startswith("_")
-    )
+    return _module_functions(fcts_energy)
 
 
 #
@@ -115,11 +125,7 @@ def time_functions() -> tuple[str, ...]:
 
     # Get all function names from functions/time.py excluding convolutions
     return tuple(
-        name
-        for name in dir(fcts_time)
-        if callable(getattr(fcts_time, name))
-        and not name.startswith("_")
-        and not name.endswith("CONV")
+        name for name in _module_functions(fcts_time) if not name.endswith("CONV")
     )
 
 
@@ -139,13 +145,7 @@ def convolution_functions() -> tuple[str, ...]:
     """
 
     # Get all function names ending in 'CONV' from functions/time.py
-    return tuple(
-        name
-        for name in dir(fcts_time)
-        if callable(getattr(fcts_time, name))
-        and name.endswith("CONV")
-        and not name.startswith("_")
-    )
+    return tuple(name for name in _module_functions(fcts_time) if name.endswith("CONV"))
 
 
 #
diff --git a/src/trspecfit/eval_2d.py b/src/trspecfit/eval_2d.py
index 40481ba..44bda7e 100644
--- a/src/trspecfit/eval_2d.py
+++ b/src/trspecfit/eval_2d.py
@@ -9,6 +9,8 @@
 
 from __future__ import annotations
 
+from collections.abc import Callable
+
 import numpy as np
 
 from trspecfit.functions import time as fcts_time
@@ -22,7 +24,7 @@
     ParamSourceKind,
     ScheduledPlan2D,
 )
-from trspecfit.utils.arrays import conv_kernel_support, my_conv
+from trspecfit.utils.arrays import ConvOperator, conv_matrix_apply
 
 # ---------------------------------------------------------------------------
 # Dynamics dispatch table
@@ -38,30 +40,28 @@
     DynFuncKind.STEPFUN: (fcts_time.stepFun, 2),
 }
 
-# Convolution kernel dispatch: kernel function plus its *_kernel_width
-# helper.  The kernel support is rebuilt from the current kernel
-# parameters at every evaluation so it tracks the fitted width.
-# Mirrors MCP's Component.value(...) conv path.
-CONV_KERNEL_DISPATCH: dict[int, tuple] = {
-    ConvKernelKind.GAUSSCONV: (fcts_time.gaussCONV, fcts_time.gaussCONV_kernel_width),
-    ConvKernelKind.LORENTZCONV: (
-        fcts_time.lorentzCONV,
-        fcts_time.lorentzCONV_kernel_width,
-    ),
-    ConvKernelKind.VOIGTCONV: (fcts_time.voigtCONV, fcts_time.voigtCONV_kernel_width),
-    ConvKernelKind.EXPSYMCONV: (
-        fcts_time.expSymCONV,
-        fcts_time.expSymCONV_kernel_width,
-    ),
-    ConvKernelKind.EXPDECAYCONV: (
-        fcts_time.expDecayCONV,
-        fcts_time.expDecayCONV_kernel_width,
-    ),
-    ConvKernelKind.EXPRISECONV: (
-        fcts_time.expRiseCONV,
-        fcts_time.expRiseCONV_kernel_width,
-    ),
-    ConvKernelKind.BOXCONV: (fcts_time.boxCONV, fcts_time.boxCONV_kernel_width),
+# Convolution kernel dispatch.  Kernel functions are elementwise in
+# their first argument, so they evaluate directly on the precomputed
+# deduplicated dt values of the kernel-matrix operator
+# (plan.conv_operator.dt_unique).  Mirrors MCP's Component.convolve.
+CONV_KERNEL_DISPATCH: dict[int, Callable] = {
+    ConvKernelKind.GAUSSCONV: fcts_time.gaussCONV,
+    ConvKernelKind.EXPSYMCONV: fcts_time.expSymCONV,
+    ConvKernelKind.EXPDECAYCONV: fcts_time.expDecayCONV,
+    ConvKernelKind.EXPRISECONV: fcts_time.expRiseCONV,
+    ConvKernelKind.BOXCONV: fcts_time.boxCONV,
+}
+
+# Edge-mass dispatch: exact analytic exterior masses per kernel
+# (edge-value padding), keyed by the same enum as the kernel dispatch.
+# Callables live in functions/time.py (CONV_EDGE_MASS); the plan itself
+# stores only numeric kernel ids, keeping it serializable.
+CONV_EDGE_MASS_DISPATCH: dict[int, Callable] = {
+    ConvKernelKind.GAUSSCONV: fcts_time.CONV_EDGE_MASS["gaussCONV"],
+    ConvKernelKind.EXPSYMCONV: fcts_time.CONV_EDGE_MASS["expSymCONV"],
+    ConvKernelKind.EXPDECAYCONV: fcts_time.CONV_EDGE_MASS["expDecayCONV"],
+    ConvKernelKind.EXPRISECONV: fcts_time.CONV_EDGE_MASS["expRiseCONV"],
+    ConvKernelKind.BOXCONV: fcts_time.CONV_EDGE_MASS["boxCONV"],
 }
 
 
@@ -149,7 +149,6 @@ def eval_expr_program(
 #
 def resolve_param_traces(
     traces: np.ndarray,
-    time: np.ndarray,
     resolution_kinds: np.ndarray,
     resolution_indices: np.ndarray,
     dyn_group_target_row: np.ndarray,
@@ -166,6 +165,7 @@ def resolve_param_traces(
     conv_func_ids: np.ndarray,
     conv_param_indptr: np.ndarray,
     conv_param_rows: np.ndarray,
+    conv_operator: ConvOperator | None,
 ) -> None:
     """Resolve dynamics, expressions, and convolutions into *traces* in place.
 
@@ -206,21 +206,26 @@ def resolve_param_traces(
             target = int(expr_target_rows[idx])
             traces[target, :] = eval_expr_program(expr_programs[idx], traces)
         else:  # kind == 2: resolved-trace convolution
+            assert conv_operator is not None  # type guard: set when steps exist
             target = int(conv_target_rows[idx])
             func_id = int(conv_func_ids[idx])
-            kernel_func, width_func = CONV_KERNEL_DISPATCH[func_id]
+            kernel_func = CONV_KERNEL_DISPATCH[func_id]
+            edge_mass_func = CONV_EDGE_MASS_DISPATCH[func_id]
             p_start = int(conv_param_indptr[idx])
             p_end = int(conv_param_indptr[idx + 1])
             # t=0 read is exact; same time-constant invariant as above
             kernel_params = [
                 float(traces[int(conv_param_rows[j]), 0]) for j in range(p_start, p_end)
             ]
-            support = conv_kernel_support(
-                kernel_params[0] * width_func(*kernel_params),
-                float(time[1] - time[0]),
+            # companion first: it validates the parameters, so the
+            # kernel body never sees a nonpositive width
+            mass_left, mass_right = edge_mass_func(
+                conv_operator.dt_left, conv_operator.dt_right, *kernel_params
+            )
+            kernel_values = kernel_func(conv_operator.dt_unique, *kernel_params)
+            traces[target, :] = conv_matrix_apply(
+                conv_operator, kernel_values, mass_left, mass_right, traces[target, :]
             )
-            kernel = kernel_func(support, *kernel_params)
-            traces[target, :] = my_conv(time, traces[target, :], kernel)
 
 
 # ---------------------------------------------------------------------------
@@ -420,7 +425,6 @@ def evaluate_2d(plan: ScheduledPlan2D, theta: np.ndarray) -> np.ndarray:
     # in interleaved topological order.
     resolve_param_traces(
         traces,
-        plan.time,
         plan.resolution_kinds,
         plan.resolution_indices,
         plan.dyn_group_target_row,
@@ -437,6 +441,7 @@ def evaluate_2d(plan: ScheduledPlan2D, theta: np.ndarray) -> np.ndarray:
         plan.conv_func_ids,
         plan.conv_param_indptr,
         plan.conv_param_rows,
+        plan.conv_operator,
     )
 
     # 1e. Profile evaluation (after parameter resolution).
diff --git a/src/trspecfit/functions/time.py b/src/trspecfit/functions/time.py
index 001bfc8..4f95009 100644
--- a/src/trspecfit/functions/time.py
+++ b/src/trspecfit/functions/time.py
@@ -14,10 +14,24 @@
 
 **Convolution Kernels:**
 Signature: funcCONV(t, par1, par2, ...)
-- t: Time axis centered at zero (from create_t_kernel)
+
+- t: Time differences centered at zero. Kernels must be elementwise in
+  this argument: the kernel-matrix convolution evaluates them on a 2D
+  matrix of time differences (see utils.arrays.conv_matrix_operator)
 - par1, par2, ...: Kernel parameters
-- Returns: Normalized kernel function
-- Must have a companion funcCONV_kernel_width(...) helper for support width
+- Returns: Kernel values (unnormalized; the convolution row-normalizes)
+
+Every kernel additionally requires a private edge-mass companion
+``_<name>_edge_mass(dt_left, dt_right, **params)`` registered in
+``CONV_EDGE_MASS``. It returns the exact exterior masses of the kernel
+body (same normalization) beyond the data window — the analytic
+integrals over ``(-inf, t[0]]`` and ``[t[-1], inf)`` used for
+edge-value padding. Use cancellation-safe tail forms (erfc, direct
+exp, clip) rather than CDF differences, and validate the parameters
+(strictly positive, finite) — companions are the runtime backstop for
+expression-driven kernel parameters that bypass model-load bound
+checks. A kernel without a companion is rejected at model validation
+(mcp) and scheduling (GIR).
 
 **Time Zero Convention:**
 All dynamics functions are zero before t0 and activate at t >= t0.
@@ -55,12 +69,14 @@
 
 1. Implement following conventions above
 2. Ensure f(t<t0) = 0 for dynamics functions
-3. Add kernel_width function for convolution kernels
+3. Keep convolution kernels elementwise in their first argument
 4. Test with realistic time-resolved data
 """
 
+from collections.abc import Callable
+
 import numpy as np
-from scipy.special import erf, wofz
+from scipy.special import erf, erfc
 
 
 #
@@ -158,7 +174,7 @@ def expFun(t: np.ndarray, A: float, tau: float, t0: float) -> np.ndarray:
     A : float
         Amplitude (initial change at t0).
         - A > 0: Jumps to A at t0, decays toward 0
-        - A < 0: Jumps to -|A| at t0, rises toward 0
+        - A < 0: Jumps to ``-|A|`` at t0, rises toward 0
     tau : float
         Time constant (1/e time). Units: [time units]
         At t = t0 + tau, signal changes by factor of e (≈2.718)
@@ -287,8 +303,9 @@ def sqrtFun(t: np.ndarray, A: float, t0: float) -> np.ndarray:
 
 
 #
-# convolution functions
-# kernels followed by respective recommended kernel width
+# convolution kernels
+# elementwise in the time-difference argument (evaluated on the dt
+# matrix of the kernel-matrix convolution operator)
 #
 
 
@@ -300,7 +317,7 @@ def gaussCONV(x: np.ndarray, SD: float) -> np.ndarray:
     Parameters
     ----------
     x : ndarray
-        Time axis (typically from Component.create_t_kernel, centered at 0)
+        Time differences (centered at 0)
     SD : float
         Standard deviation (Gaussian width).
         FWHM = 2.355 * SD = 2*√(2ln2) * SD
@@ -314,84 +331,6 @@ def gaussCONV(x: np.ndarray, SD: float) -> np.ndarray:
     return np.exp(-1 / 2 * (x / SD) ** 2)
 
 
-#
-def gaussCONV_kernel_width(SD: float | None = None) -> int:
-    """
-    Kernel width multiplier for Gaussian convolution.
-    Kernel extends to ±4*SD from center.
-    At 4*SD, Gaussian has decayed to exp(-8) ≈ 3×10⁻⁴ of peak value.
-    """
-
-    return 4
-
-
-#
-def lorentzCONV(x: np.ndarray, W: float) -> np.ndarray:
-    """
-    Lorentzian convolution kernel.
-
-    Parameters
-    ----------
-    x : ndarray
-        Time axis (centered at 0)
-    W : float
-        Full width at half maximum (FWHM) of Lorentzian
-
-    Returns
-    -------
-    ndarray
-        Lorentzian kernel (unnormalized)
-    """
-
-    return 1 / (1 + (2 * x / W) ** 2)
-
-
-#
-def lorentzCONV_kernel_width(W: float | None = None) -> int:
-    """Kernel width multiplier for Lorentzian (10×W)."""
-
-    return 10
-
-
-#
-def voigtCONV(x: np.ndarray, SD: float, W: float) -> np.ndarray:
-    """
-    Voigt convolution kernel (Gaussian and Lorentzian combined).
-
-    Parameters
-    ----------
-    x : ndarray
-        Time axis (centered at 0)
-    SD : float
-        Gaussian standard deviation
-    W : float
-        Lorentzian FWHM
-
-    Returns
-    -------
-    ndarray
-        Voigt kernel (normalized to peak = 1)
-    """
-
-    voigt = np.real(wofz((x + 1j * (W / 2)) / SD / np.sqrt(2)))
-    return np.asarray(voigt / np.max(voigt))
-
-
-#
-def voigtCONV_kernel_width(SD: float = 1.0, W: float = 0.0) -> float:
-    """Kernel width multiplier for Voigt support.
-
-    ``create_t_kernel`` multiplies the first kernel parameter by this
-    value. For ``voigtCONV`` the first parameter is ``SD``, but broad
-    Lorentzian tails are controlled by ``W``. Return a multiplier large
-    enough that the support spans at least ``max(12*SD, 10*W)``.
-    """
-
-    if SD <= 0:
-        return 12.0
-    return max(12.0, 10.0 * W / SD)
-
-
 #
 def expSymCONV(x: np.ndarray, tau: float) -> np.ndarray:
     """
@@ -415,13 +354,6 @@ def expSymCONV(x: np.ndarray, tau: float) -> np.ndarray:
     return np.asarray(np.exp(-1 / tau * np.abs(x)))
 
 
-#
-def expSymCONV_kernel_width(tau: float | None = None) -> int:
-    """Kernel width multiplier for symmetric exponential (6×tau)."""
-
-    return 6
-
-
 #
 def expDecayCONV(x: np.ndarray, tau: float) -> np.ndarray:
     """
@@ -443,13 +375,6 @@ def expDecayCONV(x: np.ndarray, tau: float) -> np.ndarray:
     return np.where(x < 0, 0.0, expSymCONV(x, tau))
 
 
-#
-def expDecayCONV_kernel_width(tau: float | None = None) -> int:
-    """Kernel width multiplier for decay exponential (6×tau)."""
-
-    return 6
-
-
 #
 def expRiseCONV(x: np.ndarray, tau: float) -> np.ndarray:
     """
@@ -475,13 +400,6 @@ def expRiseCONV(x: np.ndarray, tau: float) -> np.ndarray:
     return np.where(x > 0, 0.0, expSymCONV(x, tau))
 
 
-#
-def expRiseCONV_kernel_width(tau: float | None = None) -> int:
-    """Kernel width multiplier for rise exponential (6×tau)."""
-
-    return 6
-
-
 #
 def boxCONV(x: np.ndarray, width: float) -> np.ndarray:
     """
@@ -504,7 +422,98 @@ def boxCONV(x: np.ndarray, width: float) -> np.ndarray:
 
 
 #
-def boxCONV_kernel_width(width: float | None = None) -> int:
-    """Kernel width multiplier for box (1×width)."""
+# edge-mass companions
+# exact exterior masses of each kernel body (same normalization as the
+# body) for the edge-value padding of the kernel-matrix convolution:
+# M_L = integral over (-inf, t[0]] = upper tail at dt_left = t - t[0],
+# M_R = integral over [t[-1], inf) = lower tail at dt_right = t - t[-1].
+# Companions validate their parameters (strictly positive, finite):
+# they run on every evaluation, so they are the backstop for
+# expression-driven kernel parameters that bypass the model-load bound
+# checks (e.g. boxCONV width = 0 would otherwise silently become the
+# identity operator). Private (excluded from registry discovery);
+# dispatched via CONV_EDGE_MASS below.
+#
+
+
+#
+def _validate_kernel_par(name: str, value: float) -> None:
+    """Reject nonpositive or non-finite kernel parameters at evaluation."""
+
+    if not (np.isfinite(value) and value > 0):
+        raise ValueError(
+            f"Convolution kernel parameter '{name}' must be strictly "
+            f"positive and finite, got {value}."
+        )
+
+
+#
+def _gaussCONV_edge_mass(
+    dt_left: np.ndarray, dt_right: np.ndarray, SD: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Exterior masses of the peak-1 Gaussian body (erfc tail forms)."""
+
+    _validate_kernel_par("SD", SD)
+    scale = SD * np.sqrt(np.pi / 2)
+    M_L = scale * erfc(dt_left / (np.sqrt(2) * SD))
+    M_R = scale * erfc(-dt_right / (np.sqrt(2) * SD))
+    return np.asarray(M_L), np.asarray(M_R)
+
+
+#
+def _expSymCONV_edge_mass(
+    dt_left: np.ndarray, dt_right: np.ndarray, tau: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Exterior masses of exp(-|x|/tau); dt_left >= 0 and dt_right <= 0."""
+
+    _validate_kernel_par("tau", tau)
+    M_L = tau * np.exp(-dt_left / tau)
+    M_R = tau * np.exp(dt_right / tau)
+    return np.asarray(M_L), np.asarray(M_R)
 
-    return 1
+
+#
+def _expDecayCONV_edge_mass(
+    dt_left: np.ndarray, dt_right: np.ndarray, tau: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Exterior masses of the causal kernel: zero body for x < 0."""
+
+    _validate_kernel_par("tau", tau)
+    M_L = tau * np.exp(-dt_left / tau)
+    M_R = np.zeros_like(dt_right)
+    return np.asarray(M_L), M_R
+
+
+#
+def _expRiseCONV_edge_mass(
+    dt_left: np.ndarray, dt_right: np.ndarray, tau: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Exterior masses of the anti-causal kernel: zero body for x > 0."""
+
+    _validate_kernel_par("tau", tau)
+    M_L = np.zeros_like(dt_left)
+    M_R = tau * np.exp(dt_right / tau)
+    return M_L, np.asarray(M_R)
+
+
+#
+def _boxCONV_edge_mass(
+    dt_left: np.ndarray, dt_right: np.ndarray, width: float
+) -> tuple[np.ndarray, np.ndarray]:
+    """Exterior masses of the unit box on [-width/2, width/2]."""
+
+    _validate_kernel_par("width", width)
+    M_L = np.clip(width / 2 - dt_left, 0.0, width)
+    M_R = np.clip(dt_right + width / 2, 0.0, width)
+    return np.asarray(M_L), np.asarray(M_R)
+
+
+# kernel name -> edge-mass companion; single source of truth consumed by
+# both evaluation paths (mcp.Component.convolve and the GIR evaluator)
+CONV_EDGE_MASS: dict[str, Callable] = {
+    "gaussCONV": _gaussCONV_edge_mass,
+    "expSymCONV": _expSymCONV_edge_mass,
+    "expDecayCONV": _expDecayCONV_edge_mass,
+    "expRiseCONV": _expRiseCONV_edge_mass,
+    "boxCONV": _boxCONV_edge_mass,
+}
diff --git a/src/trspecfit/graph_ir.py b/src/trspecfit/graph_ir.py
index 0db9126..2540e18 100644
--- a/src/trspecfit/graph_ir.py
+++ b/src/trspecfit/graph_ir.py
@@ -27,6 +27,8 @@
 
 from trspecfit.functions import energy as fcts_energy
 from trspecfit.functions import profile as fcts_profile
+from trspecfit.functions import time as fcts_time
+from trspecfit.utils.arrays import ConvOperator, conv_matrix_operator
 
 if TYPE_CHECKING:
     from trspecfit.mcp import Component, Model, Par
@@ -178,18 +180,14 @@ class ConvKernelKind(IntEnum):
     """
 
     GAUSSCONV = 0
-    LORENTZCONV = 1
-    VOIGTCONV = 2
-    EXPSYMCONV = 3
-    EXPDECAYCONV = 4
-    EXPRISECONV = 5
-    BOXCONV = 6
+    EXPSYMCONV = 1
+    EXPDECAYCONV = 2
+    EXPRISECONV = 3
+    BOXCONV = 4
 
 
 _FUNCTION_NAME_TO_CONV_KERNEL: dict[str, ConvKernelKind] = {
     "gaussCONV": ConvKernelKind.GAUSSCONV,
-    "lorentzCONV": ConvKernelKind.LORENTZCONV,
-    "voigtCONV": ConvKernelKind.VOIGTCONV,
     "expSymCONV": ConvKernelKind.EXPSYMCONV,
     "expDecayCONV": ConvKernelKind.EXPDECAYCONV,
     "expRiseCONV": ConvKernelKind.EXPRISECONV,
@@ -518,15 +516,19 @@ class ScheduledPlan2D:
     # --- Resolved-trace convolution program ---
     # Each conv step rewrites a trace row in-place after its PARAM_PLUS_TRACE
     # is fully resolved.  Chained CONVOLUTION nodes emit multiple steps
-    # targeting the same row, executed in order.  Kernel values and the
-    # kernel support are recomputed per theta from conv_param_rows, so the
-    # support tracks the fitted width.  Only ``package == "time"`` kernels
-    # are lowered.
+    # targeting the same row, executed in order.  The kernel-matrix
+    # operator (conv_operator) is theta-independent and shared by all
+    # steps; per theta only the elementwise kernel evaluation on the
+    # deduplicated dt values, the analytic edge masses (resolved via
+    # CONV_EDGE_MASS_DISPATCH by conv_func_ids -- no callables stored
+    # here), and a matmul remain, so all array shapes are static.
+    # Only ``package == "time"`` kernels are lowered.
     n_conv_steps: int
     conv_target_rows: np.ndarray  # (n_conv_steps,) int -- trace row rewritten
     conv_func_ids: np.ndarray  # (n_conv_steps,) int -- kernel function registry id
     conv_param_indptr: np.ndarray  # (n_conv_steps + 1,) int -- CSR row pointers
     conv_param_rows: np.ndarray  # (total_conv_params,) int -- kernel param trace rows
+    conv_operator: ConvOperator | None  # None when n_conv_steps == 0
 
     # --- Profile-varying parameter groups (fixed aux_axis shape) ---
     n_aux: int
@@ -2375,9 +2377,9 @@ def schedule_2d(graph: GraphIR) -> ScheduledPlan2D:
     n_conv_steps = len(conv_nodes_topo)
     if n_conv_steps > 0 and n_time < 2:
         raise ValueError(
-            "Convolution requires a time axis with at least 2 points "
-            f"to determine the kernel step size, got {n_time}."
+            f"Convolution requires a time axis with at least 2 points, got {n_time}."
         )
+    conv_operator = conv_matrix_operator(graph.time) if n_conv_steps > 0 else None
 
     conv_target_rows_list: list[int] = []
     conv_func_ids_list: list[int] = []
@@ -2389,6 +2391,13 @@ def schedule_2d(graph: GraphIR) -> ScheduledPlan2D:
         kernel_kind = _FUNCTION_NAME_TO_CONV_KERNEL.get(conv_node.function_name)
         if kernel_kind is None:
             raise ValueError(f"Unknown convolution kernel: {conv_node.function_name!r}")
+        if conv_node.function_name not in fcts_time.CONV_EDGE_MASS:
+            raise ValueError(
+                f"Convolution kernel '{conv_node.function_name}' has no "
+                "edge-mass companion in functions.time.CONV_EDGE_MASS; "
+                "register one (exact exterior masses of the kernel body) "
+                "before scheduling."
+            )
         conv_func_ids_list.append(int(kernel_kind))
 
         target_row = _resolve_convolution_target_row(
@@ -2514,7 +2523,6 @@ def schedule_2d(graph: GraphIR) -> ScheduledPlan2D:
 
     resolve_param_traces(
         param_traces_init,
-        graph.time,
         resolution_kinds,
         resolution_indices,
         dyn_group_target_row,
@@ -2531,6 +2539,7 @@ def schedule_2d(graph: GraphIR) -> ScheduledPlan2D:
         conv_func_ids,
         conv_param_indptr,
         conv_param_rows,
+        conv_operator,
     )
 
     # ------------------------------------------------------------------ #
@@ -2649,6 +2658,7 @@ def schedule_2d(graph: GraphIR) -> ScheduledPlan2D:
         conv_func_ids=conv_func_ids,
         conv_param_indptr=conv_param_indptr,
         conv_param_rows=conv_param_rows,
+        conv_operator=conv_operator,
     )
 
 
diff --git a/src/trspecfit/mcp.py b/src/trspecfit/mcp.py
index e7c6513..2555957 100644
--- a/src/trspecfit/mcp.py
+++ b/src/trspecfit/mcp.py
@@ -434,7 +434,7 @@ def add_components(self, comps_list: list["Component"]) -> None:
         - energy/time axes from model
         - parent_model reference (for finding other parameters)
         - subcycle time axis (for multi-cycle Dynamics)
-        - kernel time axis (for convolution components)
+        - kernel-matrix convolution operator (for convolution components)
 
         **Model Updates:**
         After adding components, the model's lmfit_pars and parameter_names
@@ -454,7 +454,6 @@ def add_components(self, comps_list: list["Component"]) -> None:
             self.peak_fcts.append(comp.fct)
             # Share axis references (not copies) with components.
             # Contract: parent must not rebind these after propagation.
-            # Exception: conv components get a kernel time axis below.
             comp.energy = self.energy
             comp.time = self.time
             comp.aux_axis = self.aux_axis
@@ -465,9 +464,35 @@ def add_components(self, comps_list: list["Component"]) -> None:
                 if self.time is None:
                     raise ValueError("Model time axis required for Dynamics components")
                 comp.time_n_sub = np.ones(len(self.time))  # initialize all active
-            # if comp should be convoluted it will be defined on a t_kernel axis
-            if comp.comp_type == "conv":
-                comp.time = Component.create_t_kernel(comp)
+            # conv components: build (and validate) the kernel-matrix
+            # operator now so a bad time axis, a kernel without an
+            # edge-mass companion, or non-positive/missing width bounds
+            # fail at model construction instead of mid-fit
+            if comp.comp_type == "conv" and comp.package == fcts_time:
+                for par_name, par_info in comp.par_dict.items():
+                    if isinstance(par_info[0], str):
+                        continue  # expressions: companions validate at eval
+                    init_val = par_info[0]
+                    vary_level = (
+                        ulmfit.vary_to_level(par_info[1])
+                        if len(par_info) >= 2
+                        else "file"
+                    )
+                    lower = par_info[2] if len(par_info) >= 4 else None
+                    if (
+                        init_val <= 0
+                        or (lower is not None and lower <= 0)
+                        or (vary_level != "static" and lower is None)
+                    ):
+                        raise ValueError(
+                            f"Convolution kernel parameter '{par_name}' of "
+                            f"'{comp.fct_str}' must be strictly positive: got "
+                            f"init={init_val}, min={lower}. Kernel widths and "
+                            "timescales require positive values, and varying "
+                            "parameters require an explicit positive lower "
+                            "bound (e.g. [0.4, True, 1e-6, 1])."
+                        )
+                comp.conv_operator()
             # populate pars attribute in the component
             comp.create_pars(prefix=prefix)
 
@@ -865,18 +890,11 @@ def combine(value: np.ndarray, comp: "Component", t_ind: int = 0) -> np.ndarray:
         # convolute component with existing spectrum
         if comp.comp_type == "conv":
             if comp.package == fcts_energy:
-                x_axis = comp.energy
-                print("convolution of spectral components not defined")
-            elif comp.package == fcts_time:
-                x_axis = comp.time
-            else:
-                x_axis = None
-            #
-            if x_axis is None:
                 raise ValueError(
-                    f"Convolution axis not defined for component '{comp.name}'"
+                    f"Convolution of spectral (energy) components is not "
+                    f"supported (component '{comp.comp_name}')."
                 )
-            return uarr.my_conv(x=x_axis, y=value, kernel=np.asarray(comp.value(t_ind)))
+            return comp.convolve(value, t_ind)
         raise ValueError(f"Unknown component type: {comp.comp_type}")
 
     #
@@ -1287,6 +1305,9 @@ def __init__(
         self.aux_axis: np.ndarray | None = None
         # parent model reference
         self.parent_model: Model | None = None
+        # lazy kernel-matrix convolution operator: (axis_ref, operator);
+        # rebuilt if the time axis is rebound
+        self._conv_cache: tuple[np.ndarray, uarr.ConvOperator] | None = None
 
     #
     def __repr__(self) -> str:
@@ -1307,6 +1328,9 @@ def __getstate__(self) -> dict[str, Any]:
         state = self.__dict__.copy()
         state["package"] = self.package.__name__
         state["parent_model"] = None
+        # drop the conv-operator cache: it holds an identity reference to
+        # the time axis that pickling would sever; it rebuilds lazily
+        state["_conv_cache"] = None
         return state
 
     #
@@ -1315,6 +1339,7 @@ def __setstate__(self, state: dict[str, Any]) -> None:
 
         package_name = state.pop("package")
         self.__dict__.update(state)
+        self.__dict__.setdefault("_conv_cache", None)
         self.package = importlib.import_module(package_name)
 
     # [automatic] create self.fct attribute that will update if either
@@ -1628,46 +1653,77 @@ def describe(self, detail: int = 1) -> None:
             print()
 
     #
-    def create_t_kernel(self, *, par_values: list[Any] | None = None) -> np.ndarray:
+    def conv_operator(self) -> uarr.ConvOperator:
         """
-        Create time axis for convolution kernel.
+        Kernel-matrix convolution operator for this component's time axis.
 
-        Convolution kernels need a time axis that extends beyond the data
-        time axis to properly handle edge effects. This method creates an
-        appropriately sized kernel axis based on the kernel width.
-
-        Parameters
-        ----------
-        par_values : list, optional
-            Current kernel parameter values. Defaults to the initial
-            values from par_dict (model construction). Component.value
-            passes the live values so the support tracks the fitted width.
+        Builds the theta-independent operator (deduplicated ``dt``
+        values, gather indices, quadrature weights, edge-mass abscissae)
+        via ``uarr.conv_matrix_operator`` and caches it. The cache is
+        keyed on the identity of ``self.time`` so a rebound axis
+        triggers a rebuild. Also validates that the kernel has an
+        edge-mass companion registered in ``CONV_EDGE_MASS``.
 
         Returns
         -------
-        ndarray
-            Kernel time axis, centered at 0 and extending ±(width * kernel_parameter)
+        ConvOperator
+            Precomputed operator for ``uarr.conv_matrix_apply``.
         """
 
-        # get kernel parameters i.e. component parameters
-        if par_values is None:
-            par_values = cast(
-                "list[Any]", ulmfit.par_extract(self.par_dict, return_type="list")
-            )
-        # define kernel time axis. Kernel-width helpers may inspect the
-        # full parameter list for multi-parameter kernels such as Voigt.
-        kernel_width = getattr(fcts_time, self.fct_str + "_kernel_width")(*par_values)
-        t_range = par_values[0] * kernel_width
         if self.time is None:
             raise ValueError(f"time axis of component {self.fct_str} not defined")
-        if len(self.time) < 2:
+        if self.fct_str not in fcts_time.CONV_EDGE_MASS:
             raise ValueError(
-                f"Convolution component {self.fct_str} requires a time axis "
-                f"with at least 2 points to determine the kernel step size, "
-                f"got {len(self.time)}."
+                f"Convolution kernel '{self.fct_str}' has no edge-mass "
+                "companion in functions.time.CONV_EDGE_MASS; register "
+                "one (exact exterior masses of the kernel body) to use "
+                "this kernel."
             )
-        t_step = self.time[1] - self.time[0]
-        return uarr.conv_kernel_support(t_range, t_step)
+        if self._conv_cache is None or self._conv_cache[0] is not self.time:
+            if len(self.time) < 2:
+                raise ValueError(
+                    f"Convolution component {self.fct_str} requires a time "
+                    f"axis with at least 2 points, got {len(self.time)}."
+                )
+            self._conv_cache = (self.time, uarr.conv_matrix_operator(self.time))
+        return self._conv_cache[1]
+
+    #
+    def convolve(self, y: np.ndarray, t_ind: int = 0) -> np.ndarray:
+        """
+        Convolve a signal with this kernel component.
+
+        Evaluates the kernel function elementwise on the precomputed
+        time-difference values at the current parameter values, computes
+        the exact analytic exterior masses via the kernel's
+        ``CONV_EDGE_MASS`` companion, and applies the
+        quadrature-weighted, row-normalized kernel matrix. Exact on any
+        strictly increasing time axis (uniform or not); kernel mass
+        beyond the axis contributes through the edge samples
+        (edge-value padding semantics, no support truncation).
+
+        Parameters
+        ----------
+        y : ndarray
+            Signal sampled on this component's time axis.
+        t_ind : int, default=0
+            Time index for parameter evaluation (kernel parameters are
+            time-constant, but expression machinery expects an index).
+
+        Returns
+        -------
+        ndarray
+            Convolved signal, same length as ``y``.
+        """
+
+        pars = [p.value(t_ind, update_t_model=t_ind == 0) for p in self.pars]
+        operator = self.conv_operator()
+        # companion first: it validates the parameters, so the kernel
+        # body never sees a nonpositive width
+        edge_mass = fcts_time.CONV_EDGE_MASS[self.fct_str]
+        mass_left, mass_right = edge_mass(operator.dt_left, operator.dt_right, *pars)
+        kernel_values = np.asarray(self.fct(operator.dt_unique, *pars), np.float64)
+        return uarr.conv_matrix_apply(operator, kernel_values, mass_left, mass_right, y)
 
     #
     def value(self, t_ind: int = 0, **kwargs) -> np.ndarray:
@@ -1738,11 +1794,10 @@ def value(self, t_ind: int = 0, **kwargs) -> np.ndarray:
                 raise ValueError(
                     f"Time axis not defined for component '{self.comp_name}'"
                 )
-            # conv kernels: rebuild the support from the current parameter
-            # values so the axis tracks the fitted width (a frozen support
-            # would truncate the kernel once the width grows past its init)
-            if self.comp_type == "conv":
-                self.time = self.create_t_kernel(par_values=pars)
+            # conv kernels evaluate on the model time axis here (kernel
+            # centered at t=0) — used for plotting/inspection only; the
+            # convolution itself goes through Component.convolve, which
+            # evaluates the kernel on the dt matrix
             if self.subcycle == 0:  # single cycle
                 return np.asarray(self.fct(self.time, *pars, **kwargs))
             # multi-cycle
diff --git a/src/trspecfit/utils/arrays.py b/src/trspecfit/utils/arrays.py
index b255746..e00f33c 100644
--- a/src/trspecfit/utils/arrays.py
+++ b/src/trspecfit/utils/arrays.py
@@ -12,7 +12,7 @@
 
 import math
 from decimal import Decimal
-from typing import Literal, cast, overload
+from typing import Literal, NamedTuple, cast, overload
 
 import numpy as np
 import pandas as pd
@@ -311,38 +311,182 @@ def pad_x_y(
 
 
 #
-def conv_kernel_support(t_range: float, t_step: float) -> NDArray[np.float64]:
+#
+class ConvOperator(NamedTuple):
+    """Theta-independent part of the kernel-matrix convolution.
+
+    Built once per time axis by ``conv_matrix_operator``; consumed per
+    kernel-parameter set by ``conv_matrix_apply``. The kernel function
+    is evaluated on ``dt_unique`` only (kernels are elementwise, and dt
+    values repeat heavily on uniform or piecewise-uniform axes), then
+    gathered back into the full matrix via ``gather_idx``.
+
+    ``dt_left``/``dt_right`` are the abscissae at which per-kernel
+    edge-mass companions evaluate the exact exterior kernel mass
+    (edge-value padding semantics; see ``conv_matrix_apply``).
+    """
+
+    dt_unique: NDArray[np.float64]  # (n_unique,) sorted unique t_i - t_j
+    gather_idx: NDArray[np.intp]  # (n_t, n_t) index into dt_unique
+    quad_weights: NDArray[np.float64]  # (n_t,) trapezoid weights
+    dt_left: NDArray[np.float64]  # (n_t,) t - t[0], >= 0
+    dt_right: NDArray[np.float64]  # (n_t,) t - t[-1], <= 0
+
+
+#
+def conv_matrix_operator(t: ArrayLike) -> ConvOperator:
+    """
+    Build the theta-independent part of the kernel-matrix convolution.
+
+    The convolution ``y_conv = K @ y`` with
+    ``K[i, j] = g(t_i - t_j; theta) * w_j`` (rows normalized) is exact
+    quadrature on any monotonic axis — the axis enters through the
+    ``dt`` matrix and the weights, so non-uniform sampling is handled
+    correctly. Everything that does not depend on the kernel parameters
+    is built here, once per axis.
+
+    Kernel mass falling outside the data window is handled analytically:
+    the signal is assumed constant beyond the window (edge-value
+    padding), so the exterior contribution of row ``i`` is
+    ``y[0] * M_L(i) + y[-1] * M_R(i)`` where ``M_L(i)`` is the exact
+    integral of the kernel body over ``(-inf, t[0]]`` (an upper-tail
+    mass at ``dt_left[i] = t_i - t[0]``) and ``M_R(i)`` the integral
+    over ``[t[-1], inf)`` (a lower-tail mass at
+    ``dt_right[i] = t_i - t[-1]``). The masses are computed by
+    per-kernel companions (``CONV_EDGE_MASS`` in ``functions/time.py``)
+    and passed to ``conv_matrix_apply`` — no ghost points, no support
+    truncation for any kernel width.
+
+    The ``(n_t, n_t)`` dt matrix is stored deduplicated: kernel
+    functions evaluate on ``dt_unique`` (typically ``O(n_t)`` values on
+    uniform or piecewise-uniform axes instead of ``O(n_t^2)``) and
+    ``conv_matrix_apply`` gathers the values back by index. This is a
+    pure optimization — the gathered matrix is bit-identical to direct
+    evaluation on the full dt matrix.
+
+    Parameters
+    ----------
+    t : array_like
+        Strictly increasing time axis, at least 2 samples.
+
+    Returns
+    -------
+    ConvOperator
+        ``(dt_unique, gather_idx, quad_weights, dt_left, dt_right)``.
+    """
+
+    t_arr = np.asarray(t, dtype=np.float64)
+    if t_arr.ndim != 1 or t_arr.size < 2:
+        raise ValueError(
+            "Convolution requires a 1D time axis with at least 2 points, "
+            f"got shape {t_arr.shape}"
+        )
+    if not np.all(np.isfinite(t_arr)):
+        raise ValueError("Convolution time axis contains non-finite values")
+    if np.any(np.diff(t_arr) <= 0):
+        raise ValueError(
+            "Convolution time axis must be strictly increasing; "
+            "sort the axis (and data) before fitting."
+        )
+
+    # True trapezoid weights: half-cells at both window edges (the
+    # exterior beyond the half-cells is covered exactly by the analytic
+    # edge masses; np.gradient would give full end cells and
+    # double-count against them).
+    steps = np.diff(t_arr)
+    quad_weights = np.empty_like(t_arr)
+    quad_weights[0] = steps[0] / 2
+    quad_weights[-1] = steps[-1] / 2
+    quad_weights[1:-1] = (t_arr[2:] - t_arr[:-2]) / 2
+
+    dt = t_arr[:, np.newaxis] - t_arr[np.newaxis, :]
+    dt_unique, inverse = np.unique(dt, return_inverse=True)
+    gather_idx = inverse.reshape(dt.shape).astype(np.intp, copy=False)
+    dt_left = t_arr - t_arr[0]
+    dt_right = t_arr - t_arr[-1]
+    return ConvOperator(dt_unique, gather_idx, quad_weights, dt_left, dt_right)
+
+
+#
+def conv_matrix_apply(
+    operator: ConvOperator,
+    kernel_values: NDArray[np.float64],
+    edge_mass_left: NDArray[np.float64],
+    edge_mass_right: NDArray[np.float64],
+    y: ArrayLike,
+) -> NDArray[np.float64]:
     """
-    Build a symmetric, odd-length time axis for a convolution kernel.
+    Apply the kernel-matrix convolution for one set of kernel parameters.
 
-    Rebuilt from the current kernel parameter values at every model
-    evaluation so the support tracks the fitted width — a frozen support
-    silently truncates the kernel when the width grows past its initial
-    value.
+    Consumes the kernel evaluated elementwise on ``operator.dt_unique``
+    plus the analytic exterior masses evaluated at ``operator.dt_left``
+    / ``operator.dt_right`` (edge-value padding semantics: the signal
+    is assumed constant beyond the window). Each row is normalized so a
+    constant signal is preserved exactly.
 
     Parameters
     ----------
-    t_range : float
-        Half-width of the kernel support, typically
-        ``kernel_par * kernel_width(...)`` from the ``*_kernel_width``
-        helpers in trspecfit.functions.time
-    t_step : float
-        Time axis step size (matches the data time axis)
+    operator : ConvOperator
+        Precomputed operator from ``conv_matrix_operator``.
+    kernel_values : ndarray
+        ``(n_unique,)`` kernel evaluated on ``operator.dt_unique``
+        (unnormalized).
+    edge_mass_left, edge_mass_right : ndarray
+        ``(n_t,)`` exterior kernel masses per row, from the kernel's
+        ``CONV_EDGE_MASS`` companion (same normalization as the body).
+    y : array_like
+        ``(n_t,)`` signal to convolve.
 
     Returns
     -------
     ndarray
-        Kernel time axis ``[-n*t_step, ..., 0, ..., n*t_step]`` with
-        ``n = max(1, ceil(|t_range| / t_step))``, guaranteed symmetric
-        and odd-length so ``mode='same'`` convolution stays centered
+        Convolved signal, same length as ``y``.
     """
 
-    if not np.isfinite(t_range):
-        raise ValueError(f"Kernel support range is not finite: {t_range}")
-    if not np.isfinite(t_step) or t_step <= 0:
-        raise ValueError(f"Kernel time step must be positive: {t_step}")
-    n = max(1, int(np.ceil(abs(t_range) / t_step)))
-    return np.arange(-n, n + 1, dtype=np.float64) * t_step
+    y_arr = np.asarray(y, dtype=np.float64)
+    n_t = operator.gather_idx.shape[0]
+    if (
+        y_arr.shape != (n_t,)
+        or edge_mass_left.shape != (n_t,)
+        or edge_mass_right.shape != (n_t,)
+        or kernel_values.shape != operator.dt_unique.shape
+    ):
+        raise ValueError(
+            "Convolution inputs have wrong shapes: kernel_values "
+            f"{kernel_values.shape} (expected {operator.dt_unique.shape}), "
+            f"edge masses {edge_mass_left.shape} / {edge_mass_right.shape} "
+            f"and signal y {y_arr.shape} (all expected ({n_t},))."
+        )
+    # Signed errors can cancel inside row sums, so validate sign and
+    # finiteness of the raw ingredients (O(n) against the O(n^2) matmul).
+    if np.any(kernel_values < 0) or not np.all(np.isfinite(kernel_values)):
+        raise ValueError(
+            "Convolution kernel values must be finite and nonnegative; "
+            "the kernel parameters are likely invalid (NaN or negative "
+            "width)."
+        )
+    if (
+        np.any(edge_mass_left < 0)
+        or np.any(edge_mass_right < 0)
+        or not np.all(np.isfinite(edge_mass_left))
+        or not np.all(np.isfinite(edge_mass_right))
+    ):
+        raise ValueError(
+            "Convolution edge masses must be finite and nonnegative; "
+            "the kernel's edge-mass companion or its parameters are "
+            "likely invalid."
+        )
+
+    interior = kernel_values[operator.gather_idx] * operator.quad_weights
+    row_sums = interior.sum(axis=1) + edge_mass_left + edge_mass_right
+    if np.any(row_sums <= 0):
+        raise ValueError(
+            "Convolution kernel matrix has non-positive row sums; the "
+            "kernel parameters are likely invalid (zero width)."
+        )
+    y_conv = interior @ y_arr + edge_mass_left * y_arr[0]
+    y_conv += edge_mass_right * y_arr[-1]
+    return cast("NDArray[np.float64]", y_conv / row_sums)
 
 
 #
diff --git a/tests/models/file_energy.yaml b/tests/models/file_energy.yaml
index a7d484e..af70a9c 100644
--- a/tests/models/file_energy.yaml
+++ b/tests/models/file_energy.yaml
@@ -204,7 +204,7 @@ background_last:
 # convolution in a top-level energy model (unsupported; IRF belongs in Dynamics)
 energy_convolution_unsupported:
     gaussCONV:
-      SD: [5.0E-2, True, 0, 1]
+      SD: [5.0E-2, True, 1.0E-6, 1]
     GLP:
       A: [20, True, 5, 25]
       x0: [84.5, True, 82, 88]
diff --git a/tests/models/file_time.yaml b/tests/models/file_time.yaml
index 5f2fb95..a23c3a7 100644
--- a/tests/models/file_time.yaml
+++ b/tests/models/file_time.yaml
@@ -16,7 +16,7 @@ IRF:
     # define Gauss to convolve everything with 
     # (instrumental response function)
     gaussCONV:
-        SD: [5.0E-2, True, 0, 1]
+        SD: [5.0E-2, True, 1.0E-6, 1]
              
 MonoExpPos:
     # expFun(t, A, tau, t0)
@@ -85,7 +85,7 @@ MonoSqrt:
 # identifiable from the data, narrow enough not to bury the expFun dynamics
 MonoExpPosIRF:
     gaussCONV:
-        SD: [0.4, True, 0, 1]
+        SD: [0.4, True, 1.0E-6, 1]
     expFun:
         A: [1, True, 0, 5]
         tau: [2.5, True, 1, 10]
@@ -97,24 +97,7 @@ MonoExpPosIRF:
 # recovery target.
 MonoExpPosIRFNarrow:
     gaussCONV:
-        SD: [5.0E-2, True, 0, 1]
-    expFun:
-        A: [1, True, 0, 5]
-        tau: [2.5, True, 1, 10]
-        t0: [0, False, 0, 1]
-
-MonoExpPosLorentzIRF:
-    lorentzCONV:
-        W: [0.5, True, 0.01, 5]
-    expFun:
-        A: [1, True, 0, 5]
-        tau: [2.5, True, 1, 10]
-        t0: [0, False, 0, 1]
-
-MonoExpPosVoigtIRF:
-    voigtCONV:
-        SD: [0.1, True, 0.01, 1]
-        W: [0.1, True, 0.01, 1]
+        SD: [5.0E-2, True, 1.0E-6, 1]
     expFun:
         A: [1, True, 0, 5]
         tau: [2.5, True, 1, 10]
@@ -156,7 +139,7 @@ MonoExpPosBoxIRF:
 # sequence (two conv steps targeting one row in the lowered plan)
 MonoExpPosDoubleIRF:
     gaussCONV:
-        SD: [0.4, True, 0, 1]
+        SD: [0.4, True, 1.0E-6, 1]
     boxCONV:
         width: [2.0, True, 0.1, 20]
     expFun:
@@ -196,7 +179,7 @@ conv_last:
         tau: [2.5, True, 1, 10]
         t0: [0, False, 0, 1]
     gaussCONV:
-        SD: [5.0E-2, True, 0, 1]
+        SD: [5.0E-2, True, 1.0E-6, 1]
 # expression referencing a parameter outside the dynamics model
 # (must be rejected at add_time_dependence; energy-model parameters
 # are not in a dynamics model's namespace)
diff --git a/tests/test_arrays.py b/tests/test_arrays.py
index d10edf1..29d7c06 100644
--- a/tests/test_arrays.py
+++ b/tests/test_arrays.py
@@ -1,17 +1,55 @@
-"""Tests for trspecfit.utils.arrays — running_mean, conv_kernel_support,
-sign_change, my_conv."""
+"""Tests for trspecfit.utils.arrays — running_mean, kernel-matrix
+convolution, sign_change, my_conv."""
 
 import numpy as np
 import pytest
-
+from scipy.stats import norm
+
+from trspecfit.functions.time import (
+    CONV_EDGE_MASS,
+    erfFun,
+    expDecayCONV,
+    expFun,
+    expRiseCONV,
+    gaussCONV,
+)
 from trspecfit.utils.arrays import (
-    conv_kernel_support,
+    conv_matrix_apply,
+    conv_matrix_operator,
     my_conv,
     running_mean,
     sign_change,
 )
 
 
+#
+def _conv_matrix(t, kernel_fct, *kernel_pars, y):
+    """Build the operator for t and convolve y with the given kernel."""
+
+    operator = conv_matrix_operator(t)
+    kernel_values = kernel_fct(operator.dt_unique, *kernel_pars)
+    edge_mass = CONV_EDGE_MASS[kernel_fct.__name__]
+    mass_left, mass_right = edge_mass(operator.dt_left, operator.dt_right, *kernel_pars)
+    return conv_matrix_apply(operator, kernel_values, mass_left, mass_right, y)
+
+
+#
+def _dense_reference(t, y_fct, kernel_fct, *kernel_pars, t_step=0.005, margin=80.0):
+    """Continuous-convolution reference on a dense uniform grid.
+
+    Evaluates the signal analytically on a fine grid extending well past
+    both ends of t (so edge effects cannot reach the window), convolves
+    with the normalized kernel, and interpolates back onto t.
+    """
+
+    t_fine = np.arange(t[0] - margin, t[-1] + margin, t_step)
+    y_fine = y_fct(t_fine)
+    kernel = kernel_fct(t_fine - t_fine[t_fine.size // 2], *kernel_pars)
+    kernel = kernel / kernel.sum()
+    y_conv_fine = np.convolve(y_fine, kernel, mode="same")
+    return np.interp(t, t_fine, y_conv_fine)
+
+
 #
 #
 class TestMyConv:
@@ -106,68 +144,305 @@ def test_no_crossing(self):
 
 #
 #
-class TestConvKernelSupport:
-    """Tests for the convolution kernel support builder."""
+class TestConvMatrixOperator:
+    """Tests for the theta-independent operator builder."""
+
+    #
+    def test_shapes(self):
+        """Operator arrays are interior-only: (n, n) matrix, (n,) vectors."""
+
+        t = np.linspace(0, 10, 21)
+        operator = conv_matrix_operator(t)
+        assert operator.gather_idx.shape == (t.size, t.size)
+        assert operator.quad_weights.shape == (t.size,)
+        assert operator.dt_left.shape == (t.size,)
+        assert operator.dt_right.shape == (t.size,)
+
+    #
+    def test_dt_matrix_reconstructs(self):
+        """Gathered dt values reconstruct to t_i - t_j."""
+
+        t = np.array([0.0, 1.0, 3.0, 7.0])
+        operator = conv_matrix_operator(t)
+        dt = operator.dt_unique[operator.gather_idx]
+        np.testing.assert_allclose(dt, t[:, None] - t[None, :])
+
+    #
+    def test_edge_mass_abscissae(self):
+        """dt_left/dt_right are the offsets from the window edges."""
+
+        t = np.array([0.0, 1.0, 3.0, 7.0])
+        operator = conv_matrix_operator(t)
+        np.testing.assert_allclose(operator.dt_left, t - t[0])
+        np.testing.assert_allclose(operator.dt_right, t - t[-1])
+        assert np.all(operator.dt_left >= 0)
+        assert np.all(operator.dt_right <= 0)
+
+    #
+    def test_dt_unique_deduplicates_uniform_axis(self):
+        """On a uniform axis dt values collapse to O(n) unique entries."""
+
+        t = np.arange(0, 10, 0.5)
+        operator = conv_matrix_operator(t)
+        # all row/column offsets on a uniform grid: 2*n_t - 1 values
+        assert operator.dt_unique.size == 2 * t.size - 1
+        assert operator.dt_unique.size < operator.gather_idx.size
+
+    #
+    def test_trapezoid_weights(self):
+        """True trapezoid weights: half-cells at both window edges.
+
+        The exterior beyond the edge half-cells is covered exactly by
+        the analytic edge masses; full end cells (np.gradient) would
+        double-count against them.
+        """
+
+        t = np.arange(0, 10, 0.5)
+        operator = conv_matrix_operator(t)
+        np.testing.assert_allclose(operator.quad_weights[1:-1], 0.5)
+        np.testing.assert_allclose(operator.quad_weights[[0, -1]], 0.25)
+        # non-uniform: interior weights are the centered half-spans
+        t_nu = np.array([0.0, 1.0, 3.0, 7.0])
+        op_nu = conv_matrix_operator(t_nu)
+        np.testing.assert_allclose(op_nu.quad_weights, [0.5, 1.5, 3.0, 2.0])
+
+    #
+    def test_single_point_axis_raises(self):
+        """A 1-point axis raises a clear error."""
+
+        with pytest.raises(ValueError, match="at least 2 points"):
+            conv_matrix_operator(np.array([0.0]))
+
+    #
+    def test_non_monotonic_axis_raises(self):
+        """A non-increasing axis raises instead of silently misconvolving."""
+
+        with pytest.raises(ValueError, match="strictly increasing"):
+            conv_matrix_operator(np.array([0.0, 1.0, 0.5]))
+        with pytest.raises(ValueError, match="strictly increasing"):
+            conv_matrix_operator(np.array([0.0, 1.0, 1.0, 2.0]))
+
+    #
+    def test_nonfinite_axis_raises(self):
+        """A NaN in the axis raises a clear error."""
+
+        with pytest.raises(ValueError, match="non-finite"):
+            conv_matrix_operator(np.array([0.0, np.nan, 1.0]))
+
+
+#
+#
+class TestConvMatrixApply:
+    """Numerical behavior of the kernel-matrix convolution."""
+
+    #
+    def test_constant_preserved_on_nonuniform_axis(self):
+        """Row normalization preserves a constant signal exactly."""
+
+        t = np.concatenate([np.arange(-5, 2, 0.25), np.arange(2, 20, 1.0)])
+        y = np.full(t.size, 3.3)
+        result = _conv_matrix(t, gaussCONV, 1.2, y=y)
+        np.testing.assert_allclose(result, 3.3, rtol=1e-12)
+
+    #
+    def test_uniform_axis_matches_my_conv(self):
+        """Uniform axis reproduces the padded-1D-kernel path.
+
+        Tolerance covers the old path's finite kernel support (±4*SD
+        for gaussCONV truncates ~3e-4 of the kernel mass).
+        """
+
+        t = np.arange(-20, 100, 0.5)
+        SD = 0.8
+        y = expFun(t, 1.0, 5.0, 0.0)
+        result = _conv_matrix(t, gaussCONV, SD, y=y)
+        n = int(np.ceil(4 * SD / 0.5))
+        support = np.arange(-n, n + 1) * 0.5
+        old = my_conv(t, y, gaussCONV(support, SD))
+        np.testing.assert_allclose(result, old, atol=1e-4)
+
+    #
+    def test_matches_dense_reference_on_nonuniform_axis(self):
+        """Non-uniform axis matches the continuous convolution.
+
+        Smooth signal (erfFun) and smooth kernel, so quadrature error is
+        the only deviation — measured ~1e-3 relative on this axis. The
+        sample-index convolution it replaced was far worse on discontinuous
+        signals over non-uniform axes (up to ~7% of trace max on example
+        21's stepped axis).
+        """
+
+        t = np.concatenate([np.arange(-15, 5, 0.25), np.arange(5, 60, 1.0)])
+        SD = 1.5
+
+        def signal(t_axis):
+            return erfFun(t_axis, 5.0, 2.0, 0.0)
+
+        result = _conv_matrix(t, gaussCONV, SD, y=signal(t))
+        reference = _dense_reference(t, signal, gaussCONV, SD)
+        scale = np.abs(reference).max()
+        assert np.abs(result - reference).max() / scale < 5e-3
 
     #
-    def test_symmetric_and_odd_length(self):
-        """Support is symmetric around 0 with an odd number of samples."""
+    def test_asymmetric_kernel_direction(self):
+        """Causal kernel (expDecayCONV) delays the signal, not advances it.
+
+        Pins the sign convention K[i, j] = g(t_i - t_j): a causal kernel
+        (nonzero for positive time differences) draws from the past.
+        Compared against the old padded-1D path, which shares the
+        sampled-kernel semantics at the dt=0 discontinuity.
+        """
 
-        axis = conv_kernel_support(3.7, 0.5)
-        assert axis.size % 2 == 1
-        np.testing.assert_allclose(axis, -axis[::-1])
-        assert axis[axis.size // 2] == 0.0
+        tau = 2.0
+        t = np.arange(-10, 40, 0.5)
+        y = expFun(t, 1.0, 8.0, 0.0)
+        result = _conv_matrix(t, expDecayCONV, tau, y=y)
+        n = int(np.ceil(6 * tau / 0.5))
+        support = np.arange(-n, n + 1) * 0.5
+        old = my_conv(t, y, expDecayCONV(support, tau))
+        # ±6*tau truncates exp(-6) ≈ 0.25% of the old kernel's mass
+        np.testing.assert_allclose(result, old, atol=5e-3)
+        # the convolved response lags the raw signal on the rising edge
+        assert result[t == 1.0] < y[t == 1.0]
+        # and is causal: nothing before the t0=0 onset
+        np.testing.assert_allclose(result[t < 0.0], 0.0, atol=1e-12)
 
     #
-    def test_covers_t_range(self):
-        """Support extends to at least ±t_range."""
+    def test_edge_mass_accumulation(self):
+        """Kernel mass beyond the window folds onto the edge samples.
+
+        A saturated signal (constant near both ends) must stay flat at
+        the edges — the edge-padding assumption — instead of decaying
+        toward zero as pure row-truncation would produce.
+        """
 
-        axis = conv_kernel_support(3.7, 0.5)
-        assert axis.max() >= 3.7
-        assert axis.min() <= -3.7
+        t = np.arange(0, 20, 0.5)
+        y = np.full(t.size, 2.0)
+        y[20:] = 5.0  # step in the middle, constant at both ends
+        result = _conv_matrix(t, gaussCONV, 1.0, y=y)
+        np.testing.assert_allclose(result[0], 2.0, rtol=1e-6)
+        np.testing.assert_allclose(result[-1], 5.0, rtol=1e-6)
 
     #
-    def test_exact_multiple(self):
-        """t_range on the grid gives endpoints exactly at ±t_range."""
+    def test_broad_kernel_fine_start_axis_edges_exact(self):
+        """Broad kernel on a fine-start axis: edge masses stay exact.
+
+        Regression for the ghost-point edge scheme this replaced: its
+        coverage was only n_t * boundary_step per side (here ~1.3 time
+        units against SD = 5), so most of the exterior kernel mass was
+        silently discarded and renormalized away. The analytic edge
+        masses have no coverage limit. Reference: identical interior
+        trapezoid discretization + exterior masses from an independent
+        implementation (scipy.stats.norm survival function).
+        """
+
+        t = np.concatenate([np.arange(0.0, 1.0, 0.01), np.arange(1.0, 31.0, 1.0)])
+        SD = 5.0
+        y = np.linspace(2.0, 4.0, t.size)
+        result = _conv_matrix(t, gaussCONV, SD, y=y)
 
-        axis = conv_kernel_support(4.0, 0.5)
-        np.testing.assert_allclose(axis[0], -4.0)
-        np.testing.assert_allclose(axis[-1], 4.0)
-        assert axis.size == 17
+        operator = conv_matrix_operator(t)
+        interior = gaussCONV(t[:, None] - t[None, :], SD) * operator.quad_weights
+        scale = SD * np.sqrt(2 * np.pi)  # peak-1 body integral
+        mass_left = scale * norm.sf((t - t[0]) / SD)
+        mass_right = scale * norm.cdf((t - t[-1]) / SD)
+        row_sums = interior.sum(axis=1) + mass_left + mass_right
+        expected = (interior @ y + mass_left * y[0] + mass_right * y[-1]) / row_sums
+        np.testing.assert_allclose(result, expected, rtol=1e-9)
 
     #
-    def test_minimum_support(self):
-        """t_range below one step still yields a 3-sample support."""
+    def test_asymmetric_kernels_broad_edge_behavior(self):
+        """One-sided kernels with window-scale tau: edges stay exact.
+
+        Left/right swap detector: a causal kernel (expDecayCONV) draws
+        only from the past, so the first sample sees nothing but
+        edge-padded y[0] and must return it exactly; the anti-causal
+        mirror (expRiseCONV) must return y[-1] at the last sample. With
+        tau comparable to the window, most of each row's mass is
+        exterior, so swapped left/right mass formulas fail loudly.
+        """
+
+        t = np.arange(0.0, 10.5, 0.5)
+        tau = 5.0
+        y = np.where(t < 5.0, 1.0, 3.0)
 
-        axis = conv_kernel_support(0.01, 0.5)
-        np.testing.assert_allclose(axis, [-0.5, 0.0, 0.5])
+        result_causal = _conv_matrix(t, expDecayCONV, tau, y=y)
+        np.testing.assert_allclose(result_causal[0], y[0], rtol=1e-12)
+        assert result_causal[-1] < y[-1]  # lags behind the step
+
+        result_anti = _conv_matrix(t, expRiseCONV, tau, y=y)
+        np.testing.assert_allclose(result_anti[-1], y[-1], rtol=1e-12)
+        assert result_anti[0] > y[0]  # anticipates the step
 
     #
-    def test_grows_with_t_range(self):
-        """Doubling t_range widens the support accordingly."""
+    def test_narrow_kernel_degrades_to_identity(self):
+        """A kernel far narrower than the step returns the input signal.
+
+        The dt=0 diagonal keeps every row sum positive, so sub-step
+        kernels degrade gracefully instead of raising (the old 1D path
+        errored out when the sampled kernel summed to zero).
+        """
 
-        narrow = conv_kernel_support(2.0, 0.5)
-        wide = conv_kernel_support(4.0, 0.5)
-        assert wide.size > narrow.size
-        assert wide.max() >= 2 * narrow.max() - 0.5
+        t = np.arange(0, 10, 1.0)
+        y = np.sin(t)
+        result = _conv_matrix(t, gaussCONV, 1e-6, y=y)
+        np.testing.assert_allclose(result, y, rtol=1e-12)
 
     #
-    def test_nonfinite_range_raises(self):
-        """Non-finite t_range raises ValueError."""
+    def test_nan_kernel_params_raise(self):
+        """Non-finite kernel parameters raise instead of propagating NaN.
+
+        The edge-mass companion validates the parameters first; the
+        apply-side finite/nonnegative check on the kernel values remains
+        as a backstop for direct calls.
+        """
 
-        with pytest.raises(ValueError, match="not finite"):
-            conv_kernel_support(np.nan, 0.5)
-        with pytest.raises(ValueError, match="not finite"):
-            conv_kernel_support(np.inf, 0.5)
+        t = np.arange(0, 10, 1.0)
+        y = np.sin(t)
+        with pytest.raises(ValueError, match="strictly positive"):
+            _conv_matrix(t, gaussCONV, np.nan, y=y)
+        operator = conv_matrix_operator(t)
+        bad_kernel = np.full(operator.dt_unique.shape, np.nan)
+        good_mass = np.full(t.size, 0.1)
+        with pytest.raises(ValueError, match="finite and nonnegative"):
+            conv_matrix_apply(operator, bad_kernel, good_mass, good_mass, y)
 
     #
-    def test_bad_step_raises(self):
-        """Non-positive or non-finite t_step raises ValueError."""
+    def test_negative_edge_mass_rejected(self):
+        """Signed mass errors cannot cancel inside row sums silently."""
+
+        t = np.arange(0, 10, 1.0)
+        y = np.sin(t)
+        operator = conv_matrix_operator(t)
+        kernel_values = gaussCONV(operator.dt_unique, 1.0)
+        bad_mass = np.full(t.size, -0.1)
+        good_mass = np.full(t.size, 0.1)
+        with pytest.raises(ValueError, match="edge masses"):
+            conv_matrix_apply(operator, kernel_values, bad_mass, good_mass, y)
 
-        with pytest.raises(ValueError, match="positive"):
-            conv_kernel_support(1.0, 0.0)
-        with pytest.raises(ValueError, match="positive"):
-            conv_kernel_support(1.0, -0.5)
+    #
+    def test_wrong_shape_inputs_rejected(self):
+        """Mismatched kernel/mass shapes raise instead of broadcasting."""
+
+        t = np.arange(0, 10, 1.0)
+        y = np.sin(t)
+        operator = conv_matrix_operator(t)
+        kernel_values = gaussCONV(operator.dt_unique, 1.0)
+        mass = np.full(t.size - 1, 0.1)  # wrong length
+        with pytest.raises(ValueError, match="wrong shapes"):
+            conv_matrix_apply(operator, kernel_values, mass, mass, y)
+
+    #
+    def test_wrong_shape_signal_rejected(self):
+        """A column-vector y raises instead of broadcasting to (n_t, n_t)."""
+
+        t = np.arange(0, 10, 1.0)
+        y_col = np.sin(t)[:, None]
+        operator = conv_matrix_operator(t)
+        kernel_values = gaussCONV(operator.dt_unique, 1.0)
+        mass = np.full(t.size, 0.1)
+        with pytest.raises(ValueError, match="wrong shapes"):
+            conv_matrix_apply(operator, kernel_values, mass, mass, y_col)
 
 
 #
diff --git a/tests/test_config_functions.py b/tests/test_config_functions.py
index 864b8c6..07f50fb 100644
--- a/tests/test_config_functions.py
+++ b/tests/test_config_functions.py
@@ -9,7 +9,11 @@
 
 import pytest
 
-from trspecfit.config.functions import get_function_parameters
+from trspecfit.config.functions import (
+    _module_functions,
+    all_functions,
+    get_function_parameters,
+)
 from trspecfit.functions import energy, profile, time
 
 
@@ -70,8 +74,8 @@ def test_none_has_no_params(self):
     def test_gaussCONV(self):
         assert get_function_parameters("gaussCONV") == ["SD"]
 
-    def test_voigtCONV(self):
-        assert get_function_parameters("voigtCONV") == ["SD", "W"]
+    def test_expDecayCONV(self):
+        assert get_function_parameters("expDecayCONV") == ["tau"]
 
     #
     # profile functions — first arg (x) stripped
@@ -99,25 +103,18 @@ class TestNoUnderscoresInNames:
     """
 
     MODULES = [energy, time, profile]
-    INTERNAL_SUFFIXES = ("_kernel_width",)
 
     #
     def _public_callables(self):
-        """Yield (module, name, func) for every public callable."""
+        """Yield (module, name, func) for every discovered registry function."""
 
         for mod in self.MODULES:
-            for name in dir(mod):
-                if name.startswith("_"):
-                    continue
-                obj = getattr(mod, name)
-                if callable(obj):
-                    yield mod, name, obj
+            for name in _module_functions(mod):
+                yield mod, name, getattr(mod, name)
 
     #
     def test_no_underscore_in_function_names(self):
         for mod, name, _func in self._public_callables():
-            if any(name.endswith(s) for s in self.INTERNAL_SUFFIXES):
-                continue
             assert "_" not in name, f"{mod.__name__}.{name} contains an underscore"
 
     #
@@ -130,8 +127,6 @@ def test_profile_functions_start_with_p(self):
     #
     def test_no_underscore_in_parameter_names(self):
         for mod, name, func in self._public_callables():
-            if any(name.endswith(s) for s in self.INTERNAL_SUFFIXES):
-                continue
             sig = inspect.signature(func)
             for par_name in sig.parameters:
                 assert "_" not in par_name, (
@@ -140,5 +135,27 @@ def test_no_underscore_in_parameter_names(self):
                 )
 
 
+#
+#
+class TestRegistryExcludesImports:
+    """Function discovery only accepts functions defined in the modules.
+
+    Imported helpers (scipy.special functions, typing constructs) are
+    public module attributes; if discovery accepted them, a malformed
+    YAML component named e.g. 'erfc' would pass function-name validation
+    and only fail during evaluation.
+    """
+
+    #
+    def test_imported_names_not_discovered(self):
+        discovered = set(all_functions())
+        assert {"erf", "erfc", "wofz", "Callable"}.isdisjoint(discovered)
+
+    #
+    def test_registry_functions_still_discovered(self):
+        discovered = set(all_functions())
+        assert {"GLP", "expFun", "gaussCONV", "pGauss", "none"} <= discovered
+
+
 if __name__ == "__main__":
     pytest.main([__file__])
diff --git a/tests/test_evaluate_2d.py b/tests/test_evaluate_2d.py
index 7e2985e..745c431 100644
--- a/tests/test_evaluate_2d.py
+++ b/tests/test_evaluate_2d.py
@@ -739,9 +739,10 @@ class TestDynamicsConvolution:
 
     Covers plan encoding (conv program layout, resolution ordering) and
     numerical parity against ``Model.create_value_2d()``.
-    The IRF path rewrites a resolved trace row in place via
-    ``my_conv`` -- the same code MCP calls -- so tolerance matches the
-    other OpKind parity tests.
+    The IRF path rewrites a resolved trace row in place via the
+    kernel-matrix operator (``conv_matrix_apply`` on the plan's
+    precomputed dt matrix) -- the same code MCP calls -- so tolerance
+    matches the other OpKind parity tests.
     """
 
     #
@@ -804,30 +805,43 @@ def test_conv_param_rows_valid(self):
             assert 0 <= int(row) < plan.n_params
 
     #
-    def test_conv_support_tracks_grown_kernel_width(self):
+    def test_conv_parity_when_kernel_width_grows(self):
         """Parity holds when the kernel width grows well past its init.
 
-        Regression guard for the frozen-support bug: the kernel support
-        used to be sized once from the initial SD, silently truncating
-        the kernel (and breaking parity) once the fitted SD grew past
-        it.  Both paths now rebuild the support from the current value.
+        Regression guard descended from the frozen-support bug of the
+        old 1D-kernel path (support sized once from the initial SD,
+        silently truncating a grown kernel).  The kernel-matrix
+        operator has no support at all -- the dt matrix spans the full
+        axis regardless of theta -- so a width far above its init must
+        stay in parity with no shape change anywhere.
         """
 
         plan, _graph, model = self._make_irf_plan(dyn_model="MonoExpPosIRFNarrow")
         theta = _compare_evaluator_vs_interpreter(model, plan)
         sd_idx = plan.opt_param_names.index("GLP_01_A_gaussCONV_SD")
-        # Narrow SD init is 5e-2 on a dt=2.2 axis; +0.6 grows the support
-        # from a sub-sample kernel to a multi-sample one (within bounds)
+        # Narrow SD init is 5e-2 on a dt=2.2 axis; +0.6 grows the kernel
+        # from sub-sample to multi-sample (within bounds)
         _perturb_theta(plan, model, theta, [sd_idx], [0.6])
 
-        # interpreter side: the kernel axis was rebuilt to span the
-        # grown width (±4*SD for gaussCONV)
-        A_par = next(p for p in model.components[0].pars if p.name == "GLP_01_A")
-        assert A_par.t_model is not None  # type guard
-        conv_comp = next(c for c in A_par.t_model.components if c.comp_type == "conv")
-        assert conv_comp.time is not None  # type guard
-        SD_grown = theta[sd_idx] + 0.6
-        assert conv_comp.time.max() >= 4 * SD_grown
+    #
+    def test_conv_operator_precomputed_on_plan(self):
+        """The plan carries the theta-independent kernel-matrix operator.
+
+        Static shapes are the point of the operator (no per-theta kernel
+        arrays): the interior gather matrix is (n_time, n_time) and the
+        edge-mass abscissae match the axis. The plan stores no
+        callables — edge-mass companions resolve via
+        CONV_EDGE_MASS_DISPATCH from the numeric conv_func_ids.
+        """
+
+        plan, _graph, _model = self._make_irf_plan()
+        op = plan.conv_operator
+        assert op is not None  # type guard
+        n_time = plan.n_time
+        assert op.gather_idx.shape == (n_time, n_time)
+        assert op.quad_weights.shape == (n_time,)
+        assert op.dt_left.shape == (n_time,)
+        assert op.dt_right.shape == (n_time,)
 
     #
     def test_conv_step_runs_after_dynamics(self):
@@ -873,11 +887,8 @@ def test_non_irf_has_empty_conv_program(self):
     # Per-kernel parity: every lowerable kernel must match MCP at
     # initial theta AND under perturbation of every kernel parameter.
     # Parametrized by dyn_model YAML and the list of (param_suffix, delta)
-    # pairs to perturb -- one entry per kernel param, so voigtCONV's
-    # two-param case is covered alongside the one-param kernels.
+    # pairs to perturb -- one entry per kernel param.
     _KERNEL_PARITY_CASES = [
-        ("MonoExpPosLorentzIRF", [("lorentzCONV_W", 0.2)]),
-        ("MonoExpPosVoigtIRF", [("voigtCONV_SD", 0.05), ("voigtCONV_W", 0.05)]),
         ("MonoExpPosExpSymIRF", [("expSymCONV_tau", 0.5)]),
         ("MonoExpPosExpDecayIRF", [("expDecayCONV_tau", 0.5)]),
         ("MonoExpPosExpRiseIRF", [("expRiseCONV_tau", 0.5)]),
diff --git a/tests/test_functions_convolution.py b/tests/test_functions_convolution.py
index a51c249..1751bf9 100644
--- a/tests/test_functions_convolution.py
+++ b/tests/test_functions_convolution.py
@@ -4,29 +4,36 @@
 - Symmetry (where applicable)
 - Peak at center (x=0)
 - Known shape properties
-- kernel_width() returns positive int/float
+
+Edge-mass companions (CONV_EDGE_MASS) are validated against numerical
+integration of the kernel bodies, and both registries are checked for
+completeness so a kernel can never ship without its companion.
 """
 
 import numpy as np
 import pytest
+from scipy.integrate import quad
 
+from trspecfit.functions import time as fcts_time
 from trspecfit.functions.time import (
+    CONV_EDGE_MASS,
     boxCONV,
-    boxCONV_kernel_width,
     expDecayCONV,
-    expDecayCONV_kernel_width,
     expRiseCONV,
-    expRiseCONV_kernel_width,
     expSymCONV,
-    expSymCONV_kernel_width,
     gaussCONV,
-    gaussCONV_kernel_width,
-    lorentzCONV,
-    lorentzCONV_kernel_width,
-    voigtCONV,
-    voigtCONV_kernel_width,
 )
 
+# one representative parameter set per kernel, used by the companion
+# consistency test; extend when adding a kernel
+_KERNEL_TEST_PARAMS = {
+    "gaussCONV": (1.7,),
+    "expSymCONV": (2.3,),
+    "expDecayCONV": (2.3,),
+    "expRiseCONV": (2.3,),
+    "boxCONV": (3.0,),
+}
+
 
 #
 def make_kernel_axis():
@@ -89,115 +96,6 @@ def test_decays_monotonically(self):
         # Left side: increasing toward center
         assert np.all(np.diff(result[:center]) >= -1e-12)
 
-    #
-    def test_kernel_width_positive(self):
-        assert gaussCONV_kernel_width() > 0
-
-
-#
-#
-class TestLorentzCONV:
-    #
-    def test_peak_at_center(self):
-        x_sym = make_kernel_axis()
-        result = lorentzCONV(x_sym, W=2.0)
-        assert np.argmax(result) == len(x_sym) // 2
-
-    #
-    def test_peak_value_is_one(self):
-        x_sym = make_kernel_axis()
-        result = lorentzCONV(x_sym, W=2.0)
-        assert result[len(x_sym) // 2] == pytest.approx(1.0)
-
-    #
-    def test_symmetry(self):
-        x_sym = make_kernel_axis()
-        result = lorentzCONV(x_sym, W=2.0)
-        np.testing.assert_allclose(result, result[::-1], atol=1e-12)
-
-    #
-    def test_half_max_at_half_width(self):
-        """At x = ±W/2, value should be 0.5 (FWHM definition)."""
-
-        x_sym = make_kernel_axis()
-        W = 2.0
-        result = lorentzCONV(x_sym, W=W)
-        idx = np.argmin(np.abs(x_sym - W / 2))
-        assert result[idx] == pytest.approx(0.5, abs=1e-3)
-
-    #
-    def test_decays_monotonically(self):
-        """Should decay monotonically away from center on both sides."""
-
-        x_sym = make_kernel_axis()
-        result = lorentzCONV(x_sym, W=2.0)
-        center = len(x_sym) // 2
-        assert np.all(np.diff(result[center:]) <= 1e-12)
-        assert np.all(np.diff(result[:center]) >= -1e-12)
-
-    #
-    def test_kernel_width_positive(self):
-        assert lorentzCONV_kernel_width() > 0
-
-
-#
-#
-class TestVoigtCONV:
-    #
-    def test_peak_at_center(self):
-        x_sym = make_kernel_axis()
-        result = voigtCONV(x_sym, SD=1.0, W=1.0)
-        assert np.argmax(result) == len(x_sym) // 2
-
-    #
-    def test_peak_normalized_to_one(self):
-        """voigtCONV divides by max, so peak = 1."""
-
-        x_sym = make_kernel_axis()
-        result = voigtCONV(x_sym, SD=1.0, W=1.0)
-        assert result[len(x_sym) // 2] == pytest.approx(1.0, rel=1e-6)
-
-    #
-    def test_symmetry(self):
-        x_sym = make_kernel_axis()
-        result = voigtCONV(x_sym, SD=1.0, W=1.0)
-        np.testing.assert_allclose(result, result[::-1], atol=1e-10)
-
-    #
-    def test_half_max_at_half_width(self):
-        """In the pure Gaussian limit (W→0), FWHM ≈ 2.355*SD."""
-
-        x = np.linspace(-20, 20, 10001)
-        SD = 2.0
-        result = voigtCONV(x, SD=SD, W=1e-10)
-        fwhm_half = np.sqrt(2 * np.log(2)) * SD
-        idx = np.argmin(np.abs(x - fwhm_half))
-        assert result[idx] == pytest.approx(0.5, abs=0.02)
-
-    #
-    def test_pure_gaussian_limit(self):
-        """With W→0, voigtCONV should approach gaussCONV shape."""
-
-        x = np.linspace(-10, 10, 2001)
-        SD = 2.0
-        voigt = voigtCONV(x, SD=SD, W=1e-10)
-        gauss = gaussCONV(x, SD=SD)
-        np.testing.assert_allclose(voigt, gauss, atol=0.02)
-
-    #
-    def test_decays_monotonically(self):
-        """Should decay monotonically away from center on both sides."""
-
-        x = make_kernel_axis()
-        result = voigtCONV(x, SD=1.0, W=1.0)
-        center = len(x) // 2
-        assert np.all(np.diff(result[center:]) <= 1e-10)
-        assert np.all(np.diff(result[:center]) >= -1e-10)
-
-    #
-    def test_kernel_width_positive(self):
-        assert voigtCONV_kernel_width() > 0
-
 
 #
 #
@@ -251,10 +149,6 @@ def test_decays_monotonically(self):
         assert np.all(np.diff(result[center:]) <= 1e-12)
         assert np.all(np.diff(result[:center]) >= -1e-12)
 
-    #
-    def test_kernel_width_positive(self):
-        assert expSymCONV_kernel_width() > 0
-
 
 #
 #
@@ -291,10 +185,6 @@ def test_half_max_at_tau_ln2(self):
         idx = np.argmin(np.abs(x_sym - half_life))
         assert result[idx] == pytest.approx(0.5, abs=0.01)
 
-    #
-    def test_kernel_width_positive(self):
-        assert expDecayCONV_kernel_width() > 0
-
 
 #
 #
@@ -341,10 +231,6 @@ def test_mirror_of_decay(self):
         decay = expDecayCONV(x_sym, tau=2.0)
         np.testing.assert_allclose(rise, decay[::-1], atol=1e-12)
 
-    #
-    def test_kernel_width_positive(self):
-        assert expRiseCONV_kernel_width() > 0
-
 
 #
 #
@@ -384,9 +270,86 @@ def test_wider_width_more_ones(self):
         wide = boxCONV(x_sym, width=3.0)
         assert np.sum(wide > 0.5) > np.sum(narrow > 0.5)
 
-    #
-    def test_kernel_width_positive(self):
-        assert boxCONV_kernel_width() > 0
+
+#
+#
+class TestConvEdgeMassCompanions:
+    """Edge-mass companions integrate the exact kernel bodies."""
+
+    #
+    @pytest.mark.parametrize("kernel_name", sorted(CONV_EDGE_MASS))
+    def test_masses_match_numerical_integration(self, kernel_name):
+        """Companion masses equal quad integrals of the kernel body.
+
+        M_L(a) must equal the body's integral over [a, inf) and M_R(b)
+        the integral over (-inf, b] — the exterior masses used for
+        edge-value padding. Guards any future companion against a
+        normalization or left/right mismatch with its kernel body.
+        """
+
+        body = getattr(fcts_time, kernel_name)
+        params = _KERNEL_TEST_PARAMS[kernel_name]
+        companion = CONV_EDGE_MASS[kernel_name]
+        # generous finite integration bounds: all kernels are negligible
+        # beyond +-50 for the test parameter values
+        bound = 50.0
+        dt_left = np.array([0.0, 0.3, 2.0, 7.0])
+        dt_right = -dt_left
+        mass_left, mass_right = companion(dt_left, dt_right, *params)
+        for i, a in enumerate(dt_left):
+            expected, _err = quad(
+                lambda x: float(body(np.array([x]), *params)[0]), a, bound
+            )
+            np.testing.assert_allclose(mass_left[i], expected, rtol=1e-6, atol=1e-12)
+        for i, b in enumerate(dt_right):
+            expected, _err = quad(
+                lambda x: float(body(np.array([x]), *params)[0]), -bound, b
+            )
+            np.testing.assert_allclose(mass_right[i], expected, rtol=1e-6, atol=1e-12)
+
+    #
+    @pytest.mark.parametrize("kernel_name", sorted(CONV_EDGE_MASS))
+    @pytest.mark.parametrize("bad_value", [0.0, -1.0, np.nan, np.inf])
+    def test_nonpositive_params_rejected(self, kernel_name, bad_value):
+        """Companions reject nonpositive/non-finite parameters loudly.
+
+        Runtime backstop for expression-driven kernel parameters, which
+        bypass the model-load bound validation: boxCONV(width=0) would
+        otherwise pass every downstream check and silently become the
+        identity operator (the dt=0 diagonal keeps row sums positive).
+        """
+
+        companion = CONV_EDGE_MASS[kernel_name]
+        dt_left = np.array([0.0, 1.0, 4.0])
+        dt_right = -dt_left
+        params = (bad_value, *_KERNEL_TEST_PARAMS[kernel_name][1:])
+        with pytest.raises(ValueError, match="strictly positive"):
+            companion(dt_left, dt_right, *params)
+
+    #
+    def test_every_kernel_has_companion(self):
+        """Registry completeness: kernels and companions stay in lockstep.
+
+        Every discoverable *CONV function needs a CONV_EDGE_MASS entry
+        (mcp path), every entry must reference an existing kernel, and
+        the GIR dispatch tables must cover the same kernel set.
+        """
+
+        from trspecfit.eval_2d import CONV_EDGE_MASS_DISPATCH, CONV_KERNEL_DISPATCH
+
+        conv_kernels = {
+            name
+            for name in dir(fcts_time)
+            if name.endswith("CONV") and not name.startswith("_")
+        }
+        assert conv_kernels == set(CONV_EDGE_MASS)
+        assert set(CONV_KERNEL_DISPATCH) == set(CONV_EDGE_MASS_DISPATCH)
+
+    #
+    def test_test_params_cover_all_companions(self):
+        """_KERNEL_TEST_PARAMS stays in sync with the registry."""
+
+        assert set(_KERNEL_TEST_PARAMS) == set(CONV_EDGE_MASS)
 
 
 if __name__ == "__main__":
diff --git a/tests/test_gir_integration.py b/tests/test_gir_integration.py
index 002947e..fdaaf44 100644
--- a/tests/test_gir_integration.py
+++ b/tests/test_gir_integration.py
@@ -31,8 +31,6 @@
 # One dynamics model per lowerable convolution kernel.
 _IRF_KERNEL_MODELS = [
     "MonoExpPosIRF",
-    "MonoExpPosLorentzIRF",
-    "MonoExpPosVoigtIRF",
     "MonoExpPosExpSymIRF",
     "MonoExpPosExpDecayIRF",
     "MonoExpPosExpRiseIRF",
diff --git a/tests/test_mcp_library.py b/tests/test_mcp_library.py
index 63fe05b..bcc7bee 100644
--- a/tests/test_mcp_library.py
+++ b/tests/test_mcp_library.py
@@ -270,7 +270,7 @@ def test_dynamics_model_creation(self):
 
         # Define instrument response function
         c_IRF = Component("gaussCONV", fcts_time)
-        c_IRF.add_pars({"SD": [80, True, 0, 1e4]})
+        c_IRF.add_pars({"SD": [80, True, 1e-6, 1e4]})
 
         # Define decay components
         c_td1 = Component("expFun", fcts_time)
@@ -327,26 +327,76 @@ def test_dynamics_parameter_handling(self):
         assert t_mod.components[0].par_dict["tau"] == [2.5, True, 1, 10]
 
     #
-    def test_voigt_kernel_axis_uses_both_width_parameters(self):
-        """Voigt kernel support widens when Lorentzian tails dominate."""
+    def test_conv_component_keeps_model_time_axis(self):
+        """Conv components share the model time axis (no kernel-support rebind).
 
-        t_mod = Model("test_voigt_irf")
+        The kernel-matrix operator replaced the per-theta 1D kernel
+        support: the component keeps the model axis, and the operator
+        (dt matrix, quadrature weights, edge-mass abscissae) is built
+        and validated at add_components time.
+        """
+
+        t_mod = Model("test_gauss_irf")
         t_mod.time = np.arange(-5, 6, 1.0)
 
-        c_irf = Component("voigtCONV", fcts_time)
-        c_irf.add_pars(
-            {
-                "SD": [0.1, True, 0.01, 1],
-                "W": [4.0, True, 0.01, 10],
-            }
-        )
+        c_irf = Component("gaussCONV", fcts_time)
+        c_irf.add_pars({"SD": [0.4, True, 0.01, 1]})
 
         t_mod.add_components([c_irf])
 
-        # Support should span the larger of 12*SD and 10*W.
-        assert c_irf.time is not None  # type guard
-        assert c_irf.time[0] == pytest.approx(-40.0)
-        assert c_irf.time[-1] == pytest.approx(40.0)
+        assert c_irf.time is t_mod.time
+        operator = c_irf.conv_operator()
+        n_time = t_mod.time.size
+        assert operator.gather_idx.shape == (n_time, n_time)
+        assert operator.quad_weights.shape == (n_time,)
+        assert operator.dt_left.shape == (n_time,)
+        assert operator.dt_right.shape == (n_time,)
+
+    #
+    def test_conv_kernel_nonpositive_bounds_rejected(self):
+        """Kernel widths must be strictly positive, enforced at model load.
+
+        A zero lower bound lets the optimizer propose width = 0, which
+        only fails deep inside a fit; add_components rejects it upfront
+        with a clear error.
+        """
+
+        t_mod = Model("test_bad_bounds")
+        t_mod.time = np.arange(-5, 6, 1.0)
+
+        c_irf = Component("gaussCONV", fcts_time)
+        c_irf.add_pars({"SD": [0.4, True, 0, 1]})
+
+        with pytest.raises(ValueError, match="strictly positive"):
+            t_mod.add_components([c_irf])
+
+    #
+    def test_conv_kernel_missing_lower_bound_rejected(self):
+        """Varying kernel widths require an explicit positive lower bound.
+
+        The unbound two-element form [value, True] creates an lmfit
+        parameter with min=-inf, letting the optimizer propose invalid
+        widths mid-fit; add_components rejects it upfront. A fixed
+        parameter ([value, False]) stays valid without bounds.
+        """
+
+        t_mod = Model("test_missing_bounds")
+        t_mod.time = np.arange(-5, 6, 1.0)
+
+        c_irf = Component("gaussCONV", fcts_time)
+        c_irf.add_pars({"SD": [0.4, True]})
+
+        with pytest.raises(ValueError, match="lower bound"):
+            t_mod.add_components([c_irf])
+
+        t_mod_fixed = Model("test_fixed_no_bounds")
+        t_mod_fixed.time = np.arange(-5, 6, 1.0)
+
+        c_irf_fixed = Component("gaussCONV", fcts_time)
+        c_irf_fixed.add_pars({"SD": [0.4, False]})
+
+        t_mod_fixed.add_components([c_irf_fixed])
+        assert c_irf_fixed.par_dict["SD"] == [0.4, False]
 
 
 #
diff --git a/tests/test_model_parser.py b/tests/test_model_parser.py
index e5e9cab..59f50f0 100644
--- a/tests/test_model_parser.py
+++ b/tests/test_model_parser.py
@@ -231,7 +231,7 @@ def test_IRF_model(self):
         # check the components
         assert model.components[0].fct_str == "gaussCONV"
         assert model.components[0].comp_name == "gaussCONV"
-        assert model.components[0].par_dict["SD"] == [0.4, True, 0, 1]
+        assert model.components[0].par_dict["SD"] == [0.4, True, 1e-06, 1]
 
         assert model.components[1].fct_str == "expFun"
         assert model.components[1].comp_name == "expFun_01"
@@ -342,7 +342,7 @@ def test_simple_2D_model(self):
         td_par_model = model.components[2].pars[1].t_model
         assert td_par_model is not None  # type guard
         assert td_par_model.components[0].comp_name == "gaussCONV"
-        assert td_par_model.components[0].par_dict["SD"] == [0.4, True, 0, 1]
+        assert td_par_model.components[0].par_dict["SD"] == [0.4, True, 1e-06, 1]
         assert td_par_model.components[1].fct_str == "expFun"
         assert td_par_model.components[1].comp_name == "expFun_01"
         assert td_par_model.components[1].par_dict["A"] == [1, True, 0, 5]