Upddate documentation part 11

Author: Johannes Lang

.github/workflows/docs.yml

@@ -51,6 +51,7 @@ jobs:
       name: github-pages
       url: ${{ steps.deployment.outputs.page_url }}
     runs-on: ubuntu-latest
+    timeout-minutes: 30
     steps:
       - id: deployment
         uses: actions/deploy-pages@v4

Cwaiting.png

@@ -21,7 +21,7 @@ For the spherical mixed p-spin model (representative), the functionals \(\mathca
 
 This reduces the asymptotic cost from \(\mathcal{O}(T^3)\) to linear in the total simulated time (see paper for precise exponents and regimes), enabling orders-of-magnitude longer runs.
 
-Important: DYNAMITE uses exactly the non-equidistant grid defined in the Phys. Rev. Lett. article. The performance gains critically rely on this grid; substituting an equidistant grid drastically reduces the accessible times. See Interpolation grids for details.
+Important: DYNAMITE uses exactly the non-equidistant grid defined in the Phys. Rev. Lett. article. The performance gains critically rely on this grid; substituting an equidistant grid drastically reduces the accessible times. See [Interpolation grids](interpolation-grids.md) for details.
 
 ## Discrete scheme and data layout
 
@@ -94,5 +94,5 @@ The nested sparse representation amortizes the cost of memory integrals, leading
 
 ## See also
 
-- EOMs and Observables: eoms-and-observables.md
-- Time Integration: time-integration.md
+- [EOMs and Observables](eoms-and-observables.md)
+- [Time Integration](time-integration.md)

docs/assets/Cwaiting.png

@@ -41,11 +41,66 @@ The monolithic save path was split into focused modules:
 - `io_save_compressed.*`: compact snapshots (`QK_compressed`, `QR_compressed`, `t1_compressed.txt`).  
 - `io_save_driver.*`: orchestrates sync/async export and progress signaling.
 
-Console/TUI behavior:
+### Compressed snapshots: file formats (`QK_compressed`, `QR_compressed`, `t1_compressed.txt`)
+
+The compressed snapshots are designed for quickly plotting/inspecting the final state
+without loading the full history (HDF5/binary) data.
+
+They consist of two binary matrices and one text file:
+
+- `QK_compressed`: a dense $L\times L$ matrix (double precision). In the current codebase this is saved from `QKB1int`.
+- `QR_compressed`: a dense $L\times L$ matrix (double precision). In the current codebase this is saved from `QRB1int`.
+- `t1_compressed.txt`: a length-$L$ vector of time points.
+
+#### Binary layout
+
+Both `QK_compressed` and `QR_compressed` share the same binary layout:
+
+1. `rows`: `size_t` (native endian)
+2. `cols`: `size_t` (native endian)
+3. `rows*cols` values of type `double` (native endian)
+
+Notes:
+
+- Because the header uses `size_t`, the header is typically 16 bytes on 64-bit systems, but can be 8 bytes on 32-bit systems.
+- Most modern machines are little-endian; if you read these files on a different architecture you must account for endianness.
+
+#### Meaning of `t1_compressed.txt` and the $(t_1,\theta)$ coordinates
+
+The text file `t1_compressed.txt` stores the values
+
+$$
+t_1[i] = t_{\mathrm{last}}\,\theta[i],\qquad i=0,\dots,L-1,
+$$
+
+where $t_{\mathrm{last}}$ is the final simulated time (the last entry in the integrator's `t1grid`) and
+$\theta=t_2/t_1\in(0,1]$ is the dimensionless ratio used by the internal compressed representation.
+
+In other words, if you load:
+
+$$
+t_1\_\text{points} = \texttt{loadtxt}(\texttt{t1\_compressed.txt}),\qquad t_{\mathrm{last}} = t_1\_\text{points}[-1],\qquad \theta\_\text{points} = t_1\_\text{points}/t_{\mathrm{last}},
+$$
+
+then the compressed matrices are interpreted as samples on the grid
+
+$$
+(t_1,\theta) \in (\theta\_\text{points}\,t_{\mathrm{last}})\times(\theta\_\text{points}).
+$$
+
+This is why typical post-processing evaluates waiting-time slices via
+
+$$
+t_1 = t_w+\tau,\qquad \theta = \frac{t_w}{t_w+\tau}.
+$$
+
+See also: `scripts/plot_correlation.py` and the “Reading outputs” tutorial.
+
+### Console/TUI behavior:
 - HDF5 libraries are loaded at runtime (dlopen); the program prints which libraries were found. If unavailable or a write error occurs, saving continues via `data.bin`.  
 - Save progress is staged: main file [0.10..0.50], params [0.50..0.65], histories [0.65..0.80], compressed [0.80..0.90], then DONE.  
 
-Accuracy knobs:
+### Accuracy knobs:
 
 - Grid length L (512/1024/2048): convergence in observables vs. runtime.  
 - Integrator tolerance `-e`, min step `-d`: trade accuracy vs. cost.  

docs/assets/energy.png

@@ -44,7 +44,7 @@ $$
 ## Notes
 - The spherical constraint fixes $\mu(t)$ such that $C(t,t)=1$.
 - The concrete prefactors and any thermal/noise terms follow the conventions published in Phys. Rev. Lett.; DYNAMITE implements those definitions directly.
-- The exact expressions and units match the paper; see source under `include/EOMs/` for the hardcoded operators used at runtime.
+- The exact expressions and units match the paper; see source under [`include/EOMs/`](https://github.com/DMFT-evolution/DMFE/tree/main/include/EOMs) for the hardcoded operators used at runtime.
 - The non-stationary (aging) regime requires both time integrals and thus benefits from the sparse 2D grid and renormalized history.
 
 ## Stored fields
@@ -54,4 +54,4 @@ $$
 - `t1grid`: time grid values used by the integrator
 - `rvec`, `drvec`: reduced observables stored along the diagonal
 
-See `include/EOMs/*` and `include/interpolation/*` for algorithmic details.
+See [`include/EOMs/`](https://github.com/DMFT-evolution/DMFE/tree/main/include/EOMs) and [`include/interpolation/`](https://github.com/DMFT-evolution/DMFE/tree/main/include/interpolation) for algorithmic details.

docs/concepts/algorithm.md

@@ -56,4 +56,4 @@ $$
 - Check that key observables (C, R) at latest times are independent of `-e`.
 - If concerned about stability, disable the lower order method SERK2 at the risk of potentially slightly lower performance at late times.
 
-Implementation details: see `include/EOMs/` and `src/EOMs/` (RK54 Dormand–Prince, SSPRK(10,4), SERK2 kernels and selection logic).
+Implementation details: see [`include/EOMs/`](https://github.com/DMFT-evolution/DMFE/tree/main/include/EOMs) and [`src/EOMs/`](https://github.com/DMFT-evolution/DMFE/tree/main/src/EOMs) (RK54 Dormand–Prince, SSPRK(10,4), SERK2 kernels and selection logic).

docs/concepts/architecture.md

@@ -119,7 +119,7 @@ The solver implements a numerical renormalization scheme with two-dimensional in
 
 - Single-site, causal effective dynamics laid out on the triangular domain t ≥ t'.
 - History terms expressible as integrals/convolutions evaluable on a 2D interpolation grid.
-- Model-specific closures supplied via an EOM module (see `concepts/eoms-and-observables.md`).
+- Model-specific closures supplied via an EOM module (see [EOMs and observables](concepts/eoms-and-observables.md)).
 
 ## Quickstart
 
@@ -157,7 +157,7 @@ The solver implements a numerical renormalization scheme with two-dimensional in
 
 ## Cite DYNAMITE & get help
 
-- Software: see **Reference → Cite** (powered by `CITATION.cff`).
+- Software: see [Reference → Cite](reference/cite.md) (powered by `CITATION.cff`).
 - Method paper: J. Lang, S. Sachdev, S. Diehl, “Numerical renormalization of glassy dynamics,” Phys. Rev. Lett. **135**, 247101 (2025), [doi:10.1103/z64g-nqs6](https://journals.aps.org/prl/abstract/10.1103/z64g-nqs6).
-- License: Apache-2.0 (see `LICENSE`).
-- Support: follow `dev/testing.md` for issue templates or open a GitHub issue with your build info (compiler/CUDA, commit hash, minimal input).
+- License: Apache-2.0 (see [`LICENSE`](https://github.com/DMFT-evolution/DMFE/blob/main/LICENSE)).
+- Support: follow [Testing](dev/testing.md) for issue templates or open a GitHub issue with your build info (compiler/CUDA, commit hash, minimal input).

docs/concepts/eoms-and-observables.md

@@ -87,7 +87,7 @@ CUDA runtime linkage (CUDA builds only):
 - `-DDMFE_STATIC_CUDART=ON|OFF` — link CUDA runtime statically (ON) or dynamically (OFF).
 - `-DDMFE_BUILD_SHARED_VARIANT=ON|OFF` — also build a shared-runtime CUDA variant.
 
-See README Build options for the full list and examples.
+See [README build options](https://github.com/DMFT-evolution/DMFE#build) for the full list and examples.
 
 ## CUDA notes
 
@@ -115,4 +115,4 @@ If you built with compile-time HDF5 (`USE_HDF5=ON`) and see HDF5 load/link error
 
 ---
 
-License: Apache-2.0. See the repository `LICENSE` file. For citation instructions, see Reference → Cite.
+License: Apache-2.0. See the repository [`LICENSE`](https://github.com/DMFT-evolution/DMFE/blob/main/LICENSE) file. For citation instructions, see [Reference → Cite](reference/cite.md).