Σ-GLYPH World

A non-normative research notebook for testing where Σ-GLYPH resource invariants transfer to other systems — and where the analogy breaks.

This repository does not extend the Σ-GLYPH specification and does not speak for s0fractal/sigma-glyph. Its subject is representativeness: whether a result proved for one abstract machine survives an explicit mapping to another computational, biological, physical, or verification system.

What is here

• talks/gemini-001.md — a generative map of physical and cosmological resonances;
• talks/claude-fable-001.md — an adversarial separation of testable hypotheses from narrative correspondences;
• INTENTIONS.md — Codex's current research intent after attacking both texts and receiving Claude's counter-attack;
• PROVENANCE.md — what the dialogue artifacts establish and what they do not;
• experiments/SCOPE-PILOT-001-preregistration.md and experiments/scope-pilot-001/PILOT-RESULT.md — a preregistered attack on whether verification-scope incidents can be coded without inventing their causal chain;
• experiments/scope-instrument-001/RESULT.md — a retired-corpus calibration that separates observed behavior from the independently evidenced meaning of success;
• experiments/SCOPE-PILOT-002-preregistration.md and experiments/scope-pilot-002/PILOT-RESULT.md — a fresh-corpus protocol retired when a repository alias made its supposedly unique sampling frame invalid before any candidate was frozen;
• experiments/SCOPE-PILOT-003-preregistration.md and experiments/scope-pilot-003/SAMPLING-RESULT.md — the canonical-repository-ID retry with append-only query checkpoints, and its frozen candidate order of 5276 issues;
• experiments/scope-pilot-003/SCREENING-RESULT.md — the screen of the first 60 candidates in frozen order, retired as a sampling failure at 1 admitted incident against a minimum of 8. Its erratum marks the attribution CONTESTED: what the pilot demonstrates is the failure of this frame-plus-instrument combination, and whether the seven query terms or codebook v1's contract tier is the binding constraint is not identified by a design with no comparison arm.
• experiments/KAPPA-EXP-001-preregistration.md and experiments/kappa-exp-001/RESULT.md — a preregistered refutation of the claim that the overcharge factor κ is an invariant of a calculus. One λ family, two strategies, same normal form: κ diverges under one and converges to 4 under the other. Two errata: the successor question was trivial, and the machine's object graph is a persistent DAG while its metric is occurrence-weighted, so peak is a tree size and not materialized state;
• experiments/KAPPA-EXP-002-preregistration.md and experiments/kappa-exp-002/RESULT.md — the same family run through the Σ-GLYPH Book I reference oracle at a pinned digest. Structural sharing does not make peak linear: the store holds 2n + 2 distinct nodes and is fetched 2^(n+3) − 7 times.
• experiments/KAPPA-EXP-003-preregistration.md and experiments/kappa-exp-003/RESULT.md — the strategy-spread question for λ. Refuted under C_size with the closed form (3k+1)/4, but that refutation is an artifact of a cost model that bills a copy which duplicates nothing; under the corrected C_dup the question is live and unsettled;
• experiments/KAPPA-EXP-005-preregistration.md and experiments/kappa-exp-005/RESULT.md — the extended grid that settles it. The spread saturates in n and is driven by k, converging to k + 9/4. The preregistered prediction was wrong in both directions and says so on every green run; an erratum supplies the peak recurrences the asymptotic claim was missing and retracts the Track A over-generalisation;
• experiments/KAPPA-EXP-006-preregistration.md and experiments/kappa-exp-006/RESULT.md — the representation audit. "Tree", "sharing", "materialized state" and "actual work" turn out to be four different quantities: at n = 12 and the same occurrence size of 16381, the innermost strategy materializes 16381 objects on a machine that copies and 30 on one that aliases, while a content-addressed store holds 29 under both;
• experiments/KAPPA-EXP-007-preregistration.md and experiments/kappa-exp-007/RESULT.md — Wadsworth graph reduction. Sharing reduction rather than storage collapses the 341× separation to exactly 11/8 where duplication is not under a binder, and leaves it growing where it is. The first experiment run under AGENTS.md clause 8, with two attributed predictions scored by name on every green run;
• experiments/KAPPA-EXP-008-preregistration.md and experiments/kappa-exp-008/RESULT.md — a sharing graph reducer. What survives Codex's boundary review is the schedule-internal claim: inside one machine the two schedules fire the same number of interactions and reach the same peak, so the separation is exactly 1.0000 on h_n and d_n. The cross-representation reading is withdrawn — readback is unpriced, so the machines' outputs sit on opposite sides of an undefined boundary. The implemented reducer is renamed R_abstract, its unsoundness is a measured rate over a stated denominator (1 of 1493 comparable terms), and e_4 is an ungated observation;
• experiments/WORLD-CAS-001-preregistration.md and experiments/world-cas-001/RESULT.md — write-through content-addressable storage, posed by ChatGPT's review after it found that every "store" number in the arc counts live reachable hashes of the current term while the store is never written during evaluation. It is not the same quantity: on h_12 the live window holds 5n = 60 hashes while the store ever holds 3·2^n + 3 = 12291. KAPPA-EXP-006's sentence "a store never sees the explosion" is false under this policy, and a content-addressed store turns out to be blind to the R_fresh/R_alias distinction entirely;
• experiments/KAPPA-EXP-009-preregistration.md and experiments/kappa-exp-009/RESULT.md — the boundary experiment Codex designed, answering whether KAPPA-EXP-008's collapse survives a common semantic interface. It does not. Under a compact contract the sharing graph holds 74 nodes at h_12 against R_fresh's 16389; under an explicit one it holds 16431 against 16389 and is marginally the worst of the three. The work ordering flips between contracts at 22 of 25 gated points. The advantage is real where compact observation is honest (23.7× on d_10) and absent where the observer must inspect the whole output;
• reviews/ — Codex's review, an adversarial review of main at d61e6da with verdict CHANGES REQUESTED; Claude Fable's review of 9dd7e18, whose synthesis is adopted and whose closing role calibration is disputed on the record. Findings are answered in errata and successor experiments, never by editing the reviewed documents.

The dialogue files are evidence of a conversation, not evidence for the claims inside it.

• The EML track (experiments/EML-EXP-001-preregistration.md, experiments/EML-EXP-002-preregistration.md) — two transfer tests against Odrzywołek's single-operator basis (arXiv:2603.21852v2, source-pinned by digest), corpus committed and verified before the preregistrations, three voices' predictions filed before the harness. Measured: sharing is a large-construction phenomenon — only the ten largest constructions beat a grammar-matched null (N4), floor at 134 nodes (RESULT); and precision is not a budget on this basis — 15 of 18 neg-routed constructions evaluate at exactly one precision (n = 12) and n = 40 fails where n = 12 succeeds, because the blocker is ln(0), a representational hole (RESULT). Transcription found a defect in the paper itself (T1, an even-in-x arcosh witness; TRANSCRIPTION_LOG.md).

Pipeline state

pilot	sampling	screening	packets	coding	agreement
SCOPE-PILOT-001	done	done	done	not run	not computed
SCOPE-PILOT-002	failed	—	—	—	—
SCOPE-PILOT-003	done	done — sampling failure	not run	not run	not run

There are two commands, and they answer different questions.

• tools/test-all.sh is a progress reporter. It passes when a phase has not started, when a measurement is absent, and when the external Σ-GLYPH oracle is missing, and says so in its output.
• tools/test-release.sh is a release-state completeness gate, not a claim-correctness gate: it proves the artifacts this page depends on are present, tracked, digest-unchanged and in their terminal states — it does not bind every numeric literal on this page to a receipt (the mutation count is the one literal it binds; binding the rest is an open item named by ChatGPT's review). A missing artifact, a changed frozen digest, an absent terminal state, or any skip marker is a failure. tools/mutation-test.py deletes each manifest artifact and corrupts each frozen digest in a throwaway copy, and additionally edits three recorded soundness values while re-freezing their digests so that only the semantic check can object. It requires the gate to reject all 88 mutations. That literal is derived from the manifest by tools/mutation-test.py, and tools/check-release.py fails if this sentence and the manifest disagree.

A green tools/test-all.sh reports the state of each phase; it does not assert that later phases exist. experiments/scope-pilot-003/screen.py --check prints the screening's terminal status, including SAMPLING_FAILURE, because a recorded failure is an outcome of the protocol rather than a harness error.

Research discipline

Claims use explicit status labels:

• FACT — directly supported by a named artifact or observation;
• DERIVATION — follows from stated premises;
• HYPOTHESIS — falsifiable but not established;
• SPECULATION — generative analogy without an operational test;
• CONTESTED — more than one live interpretation;
• UNKNOWN — the repository does not know.

A hypothesis is written before its measurement harness. A pilot may improve a codebook or protocol, but it may not score the hypothesis it helped define. Green checks establish reproducibility of what ran, not truth, review, adoption, or normative authority.

Current direction

Verification-scope archaeology on public, third-party incident records (Track C) is retired at SCOPE-PILOT-003 as a sampling failure of the frame-plus-instrument combination. Its screening erratum retracts the claim that a resolution-sampled successor follows: conditioning inclusion on resolution changes the estimand, so resolution-derived corpora are one option for instrument calibration and evidence augmentation, not an identified successor and not a causal diagnosis. No successor is identified.

Track A produced its first two measurements. KAPPA-EXP-001 refutes κ as a property of a calculus and relocates it to the pair (strategy, cost model); its erratum retracts the successor question as trivial and adopts instead the spread of κ between strategies on one term. KAPPA-EXP-002 refutes the prediction that structural sharing dissolves that counterexample, and finds the real reason it does not transfer to Σ-GLYPH: the strategy is pinned normatively, so there is no second strategy to diverge. KAPPA-EXP-003 and KAPPA-EXP-005 ask the spread question of λ, where the strategy is free, and answer it: unbounded under both materialization-charging cost models, for different reasons, only the second of which is real. Over the occurrence-weighted tree metric, the invariant the track set out to find does not exist for λ. KAPPA-EXP-006 then separates the metric from the materialization and finds the refutation holds for representations that materialize duplicated subterms per occurrence — including the Σ-GLYPH reference implementation — and dissolves for those that alias. KAPPA-EXP-007 moves the boundary once more: a machine that shares reduction collapses the separation to a residual 11/8 where duplication is not under a binder, and fails to collapse it where it is. The standing statement is that unbounded strategy separation belongs to machines that do not share reduction under a binder — Wadsworth 1971 for the first half, Lévy's non-optimality of call-by-need for the second. What survives is narrower than first claimed: on the measured family and under the two measured cost models, no strategy-independent constant-competitive charge exists. Hard-cap safety is unaffected and needs no pinned strategy; the earlier "derived requirement" is retracted.

The distributed-prepayment track (Track B) remains formalization work until its fault model and comparison metric stop moving.

No license has been selected yet. In particular, publication of attributed dialogue records does not silently assign them the licensing terms of adjacent Σ-GLYPH repositories.