Σ-GLYPH

A claim with an executable check is worth exactly as much as your ability to run the check yourself. Usually you cannot safely run a stranger's program.

Σ-GLYPH makes a check a content-addressed object rather than mutable code you must trust. Evaluation is deterministic, integer-only and total over its canonical outcomes; one ATP budget prices both semantic work and peak semantic materialization.

Receipt = eval(term_hash, atp: uint32, content_environment)

Two machines given the same term hash, budget and valid demanded content return the same exit, result hash and ATP spent. Missing demanded content is an explicit input and yields Unresolved Reference; local process/resource faults stay outside canonical outcomes. Implementations must apply local admission limits before reading untrusted terms or stores.

The three-input form above is normative since Book I 0.6.0.

What it establishes

Σ-GLYPH owns two things: Book I (deterministic reduction, content addressing, one ATP budget for work and memory) and sigma-resume (budgeted segments, checkpoints, resume and verification by replay). Everything else this repository once carried (Books II and III, the GOV-anchors governance, the Warrant 0.x apparatus, gate and review material) was retired on 2026-10-31; history/RETIREMENT-2026-10-ECHO.md says what left, why and where its bytes are.

Two implementations agree on all 49 Book I conformance vectors and on generated terms: the Python reference and a from-scratch Rust implementation, from one author/model lineage. Lean 4 checks determinism, totality, the semantic-size bound and valid-store monotonicity of Book I, and for sigma-resume segmentation invariance, one state per spent and what an accepted cycle witness establishes. This is strong internal conformance evidence, not independent custody, outside adoption, semantic truth or immunity of a binary to local faults.

The cheapest attacks have repeatedly targeted the apparatus around the kernel: hidden theorem scope, weakened statements, omitted files and guards that stopped observing their subjects. proofs/README.md separates what the Lean kernel checks from what bridges, registries and generated inputs must still be trusted to supply.

Run it

From a checkout:

python3 impl/sigma_glyph.py                     # Book I
python3 tests/spec_conformance/run_reference.py # the conformance vectors
python3 tests/resume_test.py                    # sigma-resume
python3 tests/book1_claims_test.py              # the claims' witnesses
tools/test-all.sh                               # full repository suite

From PyPI (latest release 0.8.0; see "Status by surface" below):

pip install sigma-glyph
python -m sigma_glyph

The wheel contains the Python modules, not the replay corpora; full re-derivation needs a checkout. The artifact boundary and release procedure are in PUBLISHING.md.

The resume provider, installed

sigma_provider is the consumer surface of the resumable kernel (impl/sigma_resume.py, specified by spec/sigma-resume.md): build a computation from a term, run a budgeted segment (PAUSED or a normal form or an explicit local refusal), resume from a checkpoint, verify a receipt by replay, verify a cycle witness. It ships from 0.8.0 (pip install sigma-glyph==0.8.0), or build the wheel from a commit and install that file.

pip wheel --no-deps -w wheelhouse "git+https://github.com/s0fractal/sigma-glyph@<commit>"
pip install wheelhouse/sigma_glyph-*.whl
python -m sigma_provider                          # self-test
echo '{"sigma_provider":1,"op":"term","args":{"expr":"S K K (K I)"}}' | python -m sigma_provider serve

The library and the one-request-per-process protocol are documented in the module's docstring. To continue someone else's checkpoint, use resume, which replays it from your own root first; raw advance trusts its checkpoint. A consumer decides which provider bytes it accepts: sigma_provider.identity_of(...) names them, and a provider reporting its own identity grants nothing.

Status by surface

Each paragraph names its authoritative source; when this section and that source disagree, the source is right. tools/version_check.py checks the distribution heading below against pyproject.toml, and the conformance suite's spec_version against Book I's.

Specification

Book I 1.0.0 and sigma-resume 1.0.0, both STANDARD, the semantics of Book I 0.6.0 unchanged. A version is the bytes at its release tag, and its identity Book I §8's SpecAnchor of those bytes; it is adopted when the roadmap goal "sigma-glyph 1.0" is met, a signed record (AGENTS.md rule 2), not a heading. The detached registry spec/ANCHORS.txt and its bundle headings were retired on 2026-11-01 (history/RETIREMENT-2026-11-ANCHORS.md): Warrant's records and the release tags hold what it held.

Distribution: 1.0.1

pyproject.toml carries 1.0.1: Book I (sigma_glyph) and the resume kernel and provider (sigma_resume, sigma_provider), without the retired Book II and III modules, implementing Book I 1.0.0 and sigma-resume 1.0.0. 1.0.0 is on PyPI since 2026-11-01, cut from tag v1.0.0 once goal G1's obligations were accepted (AGENTS.md rule 5 says by whom and on what evidence). Its provider did not conform to sigma-resume §5: it normalized a non-canonical cycle witness and replayed it (Codex's challenge on G1). 1.0.1 refuses those bytes before replay; the documents are unchanged. Releases and what was checked about each are in PUBLISHING.md and CHANGELOG.md; PyPI is right about what it holds.

The specification

spec/GLOSSARY.md fixes the local meaning of work, size, memory and materialization; WHY-THESE-THREE.md explains why determinism, addressing and one semantic bound are combined.

Implement and verify

impl/sigma_glyph.py is the Book I Python reference and impl/sigma_resume.py the resumable kernel. impl-rs/ independently implements Book I (and impl-rs/wasm-resume/ the resume kernel) within the same author/model lineage.

(cd impl-rs && cargo build --release)
./impl-rs/target/release/book1 conformance tests/spec_conformance/vectors.json
python3 proofs/proof_guard.py
python3 tools/spec_audit.py
python3 tools/version_check.py

Implementation guidance is in spec/IMPLEMENTING.md. A released version is the bytes at its tag, and its identity the SpecAnchor of those bytes; a specification update is an explicit fork, not a mutable page edit (Book I §8).

For AI or human review, run the reference suite first and attack one exact claim/operand boundary. Green tests are baseline evidence, not an independent gate or governance adoption.

Every RFC 2119 keyword of Book I and sigma-resume (MUST, SHALL, REQUIRED) lies in some claim's sentence, and warrant claims check refuses one that does not (coverage): .warrant/claims.json names both documents, the witness files (tests/book1_claims_test.py, tests/resume_claims_test.py) and the mutant harness (tests/claims_mutants.py); each claim@1 record quotes one sentence verbatim and cites the cases that witness it and the mutants that must break them, or says why it is unbacked. warrant claims check refuses a sentence its document no longer holds, a witness nobody prints or a mutant off its claim; warrant claims view prints them. A backed claim is accepted by the claims checker (claim/verifier), a key bound in .warrant/v3.json whose acceptance is a replay of the witnesses and mutants at one commit; CI re-executes every new acceptance.

Reviews are records, not prose: .warrant/ is this repository's Warrant 3 store (warrant-graph, pinned in .github/warrant-requirements.txt). A pull request's head is a pr-head@1 version; the reviewer named by .warrant/v3.json (pr/acceptor) accepts it or files finding@1 challenges against it, signed with its own key. warrant status and warrant review view read them. The owner merges (AGENTS.md rule 5).

Published evidence

• One Integer for Semantic Work and Materialization — Zenodo 10.5281/zenodo.22646920 (v2, 2026-09-07, repository snapshot 47cf57d; concept DOI 10.5281/zenodo.22069650); v1 is 10.5281/zenodo.22069651 (snapshot 7ecba6a). Deposited, not peer reviewed.
• Does One Integer Still Price Work and Memory in Parallel? — Zenodo 10.5281/zenodo.22073568, a preregistered experiment: the aggregate bound survived the measured parallel reducer while per-redex refusal did not. Its harness is in the deposit and at commit 96414ab.

Prior eras and their historical hashes are preserved in git history and in the deposited snapshot, not in the default tree: history/ holds the retirement ledgers that say what left the surface, why, what was lost and how to retrieve it with status. Current provenance does not erase superseded semantics; current admission does not reactivate them.

MIT for implementations; CC BY 4.0 for specification texts.