LEGACY-APL — SOVEREIGN APL CORRECTIONS

Pure APL proofs of domain orthogonality, entropy isolation, and contractive stability. No Python. No wrappers. No MLIR. Just APL and the WORM chain.

This repository is the APL proof substrate of the SNAPKITTYWEST sovereign-compute constellation. Extracted from the all-apl workspace, it collects pure-APL corrections and demonstrations that establish sovereign-domain isolation and PIRTM/Ω-correctness as structural facts, not policy rules.

WHAT IT IS

legacy-apl is a collection of self-contained APL modules plus the metadata/state model that anchors them to the Bifrost WORM chain. Every module is written in idiomatic APL (index origin 1, ⍝ comments) and runs in a plain APL session — no host-language glue.

Core themes proven in APL:

• INTERCOL — sovereign domain orthogonality: distinct domains are orthogonal vectors; cross-domain transition returns ⊥ (Null State). Includes the PIRTM transition_108_cycle collapse proof.
• Domain isolation — the "mathematical wall": no asset from domain A can reach domain B.
• Ω isolation — local uncertainty/entropy I% must be strictly below bound Ic.
• PIRTM stability — finite-gain contraction certificate; spectral radius < 1 required.
• Morphism composition — correct f∘g order.
• Zeroproof substrate — refutes literal proof hashes and tautological factorization claims.
• Transforms — Fibonacci/phinary contraction, entropy mapping, trust-vector reduction, semantic-agreement fold (feeds the INTERCOL Swift/C++ UI via JSON).

ARCHITECTURE / COMPONENTS

Path	Purpose
README.md	Repo marker (Apache-2.0, extracted from all-apl).
apl-corrections/	The pure-APL proof modules (see below).
apl-corrections/metadata.json	Sealing metadata: MATHLIB5-20260710-APLCORRE-001, SHA-256 tamper chain, AES-256-GCM, Ed25519 Plasma Gate, Bifrost WORM provenance, awaiting_worm_seal.
apl-corrections/state-model.json	INTERCOL UI runtime state: 7-axis EDAULC trust vector, 5-pass ERE gates, 13-node Metatron resonance graph, WORM receipt schema (append-only: append | verify | replay).
docs/generate-docs.mjs	Continuous docs generator (.rs .lean .py .apl .hs .mjs .js .pl .md); --watch mode; auto git-commit/push.
docs/README.md	Usage note for the generator.
theorems/THEOREMS.md	Local theorem pointer (full list in theorems repo index).

APL proof modules (apl-corrections/)

File	Proves
intercol.apl	INTERCOL inner product, orthonormality, Null-State transition, PIRTM 108-cycle collapse, sovereign isolation.
sovereign_domain.apl	Domain boundary encoding (name lower upper omega cap).
omega_isolation.apl	I% < Ic isolation boundary.
pirtm_stability.apl	Finite-gain contraction certificate (spectral radius < 1).
morphism_composition.apl	Correct (f Compose g) x = f(g(x)) order.
zeroproof_substrate.apl	Refutes literal proof hashes / tautological factorization.
transforms.apl	Phinary/Fibonacci transforms + trust-vector/semantic folds for the UI.
run_all.apl	RunAll demo runner wiring the modules together.

A shared primitive appears across modules: Assert (guard + ⎕SIGNAL 11) and BOB (proof-step checker) — the APL analogue of a verifier witness.

HOW IT FITS THE CONSTELLATION

legacy-apl is the structural-correctness witness layer:

• WORM Chain / Bifrost — metadata.json chains each correction to Bifrost_WORM_Chain_20260710_01; state-model.json defines the append-only WORM receipt schema.
• Plasma Gate (Ed25519) — security_audit.plasma_gate: "Ed25519_Enforced"; tamper evidence is a SHA-256 append-only chain.
• P/NP Swarm — the BOB/Assert proofs are P-verifiable certificates; swarm agents submit witnesses that a domain really is isolated.
• 3-Witness Verification — a sovereign-domain claim is accepted only after three independent APL runs reproduce the ⊥ Null State.

Ω ← TRUST ∧ CODE: a domain wall holds only when the Ed25519/WORM trust ∧ the APL INTERCOL = 0 code both verify.

Related repos: handoff (continuity), theorems (central index where legacy-apl is tracked).

BUILD / USAGE / INSTALL

No build. Requires an APL interpreter (e.g. GNU APL, Dyalog).

cd legacy-apl

# Load the proof modules in an APL session, then:
)LOAD apl-corrections/run_all.apl
RunAll                         ⍝ runs all demos, returns stability/domain/omega/zero/morphism

# Generate/refresh docs:
node docs/generate-docs.mjs          # one-shot
node docs/generate-docs.mjs --watch  # continuous; auto-commits + pushes

run_all.apl expects ⎕IO←1 and the src modules loaded first (see state-model.json intercol_state._apl_source).

KEY FILES REFERENCE

• apl-corrections/intercol.apl — the centerpiece: orthonormal domain space, DomainTransition returning ⊥ on cross-domain, and PIRTMCollapseProof showing transition_108_cycle = ⊥ by construction.
• apl-corrections/metadata.json — review_status: human_review_required, split across 9 layers (audit, kernel, proofs, runtime, witnesses, refinements, asp_gate, fol_engine, prism_skills).
• apl-corrections/state-model.json — 13-node Metatron resonance graph, 7-axis EDAULC trust vector, entropy gate threshold 0.21, WORM receipt schema.

LICENSE

Apache-2.0.