PAL v2.3 — Primitive Axiom Layers
Christopher D. Pang · Zenodo (CERN European Organization for Nuclear Research) · 2026
Primitive Axiom Layers (PAL) is a mechanical framework for recording what distinction was supplied, which witness licensed it, what trace survives, what authority remains unavailable, and which residuals or reopening conditions must be preserved. It is designed to keep accountable reasoning from hiding missing evidence, unresolved possibility, or borrowed authority inside a finished-looking result. PAL v2.3 is coordinated across five authority faces with distinct roles. The Mechanical Structural Spine controls PAL identity, order, invariants, canonical cards, account and receipt grammar, and local closure grammar. The Mathematical Realization Atlas supplies removable bounded mathematical models, fixtures, and countermodels without redefining the Spine. The Obligation and Decision Ledger preserves decisions, obligations, residuals, open burdens, and reopening addresses. The Conformance Tests provide bounded evidence about declared artifacts and implementations; a TestReceipt is not an A15 status receipt. The Compatibility Note governs receipt-preserving migration from PAL 1.x through v2.2 without rewriting historical claims or authority. Each face is authoritative only within its named role. Version 2.3 preserves the complete primitive floor Ω, A0, Ω*, and θ; the A1–A15 identities; SC-00–SC-20; the four A15 statuses; and PAL’s account and receipt lineage. It preserves D01–D30, O01–O51, and T01–T48 as predecessor records and keeps D-FIRST-OCCURRENCE, O04, O25, and the multi-parent-lineage boundary open. The release adds SC-21 and a typed boundary-role registry; clarifies structural versus resolution-qualified minimality; separates reachable-image factorization from total decoder, computation, efficiency, permission, and authority claims; and distinguishes exact return, work-projected stutter, hidden motion, direct residual, audit export, resource change, and progress. New Atlas cards treat resolution-qualified asymmetric splitting, interface fibers, return and projection, action-trace lift, exact checkpoint capsules, stutter-refined cadence, slack, and bounded geometric fixtures. The coordinated Ledger contains D31–D39 and O52–O62, and the Tests add T49–T72. The Compatibility Note records the exact v2.2→v2.3 dispositions and separates Zenodo publication succession from PAL-native account operations. The opening asks seven frame-dependent questions only to mark a scope firewall. PAL does not answer those questions as posed. Ω is not their hidden answer, and A0 is not the first event, cause, or boundary of reality. PAL begins with a supplied cut inside a declared account and asks only what can honestly be distinguished, traced, and carried forward from there. D38 and O61 preserve that author-directed boundary. RAINBOW — Ribbon-Amplitude Interference Norms: Boundary-Orbit Weaves is a removable Atlas-local realization family governed by D39 and O62. Its established mathematics is Eisenstein and hexagonal-lattice norm arithmetic, including bounded shell representation and orbit counts. Its cut-indexed local-frame adapter, log-phase cylinder, and retained factor-history weave are constructed PAL realizations. Coherent amplitudes and interference readout are optional constructed adapters that require a declared amplitude space, combination rule, and readout. Color, decorative accents, camera choice, ribbon thickness, blur, and similar visual encodings are presentation only unless separately typed. Lagrange-point dynamics and wavefunction collapse remain open analogies only. RAINBOW is not a primitive, layer, authority face, quantum model, physical theory, cosmology, or ontology. The bounded source roles are explicit. GOLD supplies geometric fixtures and the primitive-floor realization lens, without becoming a primitive or physical blueprint. APCI supplies reachable-fiber factorization and decoder controls; Compactification Costs supplies the specialized boundary bridge and typed extension profile, without a universal scalar or automatic decoder. Abstract Loops supplies common-refinement and return/export axes, not an unbounded-growth or physical result. The Single-Cut Transport Lemma and Stanley P. Y. Fung’s separately credited ordered-pair result support finite scheduling, action-trace, checkpoint, stutter, and transport fixtures without proving formal simplicity or practical optimality. GPPR remains an O22 branch fixture with no finite-bit, efficient-inverse, secrecy, ordering, factoring, or measured-advantage claim. Cadence material supplies bounded descriptive vocabulary and namespace separation; heartbeat emission is not progress. PAL v2.3 introduces no new primitive, numbered layer, constructor from Ω, fifth claim status, authority source, physical law, universal geometry, universal scalar information-loss quantity, wavefunction-collapse account, cosmological or consciousness claim, or independent validation. Same-author sources, internal conformance checks, finite runs, regenerated figures, hashes, formal receipts, and AI-assisted review may add reproducibility evidence but are not independent corroboration. Christopher D. Pang is the sole author, steward, and release authority. AI tools assisted drafting, editing, mathematical exploration, code and fixture development, adversarial review, source reconciliation, testing, document generation, and formatting. They are not authors, co-authors, inventors, owners, stewards, witnesses, release authorities, or independent corroborators. PAL v2.3 — Primitive Axiom LayersVersion: 2.3Publication date: 2 September 2026DOI: 10.5281/zenodo.22240134Status: Author release; not peer reviewedLicense: Creative Commons Attribution 4.0 International (CC BY 4.0)