PAL v2.4 — Primitive Axiom Layers

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 begins with unresolved possibility, admits a supplied cut within a declared account, and carries the cut’s reflection and trace. Its layers connect readable distinction and recoverable consequence to relations, transport, feedback, organization, access and response, task-relative representation, comparison and jointness, re-entry, cadence, resource slack, and scoped closure. Each stage retains the sources, witnesses, assumptions, costs, limits, and reopening conditions relevant to its claims. Evidence and authority remain separate throughout. A receipt preserves an account of an action and its consequence; it does not make that account true or the action authorized. Closure applies to a named claim within a declared scope, and reopening preserves the history it revisits. PAL v2.4 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 v2.3 without rewriting historical claims or authority. Each face is authoritative only within its named role. Version 2.4 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. Mathematical realizations and formal verification test specific claims under declared assumptions. They do not prove the entire framework. PAL does not claim to be a physical theory, a theory of consciousness, an ethical authorization system, or a complete ontology. Its aim is local, earned, and reopenable closure. A generated omnibus provides a convenient combined reading copy. The five component documents remain controlling within their stated roles. 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 v2.4 — Primitive Axiom LayersVersion: 2.4Publication date: 22 September 2026DOI: 10.5281/zenodo.22888036Status: Author release; not peer reviewedLicense: Creative Commons Attribution 4.0 International (CC BY 4.0)