Octomorphic Spine— Core Specifications

or the current Octomorphic Framework and latest guide, begin here: https://doi.org/10.5281/zenodo.17795686 CLASSIFICATION: Corpus Tier: Tier 3 — Constitution / Structural Law Authority Status: [AXIOMATIC] Substrate Layer: Layer A — Law ROLE IN FRAMEWORK: This record contains the Octomorphic Spine — Core Specifications, the authoritative constitutional layer of the Octomorphic Framework. The Spine defines the non-negotiable axioms, primitives, legality rules, invariants, computation recipes, implementation mandates, falsifiability conditions, and governance constraints that apply uniformly across the corpus. It determines what counts as Law, what counts as derived structure, what belongs to downstream translation, and what is explicitly prohibited from reinterpretation by later modules. SCOPE: The Spine formalizes and freezes: - the Axiom of Returnability and persistence criteria - the finite discrete registry as the sole state space - registry cardinality: N = 84 - the capacity vector: U = [7,3,6,10,15,16,15,12] - the prohibition against re-indexing, permuting, reallocating, or silently modifying the capacity vector - lawful adjacency and forbidden transitions - phase strain bounds: DeltaL = 0.60 - curvature / tension bounds: lambda_squared < 25 unless explicitly deformed by Canon-approved extension - NULL state definition and propagation rules - nonassociative composition as a structural necessity - parameter policy: frozen, environment-calibrated, exploratory - framework-level killswitches and falsifiability conditions All computation recipes referenced in the framework, including DeltaL, TB, lambda_squared / MCC, NULL behavior, legal adjacency, graph construction, and persistence predicates, are normatively defined here. Downstream applications, translations, simulations, and domain modules may consume these definitions but may not alter them. TB COMPUTATION NOTE: Triality Balance is a closed-loop functional, not a raw per-seat, per-edge, or open-path predicate. TB is evaluated on closed loops of lawful adjacency transitions using the canonical wrapping rule: W(s) = s - floor(s + 0.5) Single-loop TB is computed from the wrapped closure defect. Multi-loop TB is aggregated over closed-loop defects. TB must not be used as an open-edge filter or as a standalone property of an isolated registry seat. IMPLEMENTATION MANDATE: Lawful graph construction must enforce the Spine’s graph-building order. 1. Construct the Local-Admissible Graph G_local by applying local admissibility rules, including the lambda_squared < 25 constraint during edge acceptance. 2. Apply closed-loop TB support only after G_local exists, producing the TB-Supported Subgraph G_TB. 3. The older ambiguous phrase “TB-lawful graph” is deprecated. Implementations must distinguish local edge admissibility from closed-loop TB support. Earlier relaxed-graph implementations that defer lambda_squared < 25 or use TB as a raw edge predicate are structurally illegal under this Spine. AUTHORITY NOTE: This document is [AXIOMATIC]. It is the highest-authority reference for Layer A — Law. It does not derive from physics, chemistry, biology, cognition, or empirical interpretation. Domain-specific claims arise only in downstream modules and must cite and obey this Spine without redefining its primitives. SUBSTRATE NOTE: The Spine defines the evaluator and legality conditions. It does not itself simulate the registry, assign physical meanings, or produce empirical predictions. Layer B registry datasets, Layer C occupancy audits, and Layer D translations are valid only insofar as they obey this Layer A specification. FALSIFIABILITY / KILLSWITCH CONDITIONS: The framework fails at the constitutional level if any of the following are required: - continuous space is needed as a primitive to resolve a transition - registry cardinality exceeds N = 84 - the capacity vector U is re-indexed, reallocated, or modified without Canon-level replacement - a stable configuration persists while violating TB >= 0.60 - lawful persistence requires lambda_squared >= 25 without explicit deformation status - DeltaL bounds must be post-hoc altered to save a downstream result - stability thresholds are tuned after observing domain outcomes - NULL propagation is bypassed to preserve an otherwise inadmissible structure - downstream translations redefine Layer A primitives RELATIONSHIP TO OTHER RECORDS: Executable realizations, such as registry engines and audit packs, implement the rules defined here. Canonical modules apply these rules to formal or domain-specific structures. Archival records may explore historical development but do not modify this specification. WHAT THIS DOCUMENT IS NOT: - not a simulator - not a domain theory - not an empirical or experimental claim - not a collection of interpretations - not a physics, chemistry, biology, or cognition paper It is the formal specification and governance backbone of the Octomorphic Framework. RECOMMENDED READING ORDER: 1. Octomorphic Framework Guide 2. Octomorphic Spine — Core Specifications 3. Axiom 0 / The Shape of Necessity 4. Registry construction and audit materials 5. Formal mathematics / CMA / Coherence Geometry 6. Domain translations only after the above