Principles of Admissibility Science — Axiomatic Foundations, Order-Theoretic State Resolution, and Zero-Allocation Boundaries for Non-Deterministic Producers

ARC-PUB-2026-CORE02: Principles of Admissibility Science Axiomatic Foundations, Order-Theoretic State Resolution, and Zero-Allocation Boundaries for Non-Deterministic Producers Abstract: Integrating non-deterministic artificial intelligence (AI) producers—such as Large Language Models (LLMs) and autonomous agentic frameworks—into deterministic operational environments introduces severe safety, liability, and verification failure modes. Traditional runtime mitigations rely on dynamic prompt guardrails, heap-allocated exception handling, or cloud API middleboxes. These mechanisms introduce unbounded state drift, high latent attack surfaces, and non-zero operational drag (C_ops > 0). This paper formalizes Admissibility Science, a distinct domain at the intersection of discrete order theory, real-time POSIX reference monitors, and cybernetic feedback loops. We define the axiomatic foundations of state admissibility, proving that non-deterministic proposal vectors can be bounded by O(1) pre-ingress gate matrices and static join-semilattice state resolution. By strictly decoupling computation from authorization authority, Admissibility Science guarantees zero external state mutation (Delta_external = 0) for non-PASS operations while preserving human epistemic sovereignty across autonomous execution surfaces. Key Systems Parameters & Invariants: Primary Suite DOI Anchor: 10.5281/zenodo.22665852 Document DOI Anchor: 10.5281/zenodo.22969294 Master Hash Anchor: A-77-DELTA-SHIELD-LOCKED Release Tag: v1.3.1-exec Canonical Handle: @admissibilityscience Temporal Override Ceiling: tau_override <= 11.99ms (11,990 microseconds) Payload Memory Bounds: S_max <= 4096B static SRAM ceiling Poset Lattice Ordering: PASS < CORRUPT < REFUSAL < FREEZE < BREACH mapped to POSIX exit signals 0, 30, 32, 10, and 40 Archival Reference Suite: ARC-PUB-2026-EXEC01: The Human-First Trust Layer ARC-PUB-2026-EXEC02: The Machine-First Execution Boundary ARC-PUB-2026-CORE01: Arcstone Continuity Core (#![no_std]) ARC-PUB-2026-EXEC03: The Hybrid Epistemic Layer ARC-PUB-2026-CORE02: Principles of Admissibility Science Arcstone Adaptive Science Systems, Inc. — Production Locked / 100% Certified Conformance