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:

1. ARC-PUB-2026-EXEC01: The Human-First Trust Layer

2. ARC-PUB-2026-EXEC02: The Machine-First Execution Boundary

3. ARC-PUB-2026-CORE01: Arcstone Continuity Core (#![no_std])

4. ARC-PUB-2026-EXEC03: The Hybrid Epistemic Layer

5. ARC-PUB-2026-CORE02: Principles of Admissibility Science

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