Deterministic Admissibility Engineering: Mechanized Type Theory, Bare-Metal Clamps, and the Regeneration Gap

Autonomous agent frameworks driving non-deterministic generative models systematically undermine classical distributed systems idempotency. While conventional network architectures assume that retry loops replay identical request payloads, autoregressive generative agents re-synthesize arguments upon encountering network timeouts or ambiguous states. This semantic drift creates a critical distributed failure: The Regeneration Gap, wherein syntactically divergent requests representing identical underlying business intents bypass transport-layer deduplication keys, inducing catastrophic duplicate mutations. This specification formalizes Deterministic Admissibility Engineering (DAE)—a mathematical, microarchitectural, and operational framework built on the governing axiom: Existence ≠ Permission. Under DAE, execution authority is fully decoupled from generative proposal synthesis and anchored into an unbroken, 4-tier mechanically checked continuum: Tier 1 (Proof Theory): Empty-axiom inductive proofs in the Coq Interactive Theorem Prover (Print Assumptions ≡ ∅, Admitted ≡ 0). Tier 2 (Functorial Bridge): Order-preserving covariant functor (Φ : L → E) mapping a 5-element join-semilattice to a 6-tier operational dominance hierarchy, enforcing POSIX 10 (FREEZE) as an internal endofunctorial scheduling yield (τ_override ≤ 11.99 ms) outside Im(Φ). Tier 3 (Bare-Metal Membrane): Zero-allocation (M_alloc = 0), bounded static stack (S_max ≤ 4096 B), #[no_std] Rust and eBPF/XDP wire-speed ingress filters. Tier 4 (Physical Clamps): Fail-closed hardware actuator interlocks ensuring unauthorized proposals guarantee zero external state mutation: D(a) = DENY ⇒ Δ_external(a) = 0. By automating invariant checks in headless CI pipelines running under 25 seconds, DAE establishes Verification-Cost Inversion (VCI): amortizing machine verification friction to O(1) constant time while imposing O(exp(N)) cognitive refutation drag on permissive architectural paradigms. Document Reference: ARC-PUB-2026-DAE-01 Master Hash Anchor: A-77-DELTA-SHIELD-LOCKED Target Baseline: Phase 7 Realization (v1.3.1-exec) Canonical Web Root: https://admissibilityscience.com Primary Repository: https://github.com/trencinodin-stack/arcstone-continuity-core