Inverse Specification: Emergent Higher-Order Formalisms in Bare-Metal Realization

Traditional software engineering and mathematical formalization follow a top-down deductive pipeline: abstract formalisms are conceived, proof-checked, and subsequently forced onto computational substrates. This paper introduces Inverse Specification via Physical Realization, a novel paradigm in applied systems engineering wherein high-order mathematical constructs—specifically covariant functors between posetal categories (Φ: L → E) and bounded join-semilattice coproducts—emerge post-hoc from bare-metal microarchitectural optimization. By prioritizing O(1) constant-time execution bounds, zero-heap allocations (S_max ≤ 4096B), and fail-closed non-authorization clamps (Δ_external = 0), the physical execution engine forces structural convergence toward category-theoretic invariants without top-down mathematical design. We formalize this "builder-first" methodology, establish the principle of Constraint-Driven Structural Convergence, demonstrate how thermodynamic and silicon boundaries mandate higher-order structural law, and present a framework for retrofitting formal academic verification onto bare-metal systems without sacrificing operational velocity. Master Anchor: A-77-DELTA-SHIELD-LOCKED Normative Errata Reference: ARC-ERR-2026-001 Primary Suite Record: 10.5281/zenodo.22665852 Category-Theoretic Monograph Reference: 10.5281/zenodo.23525986