Constraint Closure and the ℓ1 Structure of Physical Law

This upload is an as-is republication and extension of an earlier constraint-closure toy model (v1.2). It is explicitly presented as a finite, exploratory toy model, not as a derivation of continuous general relativity, quantum gravity, the Standard Model, or physical law. The paper studies ℓ¹ residual accounting on finite simplicial and cochain complexes. Within that finite setting, it develops gauge-invariant quotient residuals, exact linear-programming dual certificates, Regge-calculus deficit-cochain examples, scoped Bianchi-style identities and counterexamples, and Wheeler-DeWitt-inspired Hamiltonian and momentum diagnostics encoded as finite cochain data. The central finite quotient norm is Φ([ω]) = infα ∈ C⁰ ‖ω − d₀α‖₁, with dual certificates of the form Φ([ω]) = supw ∈ Z₁, ‖w‖∞ ≤ 1 ⟨w, ω⟩. The included Python and Lean 4 artifacts are intended as best-effort executable evidence for finite, discrete, linear-algebraic claims and for falsification receipts around overextended high-energy analogies. Speculative extensions toward Standard Model gauge structure, electroweak symmetry breaking, supersymmetry scales, fine-structure numerology, and dark-sector interpretations are explicitly quarantined or refuted within the model. This package includes the manuscript, generated PDF, plain-text export, Python code and tests, Lean 4 manifest evidence, notebooks, a publication manifest with SHA-256 hashes, and a replayable source bundle. AuthorityEffect: None. Draft / upload record:https://zenodo.org/uploads/22715569