The Constructor Alphabet Under a Dependency-Conditioned Null Model: Corpus-Wide Trials Audit, Finite Source-Word Certificates, and the Retrospective Significance Firewall

How Often Can a Frozen Symbolic Language Imitate a Physical Constant? Version: 2.0 Concept DOI: 10.5281/zenodo.21182091 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory, v10.01 A close numerical match is not its own explanation. This paper asks the harder question: once the allowed leaves, operators, macro history, complexity measure, and observation corridor are frozen, how much search exposure remains? The ordered syntax class is counted exactly by \[ T_1=L, T_K=U TK-1+B∑ᵢ₌₁K-2T_iTK-1-i. \] Exact semantic enumeration is carried through \(K=7\). The tail is sampled uniformly through \(K=32\), with 50,000 proposals at every complexity, Wilson upper bounds, a nonzero plus-one rule, and an explicit geometric-tail bound. The central theorem is that one statistical null cannot honestly represent every kind of source claim: \[ { M_r∈\{ S, X, F, I\} } \] for scalar corridors, exact identities, finite legal-class enumerations, and structural or functional laws. The twelve audited rows close as \[ { 3\, S+1\, X+3\, F+4\, I+1\,(mixed\ U/A)=12. } \] The three finite source-word certificates reproduce directly: \[ { CKM:2187→1, PMNS:36→1, charged\ leptons:288→1. } \] The three scalar rows share the \(ρ=2πcos(π/8)\) rail, so their family audit uses the dependence-safe inequality \[ { \!(_r A_r)≤∑_r(A_r), } \] not an independence product. Across the declared geometric priors, the scalar-family upper compression diagnostic ranges from \(5.63×10⁻⁴\) to \(1.23×10⁻³\). The result is deliberately scoped: this measures compactness under the frozen coding languages; it is not presented as prospective discovery significance because the historical human search was not pre-registered. The scientific standard extracted from the audit is \[ { source legality +no-smuggling +dependency disclosure +independent reuse +prospective falsifier. } \] Precision without that ledger is not accepted as structural evidence. Reproducibility package PDF and LaTeX source standard-library exact/Monte Carlo audit engine independent release verifier twelve JSON/CSV row cards CKM, PMNS, and charged-lepton finite certificates full computation, scientific, and render receipts