Static-to-Adaptive Phase Structure of Five-Qubit Logical Bell Measurements under Photon Erasure: Exact \(q=2/3\) Basis Switching, Feedforward Optimality, and Failure-Record Gauge Equivalence

This reproducibility package accompanies the paper “Static-to-Adaptive Phase Structure of Five-Qubit Logical Bell Measurements under Photon Erasure.” For the non-CSS five-qubit [[5,1,3]][[5,1,3]] perfect code, the work gives an exact finite-resource analysis of transversal ancilla-free X/Y/ZX/Y/Z-guaranteed logical Bell measurements under independent heralded photon erasure. Exact exhaustion of all 65=77766^5=7776 static analyzer schemes yields four rational loss-response classes and an algebraic measurement-basis transition at intact-pair survival q=2/3q=2/3. The adaptive problem is reconstructed as a finite Bellman graph with 49,312 information states and 313,200 action comparisons, yielding the global optimum Pad⋆(q)=54q3+74q4−6532q5P^\star_{\rm ad}(q)=\frac54q^3+\frac74q^4-\frac{65}{32}q^5. All Bellman action gaps reduce to twelve exact nonnegative polynomial forms, proving that one feedforward policy is optimal throughout 0≤q≤10\le q\le1. Adaptive feedforward removes the static q=2/3q=2/3 phase boundary. A doubled-stabilizer gauge argument further proves that the complete local failure-sign record does not improve logical Bell discrimination within the declared measurement grammar. The accompanying Python verifier reconstructs the static classification, adaptive Bellman theorem, and failure-record gauge result from scratch using standard-library exact arithmetic.