UFP-NB1 v0.2.0 Candidate: Corrected Mathematics and Executable Projection Laboratory

UFP-NB1 v0.2.0 Candidate is the first executable research candidate in the Unity-First Physics / Nested Bounded Relational Dynamics program. It supersedes v0.1.0 as the current research specification while preserving the original published v0.1.0 files unchanged as historical provenance. UFP-NB1 investigates whether stable and informative effective descriptions can arise from a single underlying relational dynamics. The guiding methodological principle remains “Assume unity. Derive separation.” This version does not claim a completed theory of fundamental physics and does not claim recovery of quantum mechanics, general relativity, gauge fields, particles, thermodynamics, physical time, or dark matter. Version 0.2.0 corrects mathematical contracts and claim boundaries identified during post-publication review of v0.1.0 and introduces an executable finite diagnostic laboratory. The central new question is whether a projected or coarse-grained state contains sufficient information to determine its own next projected state. An exact projection-closure criterion and finite refinement algorithm are implemented to test this condition and preserve explicit counterexamples. The included NB1-R0 candidate uses a finite undirected relational graph with a deterministic permutation-equivariant update rule. Exhaustive checks cover all 64 labelled four-node graphs and all 1,024 labelled five-node graphs. A degree-histogram projection is closed for all four-node states but fails at five nodes, providing a preserved scale-dependent counterexample rather than a promoted recovery claim. The supplied executable package includes source code, a frozen experiment contract, exact finite-analysis results, deterministic run receipts, replay checks, preserved failure witnesses, verification scripts, manifests, and the byte-preserved v0.1.0 historical archive. Four hundred exploratory trajectories across N = 16, 32, 64, and 128 are recorded, and 15 software tests cover equivariance, projection invariance, exact closure failure, refinement, controls, source/contract tampering, and replay. No U1–U10 physics-recovery gate or N1–N8 NB1-recovery gate is established by this release. The results are finite mathematical and software evidence for the declared NB1-R0 diagnostic only. They do not establish that the model describes nature. The previously discussed LZ230616 / H1 benchmark is classified in this version as HISTORICAL EXPOSED, because the relevant measurement and rare-event motifs were already visible during earlier design work. It therefore cannot serve as an independent prospective validation benchmark for v0.2.0. Future external predictions require genuinely unused observations, a frozen comparison protocol, and an appropriate detector-response model. The next research phase studies the information cost of predictively sufficient effective descriptions, scaling under larger systems and alternative frozen microscopic rules, and robustness across multiple projection families before any physical interpretation is promoted. Status: Research candidate / executable diagnosticVersion: v0.2.0Previous version: UFP-NB1 v0.1.0Publication authority: Michael Wayne Hughes