Boundary Histories, Target-Specific Observability, and Physical Calibration: A Claim-Bounded Synthesis of the BIG-B42 Research Programme

Boundary Information Geometry (BIG) is an exploratory mathematical and computational research programme that studies boundary fields, response geometry, and history-dependent dynamics through several distinct model families. The BIG-B42 programme examines whether history retention, observable response, counterfactual history contributions, elapsed progression, and cross-system calibration can be connected without conflating their mathematical requirements. This paper synthesizes its conditional propositions, frozen synthetic-model tests, source-implementation audits, and physical-calibration constraints. We formulate target-specific identifiability through observational equivalence: a deterministic target is recoverable from noiseless observations exactly when it is constant on every observational fiber. Under bounded noise, the range of target values compatible with a record determines an optimal worst-case error radius. We distinguish these standard results from stronger requirements for dynamic state closure, causal-effect identification, and physical measurement. A restricted integrability obstruction applies to the original one-way history-to-response coupling under fixed block-diagonal gradient mobility, whereas separately introduced reciprocal thermodynamic completions admit conventional distributed-Maxwell representations. In the frozen B17.4 synthetic-PDE studies, an estimator achieves limited accuracy for weak history-dependent responses but fails predetermined ordering and preparation-transfer gates. The B27 continuum description and legacy two-dimensional numerical flux also require explicit version separation. Across these results, no independently calibrated BIG-specific physical law, unique boundary-history variable, or emergent physical time has been established. We conclude by specifying what independently measured state variables, work-conjugate observables, and equal-information conventional comparisons would be needed for a discriminating physical test. Publication scope and files: English primary preprint (35 pages), with a Japanese reference translation (26 pages), version 1.0. BIG-B42 formal scientific verdict NONE; independent external-validation R4 selected/opened/evaluator counts 0/0/0. Original CP-series FAIL and mixed outcomes and the B27 source–implementation discrepancy are retained. Basic reproduction materials are available, but an independent full computational rerun audit has not been completed. The small Zenodo_Preprint_Upload_Package ZIP contains byte-identical copies of the two standalone PDFs, their editable DOCX files, selected CP9/CP10 figure inputs, a historical metadata proposal, a scope README and its original SHA256 list. The separate Integrated_Assessment_Reproducibility ZIP contains the archived integrated audit and eight source-study packages. It is a scoped collection, not a newly completed full rerun or a complete reassembly of every B42 branch. The metadata proposal inside the small ZIP is historical; the Zenodo record metadata governs the actual publication status and author-selected license. Reproduction archive reconstruction: The integrated reproduction ZIP is supplied as 10 sequential byte parts named BIG_B42_Integrated_Assessment_Reproducibility_v1_0.zip.part001 through .part010. These parts are not separate ZIP archives. Save all ten parts, B42_REPRO_TRANSPORT_MANIFEST.json, B42_reassemble.py and README_B42_REPRO_TRANSPORT.txt in one directory, then run python3 B42_reassemble.py. The script verifies every part and restores BIG_B42_Integrated_Assessment_Reproducibility_v1_0.zip (97,023,337 bytes; SHA256 3a5ac10d6f0b900d9e4a2ae9232065fccd617a323b0a220263ae2a98491da08b). To verify the complete data without writing the restored ZIP, run python3 B42_reassemble.py --verify-only. Only the transport representation has changed; the archived research data and scientific verdicts are unchanged. Manuscript status: This version is released as a working preprint. Editorial proof notes and explicitly unresolved checks on mathematical assumptions, the B17.4 weighted reader, and source-label/version mapping remain in the manuscripts. File-integrity verification and successful archive reconstruction do not complete or certify those outstanding mathematical or computational checks. The stated scientific verdicts and limitations are retained.