The ORIGAS Red Line: Source Recoverability, Four-Sector History, and the Limits of Algorithmic Completion Cabin 1/2

The ORIGAS Red Line Cabin 1/2 Thierry Origas Independent Researcher, FranceORCID: 0009-0009-2226-7033Published version DOI: 10.5281/zenodo.23777835 Abstract This technical preprint presents the ORIGAS Cabin 1/2 Red Line, a research programme concerned with source recoverability, task-relative mathematical completeness, noncommutative order, four-sector history, and the limits of algorithmic completion. The central question is: When does an exact representation for one declared task cease to be sufficient for a different task because source-dependent distinctions have been projected away? For a source space Q, a declared readout P, and a target task J, the manuscript develops the fibre criterion: J can be universally recovered from P if and only if J is constant on every nonempty fibre of P. When two admissible source descriptions have the same readout but require different task outputs, no computation restricted to that readout can universally distinguish them. The programme investigates the consequences of this distinction for complexity theory, Karchmer–Wigderson relations, four-sector representations, noncommutative history, catalytic computation, and the proposed A+B–K–T conservative bridge. Confrontation with the 2026 scientific results The manuscript examines the October 2026 OpenAI result concerning the Exponential Time Hypothesis, alongside the catalytic-memory results of Orozco, Sheffield and Williams. It distinguishes computational acceleration within a declared machine model from the recovery of information absent from an input representation. It also provides negative controls, including the equality-function OBDD example, to prevent representation-specific complexity from being mistaken for unrestricted circuit complexity. The conditional P versus NP programme remains subject to explicit open obligations, including H6' and H7'. The manuscript does not claim an unconditional resolution of P versus NP. A separate technical section addresses the September 2026 OpenAI construction of finite-time blow-up in forced three-dimensional Navier–Stokes equations. It compares the declared scope of that dynamical theorem with the task-relative source/readout limitation studied in the ORIGAS framework. These are mathematically distinct results. The A+B–K–T framework The wider ORIGAS programme proposes a structured source description containing observable sector A, complementary sector B, coupling K, ordered history directions +t and -t, common history coordinate T, and provenance. The four-sector structure is intended to preserve distinctions that may be lost when a richer representation is reduced to a single observable. The author proposes that this framework may provide experimentally testable questions concerning EPR completeness, noncommutative geometry, information preservation, and physical measurement. The mathematical consistency of a proposed coupling is not, by itself, evidence of a physical World B or of a universal quantum connection among distinct scientific domains. Such physical claims require independent measurements, quantitative predictions and falsifiable controls. Three complementary documents This Zenodo record contains: Main manuscript 84 pages, English. Mathematical foundations, complexity-theoretic comparisons, conditional proof obligations, data registers, Navier–Stokes analysis, authorial conclusions, and a final reviewer compass. Annex A 20 pages, French. An illustrated manifesto presenting the author's conceptual architecture, research aims and precautionary position. The diagrams are explanatory rather than independent experimental evidence. Annex B 11 pages, French. An interpretive scientific report offering a transversal reading of the mathematical and philosophical programme. Its interpretations should be evaluated against the exact arguments in the principal manuscript. Cumulative DOI architecture This publication constitutes one limited component of a cumulative and versioned ORIGAS research corpus. The author's intended reading is transversal: the present source-recoverability questions are linked to earlier DOI records on conservative lifting, EPR conditional completion, source-sensitive observables, and representational jurisdiction. Earlier deposits retain their original timestamps, definitions, claims and restrictions. Later formulations must not silently rewrite those historical records. Key linked records include: 10.5281/zenodo.22680828 Three-volume Red Line corpus 10.5281/zenodo.22640293 Prior Red Line formalization 10.5281/zenodo.22549313 Earlier source-sensitive programme 10.5281/zenodo.22237277 Linked representational-jurisdiction work 10.5281/zenodo.22123940 Natural Chance programme 10.5281/zenodo.22100628 Four-path conservative lifting 10.5281/zenodo.22966540 Complete EPR Framework 10.5281/zenodo.23087504 Fibre Geometry of Cabin 1/2 These identifiers establish provenance and intellectual continuity, not independent validation of the proposed physical mechanisms. Scientific status and attribution This record is a technical research preprint. It distinguishes exact mathematical results, external scientific results, model-conditional consequences, open proof obligations, prospective physical hypotheses, and the author's normative proposals. The OpenAI, MIT and other external scientific results retain their original attribution. Zenodo registration and file integrity establish archival identification and provenance; they do not constitute peer review, experimental confirmation, or endorsement by Zenodo, CERN, OpenAI or other institutions. Authorial statement: “A proof may close a task without closing the source.” The ORIGAS programme further proposes a precautionary principle: a demonstrated computational capability does not, by itself, authorize claims of complete physical knowledge or the safety of irreversible interventions. Annexe B, page 4 La coquille \(J(q_1)=J(q_2)\) doit être corrigée en \(J(q_1)≠ J(q_2)\) dans le contexte de la non-identifiabilité