From Exactness to Decidability: The 2026 Conservativity Requirement

Abstract

CENTRAL STATEMENT For the first time in this framework, the decisive question is not whether a representation is formally correct, but whether it is sufficient for the task and that question is operationally decidable. What has traditionally been treated as an epistemological question is reformulated here as a task-relative mathematical decision problem.The accompanying HD figures provide the mathematical expressions, audit structure, conservative lift, independent witness, H+ prudence question, GPS analogy and 2026 scientific-adjudication framework. ABSTRACT This publication develops a task-relative criterion for determining whether an exact representation preserves the source distinctions required by a later inference, decision or intervention. Its central mathematical mechanism is non-injectivity: when distinct source states are merged by the same representation while remaining different for a task-relevant variable, no downstream process receiving only that representation can universally reconstruct the erased distinction. The proposed response is conservative lifting: preserve the validated output while retaining the minimum separating information required by the task, represented by the triplet (P, K, T), where P denotes the validated output, K a source-separating datum, and T order, history, memory or provenance. Shuoxing Zhou's 2026 counterexample to Connes' rigidity conjecture is used as an independent exact witness of the underlying non-injectivity mechanism. The publication explicitly distinguishes formal correctness, conservativity, transportability and deployment sufficiency, and proposes that a representation should govern only the tasks for which its sufficiency has been established. The broader Protective T Framework extends this prudence principle to AI, autonomous agents, scientific adjudication and critical complex systems. Physical interpretations involving +t, -t, a global time T, EPR extensions or RingCross structures remain explicitly separated from the demonstrated mathematical layer and require independent experimental validation. https://zenodo.org/api/records/21983821/draft/files/DESCRIPTION%20DOI%20ZENODO%20ORIGAS%2017%2008%202026%201.png/contentcontent (1024×1536)content (1024×1536)A REAL-TIME QUESTION FOR SCIENTIFIC ADJUDICATION IN 2026Can formal exactness alone justify the highest level of scientific attribution when the conservativity, transportability or deployment sufficiency of the underlying representation remains unresolved? SEVEN COMPLEMENTARY INTERLOCUTORS ONE CROSSDISCIPLINARY QUESTION The accompanying synthesis identifies seven specifically named scientific and institutional interlocutors whose respective fields illuminate different layers of the question: experimental physics, operator algebras and non-commutativity, fundamental physics, geometry and irreducibility, astrophysics, artificial intelligence and decision systems, and the institutional responsibility associated with the Nobel framework. They are not presented as the only persons capable of examining the work, nor as a substitute Nobel jury. They are addressed as seven complementary viewpoints on one superposed methodological problem: What must a valid representation preserve before its conclusions can legitimately be extended from a local formal result to a claim about a larger real system? The purpose of naming these interlocutors is therefore not to appeal to authority or consensus. It is the opposite: each viewpoint is invited to evaluate the part of the problem falling within its competence while the complete question remains visible. No single disciplinary answer is assumed to settle all the others. The proposed procedure is a cross-audit rather than a vote: preserve the distinctions, keep the questions separated, identify what has been proved, identify what has been lost, and state explicitly what remains open.