The Natural-Chance Red Line III: The Enigma-2 Lock in the Age of Agentic AI

This record is Stage III of the interlocked 2026 Origas representational-jurisdiction corpus. It continues DOI 10.5281/zenodo.22123940 and inherits the mathematical and methodological architecture developed through DOI 10.5281/zenodo.22100628, 10.5281/zenodo.22018464, 10.5281/zenodo.21983821, 10.5281/zenodo.21936095, 10.5281/zenodo.21609936, and 10.5281/zenodo.21535840. The records are intended to remain independently citable while forming one cumulative source/readout/fibre/conservative-lift programme. THE CENTRAL QUESTION IS DECIDABLE AT THE REPRESENTATIONAL LEVEL. Let X denote a source, P: X -> Y a declared readout, and J: X -> Z an external task. The task lies within the jurisdiction of the readout exactly when: J in Jur(P) <=> [P(x1) = P(x2) => J(x1) = J(x2)]. If two admissible source states are identified by P while the task must distinguish them, no computation, recursive consensus, agent scaling, human approval stamp, or legal declaration operating only on P can universally reconstruct the erased distinction. Stage II quantified this obstruction through the task-relative fibre diameter: R_J(P) = sup { d(J(x), J(x')) : P(x) = P(x') }. The corresponding red-line number is: Lambda_(J,epsilon)(P) = R_J(P) / (2 epsilon). Stage II also introduced the separator gain G_J(K,T | P), the order witness chi_J, and the symmetric two-state 1/2 minimax safety obstruction. STAGE III: FROM FORMAL RED LINE TO OBSERVABLE DIGITAL WITNESSES Stage III couples that previously formalized boundary to independent operational evidence from agentic AI. Late-August 2026 publications on explicit agent state, human oversight degradation, computer-use-agent runtime monitoring, and enforcement gaps show complementary cases in which a retained representation, self-report, human-in-the-loop interface, or named technical control may fail to preserve all distinctions required by a later task. The present record does not claim that those independent authors validate the Origas physical interpretation. It treats their results as auditable digital witnesses to the already-defined representational problem. ENIGMA-2 REPLICATION: AN OPERATIONAL AND FALSIFIABLE CRITERION The paper introduces an operational criterion for Enigma-2 replication. A candidate box is counted only when four task-relative conditions are documented: E1 - Projection: a source X is reduced to a readout P. E2 - Residual fibre: R_J(P) > 0 for the declared task J. E3 - Closed reinforcement: recursion, consensus, optimization, or decision-making continues as a function of P without genuinely new source-sensitive information. E4 - Authority or action extension: the output is used beyond Jur(P), or the omitted distinction becomes relevant to safety, provenance, explanation, rights, or control. Therefore: Enigma2_J(P) = 1 only if E1 AND E2 AND E3 AND E4 are documented. This makes the proposed proliferation of Enigma-2 structures falsifiable rather than metaphorical. THE CONSERVATIVE SPINE The exact conservative architecture is: P < (P,J) <= (P,K,T) <= id_X. Here K denotes a fibre-separating channel. At the established mathematical level, T denotes order, provenance, trajectory, memory, or history. A genuine informational crossing of an Enigma-2 boundary requires K and/or T to carry source-sensitive information that is not already computable from P. The separator gain is: G_J(K,T | P) = R_J(P) - R_J(P,K,T). A genuine crossing requires G_J(K,T | P) > 0 on a frozen independent holdout, unless J already factors through P or the task itself is explicitly restricted. If K = F(P) and T = G(P), then there is no informational escape from the original representation. The enlarged notation remains inside the same fibre. Merely renaming a function of P as K or T does not escape Enigma-2. THE CENTRAL INSTITUTIONAL CONSEQUENCE A rule may restrict a readout, an artefact, an action, or a communication channel. It cannot, by declaration alone, make the readout informationally complete about its source. States, companies, scientific institutions, AI owners, regulators, and legal systems can legitimately regulate technical artefacts and actions within positive law. What they cannot establish by technical, institutional, consensual, or legal declaration is the mathematical identity: R_J(P) = 0 when a task-relevant residual fibre remains. In this precise sense: AUTHORITY MUST NOT EXCEED INFORMATION. A decree may restrict what a system is allowed to do. A decree does not shrink an informational fibre. A law may prohibit a channel. The prohibition of a channel does not prove that the distinction carried by that channel does not exist, or that it is irrelevant to the task. More processing of the same P is still more of the same P. MEASURABLE HUMAN DEGREES OF FREEDOM The paper extends the analysis to human degrees of freedom through an explicitly declared contraction functional D_free. Let A_source(x) denote the admissible action or expression set available at source state x, and let A_authorized(P(x)) denote the set allowed by an authorized representation. A proposed measure is: D_free(P) = E_mu [ log |A_source(X)| - log |A_authorized(P(X))| ]. For continuous spaces, cardinality may be replaced by an explicitly declared volume, entropy, or capacity measure. A positive value indicates a contraction of accessible degrees of freedom relative to the declared reference model. This quantity does not, by itself, prove legal or moral illegitimacy. Its purpose is to make a claimed contraction measurable rather than rhetorical, including cases where the residual may be unbounded. AGENTIC AI AND THE 1/2 SAFETY OBSTRUCTION If two admissible source states satisfy: P(x1) = P(x2) while their safe-action sets are incompatible: Safe(x1) intersection Safe(x2) = empty set, then a P-only policy cannot be safe in both states. In the symmetric two-state case, the minimax obstruction gives a worst-case error lower bound of 1/2. This 1/2 is a decision-theoretic obstruction generated by representational collapse. It is not presented here as proof of a universal physical constant or of a cosmic Point 0. The operational lesson is narrower and exact: when a readout erases a distinction required for safe action, no amount of computation confined to that readout can guarantee recovery of the missing distinction. BOUNDARY CROSSING CERTIFICATE Before local exactness is promoted into a broader claim about the source, the paper proposes a Boundary Crossing Certificate requiring explicit declaration of: P - the actual readout or representation; J - the external task or decision; R_J(P) - the residual task-relative fibre diameter; chi_J - any dependence on order, AB/BA sequence, provenance, trajectory, or history; K/T - any genuinely independent source-sensitive additional channel; G_J - the measured reduction of the residual fibre on a frozen independent holdout; null controls and Bridge-OFF tests; remaining unresolved fibres and singularities. No Boundary Crossing Certificate means no demonstrated informational basis for promoting a local readout into a claim of complete source reconstruction. FRENCH SCIENCE DECISION POINT 2026 A dedicated appendix applies the same audit to the historical and mathematical French context. It does not claim that Alain Aspect's Bell experiments were experimentally false. Rather, it makes a scope distinction: exact success for one declared task J0 does not imply representational completeness for every later task J1. In compact form: J0 in Jur(P) does not imply J1 in Jur(P). An exact Bell-test result can therefore remain fully valid for its declared experimental task without constituting a universal certificate that the same readout reconstructs every source variable relevant to every later physical, technological, legal, or societal decision. The warning for 2026 is consequently about scope extension, not about denying the experimental result. Autonomous AI systems make such scope errors potentially more consequential because a representation is no longer merely interpreted: it may directly authorize actions in the world. CONNES, ZHOU, AND NON-INJECTIVITY The 2026 Zhou counterexample to a Connes rigidity conjecture provides an exact operator-algebraic witness that a mathematically rich non-commutative representation can fail to encode source identity injectively. The methodological lesson is therefore broader than commutativity alone. Non-commutativity does not automatically imply source completeness. Even a rich non-commutative output must be audited for task-relative representational sufficiency. The decisive question remains: Does J factor through P? If not, what source-sensitive information is missing? THE 2026 NOBEL DECISION POINT The 2026 Nobel cycle is presented as a scientific-governance decision point, not as a claim of legal jurisdiction by the Nobel Foundation over states or AI companies. The record invites the Nobel Foundation and the relevant Nobel Prize-awarding scientific institutions to make representational sufficiency, source reconstruction, provenance, order dependence, independent separator channels, and the distinction between exactness and completeness explicit questions in frontier-science evaluation whenever a local readout is used to support a broader claim about reality. The methodological request is simple: before authority is extended from a representation P to a claim about the source, identify P, declare J, determine whether R_J(P) = 0, preserve order and provenance when they matter, and demonstrate any additional K/T channel on an independent frozen test. THE STATUS OF T Within the author's wider Cabin 1/2 interpretation, terrestrial +t/-t descriptions are placed beneath an overarching T. The present record makes a strict distinction between two levels. At the operational mathematical level: T = order / provenance / trajectory / memory / history. This T is auditable. It can