Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026. The recursive-intelligence arc (Papers 56–60) establishes that what matters, what is known, and what affects structure must be semantically represented on-ledger. The remaining escape is: maybe there are real off-ledger entities—ghostly things not represented in the ledger. Paper 61 kills that move. We prove that any purported off-ledger entity is either determinacy-relevant (hence illicit under no-free-bits, Paper 27) or semantically inert (hence theory-null). No viable ontology of real-but-off-ledger ghost entities survives. Results are machine-checked in Lean 4 in the \pathGhostCollapse library of reflexive-closure-lean , with bridges to no-free-bits and \pathQualiaLedger. Trust boundary. The theorem targets ghost ontology (purported real-but-off-ledger entities), not every scientific use of "unobserved" structure. Hidden variables that affect adjudicatory structure must be ledger-relevant in the Paper 27 sense. See .
Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026. The recursive-intelligence arc (Papers 56–60) establishes that what matters, what is known, and what affects structure must be semantically represented on-ledger. The remaining escape is: maybe there are real off-ledger entities—ghostly things not represented in the ledger. Paper 61 kills that move. We prove that any purported off-ledger entity is either determinacy-relevant (hence illicit under no-free-bits, Paper 27) or semantically inert (hence theory-null). No viable ontology of real-but-off-ledger ghost entities survives. Results are machine-checked in Lean 4 in the \pathGhostCollapse library of reflexive-closure-lean , with bridges to no-free-bits and \pathQualiaLedger. Trust boundary. The theorem targets ghost ontology (purported real-but-off-ledger entities), not every scientific use of "unobserved" structure. Hidden variables that affect adjudicatory structure must be ledger-relevant in the Paper 27 sense. See .
STATUS (18 October 2026). The research programme this paper belongs to — the finite-QEC substrate ("It from Bit") framework — was concluded in October 2026. The author's review found that the framework's Standard-Model content is assigned rather than derived and that no verified prediction yet distinguishes it from standard physics. The claim of a unified derivation is withdrawn. This paper's results are unaffected except where noted below. Current gravity work: 10.5281/zenodo.23458252. ERRATUM — fine-structure constant (18 October 2026). This paper quotes the framework's value of the fine-structure constant, α−1(0) = 137.035999106904 (or the earlier 137.035999077), as agreeing with experiment. That statement is withdrawn. (1) On 11 August 2026 the value was corrected to 137.0359991069051: the earlier figure came from an extrapolation fitted at the wrong order. Against current determinations the corrected value sits −2.26σ from the caesium-recoil value, +9.01σ from the rubidium-recoil value and +3.94σ from the electron-g−2 route. Those determinations disagree with one another, so no single agreement figure can be quoted [K13]. (2) The second-order coefficient behind the value was computed on a four-dimensional hypercubic lattice that the framework's own geometry does not supply. Recomputed on that geometry under a pre-registered procedure, the same formula gives 137.0359985927, 4.26 parts per billion below CODATA 2022, so the claimed agreement does not survive [G87, G88, 24 September 2026]. The bare count α0 = 1/137 used in the paper is a premise of the framework, not a derived result. Noted: the methodology, the byte construction (with its CSS step stated as a hypothesis, consistent with [R22]) and the 28-step clock stand. Its fine-structure value is corrected by the erratum above; its "bi-cubic" picture of the cell differs from the framework's locked bond-bipyramid cell [G84]; and full strain readout does not preserve all logical coherence [G90]. States the foundational objects and audit methodology of the finite-QEC (quantum-error-correction) substrate program: the eight-bit local code, the bi-cubic crystallisation picture, the distinction between syndrome and strain readouts, the 28 = 2×14 service-clock construction, and the methodological rules that classify every claim as locked, computed, conditional, retired, or open. The goal is to make the companion physics papers auditable: every coefficient must name its carrier, event unit, scheduler, observable map, and reproducibility check. Version 3.0. Added a radiation-sector domain-of-validity caveat (the emergent gauge sector is an effective theory below the substrate's Brillouin scale; trans-cutoff single photons are an open foundational question) and the relativity companion citation. Copyright (C) 2026 D. G. Elliman.
Note on this consolidation This document merges three previously separate pieces (A GitHub repository with numerical checks has been added) (1) The No-Chaos Theorem, now in its corrected form: ontic chaos is impossible (§5), and - after two earlier, retracted attempts (a geometric leakage estimate with the wrong sign; an entanglement-growth mechanism that conflated entropy growth with a Lyapunov exponent and depended silently on ETH) - dynamical chaos at any fixed coarse-graining scale ℓ is proven structurally impossible (§7), with level statistics introduced as the one chaos diagnostic that survives (§7.3). (2) The thermalization content that used to be misattributed to "chaos": real physics (Calabrese–Cardy growth, Page saturation), relocated here as what it actually is (§9), together with its genuine connection to the construction used elsewhere in this work via ETH. (3) New in this consolidation: the Embedded-Observer No-Go Theorem (§8), which answers a related but logically distinct question - not whether an observer sees chaos, but whether an observer confined to a proper subgraph can ever completely reconstruct the global state or evolve autonomously. This is a better-grounded reason for an embedded observer's limited picture of reality than either chaos or thermalization, and does not depend on ETH, Page's theorem, or any genericity assumption beyond an entangling (generic) boundary coupling.
Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026. This short note provides a fast, technically correct entry point into the NEMS Suite. The suite establishes a fixed-point architecture linking closure (Perfect Self-Containment, PSC) to quantum probability semantics (Born rule) at the level of macroscopic records. The core contributions are stated as a compact theorem ledger with explicit assumptions and a precise map of what is machine-checked in Lean versus what is cited as classical mathematics. We also provide an audit-style "where disagreement must occur" checklist: any critic must reject a specific named premise (records, closure, computation, semantic completeness, or classical linear-algebraic facts), rather than dismissing the framework as interpretive.
Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different settings, there is still no consensus on which properties of a dynamics reflect genuine quantum features and which arise from classical or non-genuine quantum sources. In this review, we provide detailed information on recent developments in characterizing quantum non-Markovianity based on information backflow and the nature of its origin. We also present a survey on how various approaches separate classical and quantum contributions, as well as how they define operational tasks that reveal genuine quantum non-Markovianity. We analyze several frameworks, including state-distinguishability -based, channel-based (``CP-divisibility''), and process-tensor methods. For each framework, we outline the underlying physical motivation, the criteria proposed to distinguish genuine quantum non-Markovianity from practical or apparent memory effects. We further compare different approaches and their strengths and limitations. The review aims to clarify the conceptual and operational aspects of quantum non-Markovian processes based on their nature and to provide a foundation for future research on quantum non-Markovianity and its role in advancing quantum information science and technology.
Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026. Under PSC-style closure, stable records, and diagonal capability (Papers 27, 29), one cannot simultaneously hold a strong factorization locality axiom (Paper 45) and local semantic determinacy—that world-type is computed from local views in a total-effective way. We prove a no-go: any such procedure would decide an extensional nontrivial predicate on a diagonal-capable domain and thus contradict the selector-strength barrier. So total-effective local semantic determinacy must fail (factorization can hold). This is semantic nonlocality in the effective sense, without implying superluminal signalling. The result is mechanized in Lean 4 (CausalNonlocality); the barrier witness is parametric in the fixed-point premise (0 axioms). Paper 47 (No Spooky-to-Signal Compiler) builds on this. Trust boundary. The no-go combines Paper 45 factorization with a total-effective local semantic determinacy hypothesis; it does not assert superluminal signalling. Mechanization is nems-lean . See .