Description (abstract): Implements the holonomy test that SIP-PHY-NOTE-04 §5 relocated to a two-dimensional parameter manifold. Transporting the squeezing-axis frame around a closed loop in the complex squeezing-parameter plane yields an orientation-reversing holonomy (det = −1) when the loop encircles the round-state singularity, and the trivial holonomy (det = +1) on a contractible control loop — a homotopy invariant, robust to loop deformation, to the two confounds NOTE-04 identified (reference-shift absent by construction; cooling defeated by a squeezed thermal state), and to thermal noise. The orientation reversal is expected from the metaplectic double cover Mp(2) → Sp(2,ℝ); the contribution is its survival under open-system dissipation and finite temperature. This is a demonstration that the relocated instrument works, not a resolution of the Klein-cluster conjecture: the holonomy is shown on the parameter manifold, while the conjecture concerns the recoherence state manifold and the thermodynamic "never both" obstruction. That bridge — the proxy gap — is named and registered as a new fork (FORK-09), not crossed. HATI³ 92.0/100 (post-steelman).
Description (abstract): Implements the holonomy test that SIP-PHY-NOTE-04 §5 relocated to a two-dimensional parameter manifold. Transporting the squeezing-axis frame around a closed loop in the complex squeezing-parameter plane yields an orientation-reversing holonomy (det = −1) when the loop encircles the round-state singularity, and the trivial holonomy (det = +1) on a contractible control loop — a homotopy invariant, robust to loop deformation, to the two confounds NOTE-04 identified (reference-shift absent by construction; cooling defeated by a squeezed thermal state), and to thermal noise. The orientation reversal is expected from the metaplectic double cover Mp(2) → Sp(2,ℝ); the contribution is its survival under open-system dissipation and finite temperature. This is a demonstration that the relocated instrument works, not a resolution of the Klein-cluster conjecture: the holonomy is shown on the parameter manifold, while the conjecture concerns the recoherence state manifold and the thermodynamic "never both" obstruction. That bridge — the proxy gap — is named and registered as a new fork (FORK-09), not crossed. HATI³ 92.0/100 (post-steelman).
Description A working methods note in the quantum-foundations layer of the GTRS / coherence– decoherence–recoherence (CDR) framework. It answers a prior question that governs whether further simulation of FORK-06 is worthwhile: can the single-oscillator toy model distinguish a deep (topological, non-orientability) explanation of the "never both" pattern from a shallow (two-confounds) one? The finding is that the question is asymmetrically decidable on the toy model. The shallow reading is the only one the instrument can adjudicate; the topological reading is untestable here — not refuted, untestable — because a single oscillator's state manifold is flat and orientable (first Stiefel–Whitney class w₁ = 0 by construction; a trivial U(1)-bundle), and symplectic reduction by the free-oscillator flow collapses the reduced space to a point, leaving nothing for an orientation to attach to. The strongest adversarial attack (the squeezing axis) was run and survived: ℝP¹ ≅ S¹ is orientable, so the axis carries no non-orientability signature, and the apparent metaplectic sign is an unobservable global phase that cancels from the work and coherence observables. The topology test is therefore relocated — not abandoned — to a holonomy check on a genuinely two-dimensional parameter manifold (Berry / Wilczek–Zee setting), which is the designated next experiment. No new simulation; no resolution claimed; no fork is closed. The note's contribution is a decidability boundary and a relocation of the topology test to where it could succeed or fail honestly. Version 1.1 (25 May 2026) hardened §3 against the named squeezing-axis attack, promoted the supporting mathematics into the text, recorded a steelman/adversary divergence visibly (Glassbox), and softened one over-strong term in §4. Version 1.2 (25 May 2026) closes the two rigour points both review passes independently flagged: the metaplectic-phase cancellation is shown explicitly in §3.1, and the Berry / Wilczek–Zee literature is cited in §5. The concrete experiment parameterisation a reviewer suggested is deliberately deferred to the next note, to preserve the instrument-reach boundary. Supersedes v1.1 and v1.0 (24–25 May 2026); v1.0 was an internal working note and was not deposited. Review record: Steelman (Kimi, initial + confirmation); Adversary (DeepSeek, initial attack + concurring re-review that found no new ground); synthesis (Claude). HATI² embedded in Appendix C (Tier 1 94/100, Tier 2 90/100, combined 92.0/100). Part of the SIP corpus, SymbioMind Research Practice. Released under CC BY-NC-SA 4.0 as a pedagogical boundary: use to teach, not to certify.
The SIP-PHY Forks Register, v2.1 A consolidated register of eight registered foundational forks — well-formed open questions, each with named branches, traced consequences, and resolution criteria — in the quantum-foundations layer of the GTRS / coherence–decoherence–recoherence (CDR) framework. A registered fork turns a hidden theoretical tension into transparent research infrastructure; the register records what is open and why, and asserts no resolutions. A working connection map (explicitly a hypothesis for examination, not established structure) proposes that the eight forks may cluster around two deeper roots — an orientability question on the state manifold and an observer/selection question. Version 2.1 propagates the decidability finding of SIP-PHY-NOTE-04 (24 May 2026) into the topological branch of FORK-02, FORK-04, and FORK-06, and sharpens §3.1 accordingly. The topological reading of the "Klein cluster" is reclassified from open, attack via the toy model to open, but untestable on the single-oscillator model — a statement about the reach of the instrument, not a refutation — with the decisive test relocated to a holonomy check on a parameter manifold. No fork is closed and no new physics is introduced; the change is record-keeping. All eight forks remain open. Part of the SIP corpus, SymbioMind Research Practice. Released under CC BY-NC-SA 4.0 as a pedagogical boundary: use to teach, not to certify.
We investigate the geometry of mixed quantum states near rank-changing points, showing that these singularities function as effective geometric defects. The Uhlmann connection is well-defined on the full-rank sector of the density-matrix manifold, while rank-deficient states form singular boundary strata where the bundle structure degenerates. By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure and identify an asymptotically robust invariant: the Uhlmann holonomy around noncontractible loops encircling the defect on a restricted two-dimensional punctured submanifold. In an exactly solvable qutrit model, a restricted submanifold emerges on which the connection is locally flat yet carries nontrivial monodromy, analogous to flat connections with Aharonov--Bohm-type transport. The holonomy depends only on the ratios of the vanishing eigenvalues under frozen radial dependence of the eigenbasis geometry and a fixed angular loop. In contrast, the Uhlmann curvature may diverge path-dependently when eigenvalues shrink with distinct powers, with a leading spectral-prefactor scaling law, establishing that the holonomy survives as a universal asymptotic invariant while the curvature remains non-universal. Within the effective SU(2) defect sector, the conjugacy class of the holonomy, equivalently the Wilson loop variable, provides a continuous, non-quantized classification of the asymptotic monodromy surrounding the rank-deficient defect. This non-quantization does not imply a lack of robustness: the asymptotic holonomy is an invariant of the restricted punctured submanifold and is insensitive to smooth deformations of the loop or the radial profile within the fixed spectral-ratio sector.
ON THE VERSION NUMBER. "v3" is the version of the NOTE, not of this Zenodo deposit. Versions 1 (February 2026) and 2 were circulated privately and never deposited; v1 contained four errors of substance, which are stated with their repairs in the "What changed" section rather than quietly removed. This is the first Zenodo deposit, so if you see a deposit counter it will not match the document version. The document version is the one that matters for citation. Preprint, version 3 (complete rewrite). This note is the synthesis of the contextuality-obstructions program; the proofs live in the companion papers. The proposal is that the Copenhagen viewpoint, stripped of its rhetoric, is a set of structural statements about one geometric object: the transformation groupoid of measurement contexts (maximal abelian subalgebras) with its canonical U(1) 2-cocycle. In that formulation: local validity, the exact classicality of every single context, is a theorem with an explicit witness; complementarity is the nonvanishing holonomy of the cocycle along closed context loops, which detects exactly the all-versus-nothing sector of contextuality; collapse is pinned by statistics, repeatability and covariance to a one-parameter family per degenerate block whose unique efficient member is the Lueders rule, with a classical twin theorem identifying the same axioms' classical solution as Bayesian conditioning; observer-relativity of facts and the movable cut are theorems of an enlarged observer-context category; and the Frauchiger-Renner argument localizes to an ordinary state-dependent violation, with contextual fraction exactly 1/6, carried by a single CHSH facet, the loop holonomy of the observer switch being provably trivial. ATTRIBUTION. The classification of achievable state-independent values, the even/odd dichotomy and the fixed value d/2, is due to Abramsky, Cercelescu and Constantin (FSCD 2024). It is recast here in certificate language; the priority is theirs and is stated in the text. HARDWARE CAVEAT, STATED UP FRONT. Two signatures were measured on superconducting hardware. The quoted significances, about 56 sigma for the triangle holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented model. They are not systematics-aware, and neither experiment is loophole-free. Read them as consistency checks on real hardware, not as precision measurements. ERRATA. Version 1 of this note contained four errors of substance. Section "What changed" states each of them and its repair. They are recorded rather than quietly removed. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. Each tenet is either a theorem of the companion papers, a machine-verified certificate in the public suite, or is explicitly labeled a conjecture. The paper offers structural characterizations within its stated axioms; it is not an interpretation-free derivation of Copenhagen and it does not claim to resolve the measurement problem. AI-ASSISTANCE DISCLOSURE. This work was carried out with substantial AI assistance. Every load-bearing claim is machine-verified by scripts that ship with the papers, and the author takes full responsibility for the contents. COMPANIONS. Paper A: https://doi.org/10.5281/zenodo.21630431 . Paper B: https://doi.org/10.5281/zenodo.21630630 . Paper D: https://doi.org/10.5281/zenodo.21630697 . Paper C: https://doi.org/10.5281/zenodo.21633744 (posted 2026-07-28, after three adversarial review passes; it carries a labelled retraction of an earlier sqrt(2) reading). VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
CT 4.0.2 is the foundational bundle for Complementarity Theory (CT): physical updating modeled as finite committed record crossing an interface aperture under a least-incoherence selection rule, with mathematical setting in synthetic differential geometry (SDG). The paper presents five contributions: (1) A conditional derivation of the local Minkowski interval at a stable aperture in the first-order single-aperture regime, from CT primitives together with named structural inputs (a smooth aperture model, an adapted-frame choice, a posited seam-budget axiom, and a saturating-history existence hypothesis). Every non-theorem input is stated where it enters. (2) A complex-amplitude structure for the soft-commit regime: composition and superposition as operational axioms; the Born probability map definitional, with a named, independently testable interference-order axiom (after Sorkin) as the stated route to its quadratic form; a finite-dimensional Hilbert structure following from the axioms. (3) A multi-subject geometric proposal: intersection-network gluing with subjects anchored at the primitive substrate. The transported Lorentz triangle product is classified as connection loop holonomy — identity marks a flat face — distinct from Čech patch consistency; the U(1) face holonomy is conditionally realized as the normalized third-order Bargmann invariant. (4) A research program for deriving the residue role H from τ₀-substrate structure in complexified SDG, with the Residue-to-Phase problem restated precisely (the in-paper result is narrowed to a valid minimal-compact-factor theorem) and a conjectural horizon-phase quantization ansatz. (5) A conditional phase-to-spin and two-spinor bridge: three orthogonal noncommuting phase flows on a distinguished C² amplitude sector generate SU(2) ≅ Spin(3), with the exact 3-2-3 correspondence and the standard Penrose two-spinor route to Lorentzian geometry — established mathematics whose CT premises are recorded as named open problems. Version note: 4.0.2 is a status-correction erratum revision of the 15 May 2026 deposit (that record carries the Zenodo version label v4.0.1; there is no intermediate content revision). Claims are re-labeled to match what is proved, in nearly every case restoring the labels the supporting notes themselves use. A new supporting note, Identity as History, proves the record/history recurrence dichotomy behind the paper's arrow-of-time remark; the P-bound diagnostic is added with a reflexive audit caveat. The full changelog is Appendix A of the paper. The bundle contains the paper, twelve supporting notes (LaTeX and PDF), two H-program notes, the standalone SDG note, the Malus note, and a navigation README. An AI-assistance disclosure is included in the paper's acknowledgments.
Description This working note preserves a foundational reframing proposal made during the 19 May 2026 SymbioMind research conversation. The proposal suggests that within the Coherence–Decoherence–Recoherence (CDR) triplet, coherence (C) may not be a third regulatory phase co-equal with decoherence (D) and recoherence (R), but rather an observer-operator that collapses a D/R superposition into a particular realisation. On this reading, D and R are bonded as the two outcomes of a quantum-state-like structure, with C functioning analogously to the slit-choice in a double-slit experiment. If the proposal holds, it restructures the foundations of CDR by making C and D/R different kinds of mathematical object (C as operator, D and R as states), introduces the observer at the foundations of the framework rather than as a late addition, opens a fourth branch on the registered fork concerning the ontological status of time, and gives the Klein-surface-like recoherence topology a sharper role as the natural geometry of D/R bondedness. The note is parked rather than developed because the proposal admits three possible versions — formal (importing the full quantum-mechanical apparatus), structural-analogy (using the quantum framing without the formalism), and heuristic (using the double-slit as a vivid picture only). Development requires deciding which version is intended. The note records the proposal cleanly so that future work can begin from an intact starting point. It is not for publication as a stand-alone paper at this stage. The note identifies five conditions that may trigger development into a formal paper: a clear decision on which version is intended; availability of a mathematical collaborator; completion of the η(Φ) thermodynamic foundation; literature search confirming originality of the configuration; or emergence of a test case that distinguishes the proposal from the alternative.