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.
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.
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).
Preprint. Third paper of the contextuality-obstructions program, alongside Paper A (the canonical class of the MASA context stack), Paper B (the obstruction spectrum of Weyl context families), Paper D (the observer-context category) and a synthesis note. The slogan "contextual holonomy encodes quantum contextuality" is attractive and, as usually stated, false. This paper gives it a sharp form. On the context stack of maximal abelian subalgebras the canonical degree-2 class has order exactly n, and its cocycle holonomy along closed context loops detects EXACTLY the all-versus-nothing sector of contextuality for closed-triple Weyl families at even local dimension. Both containments are strict, each by an explicit certificate: at d=3 the class is nontrivial of order 3 while the achievable state-independent AvN value is 0, and KCBS exhibits state-dependent contextuality where the class shadow vanishes. The Wigner-friend loop generated by H and S splits by level: its projective (Pancharatnam) holonomy is +1 while its determinant-section holonomy is exactly -i, so any interpretational claim about "the" holonomy of that loop must state which one it means. ATTRIBUTION. The classification of state-independent values for qudit Weyl families, the even/odd dichotomy and the fixed value d/2, on which the state-independent side of the equivalence rests, is DUE TO Abramsky, Cercelescu and Constantin (FSCD 2024). Attainment at general even d is the Raussendorf-Okay-Zurel-Feldmann construction. This paper uses both and rediscovers neither. A RETRACTION IS CARRIED IN THIS PAPER, NOT BURIED. An earlier draft presented the tier-two facets of the d=4 census on a (1/(2*sqrt2))Z grid with a single coefficient magnitude 3/(2*sqrt2), and read the resulting unit-coefficient bounds 4*sqrt2 and 14*sqrt2/3 as placing Tsirelson's sqrt2 inside the tier-two geometry. The whole presentation was a normalization artifact and is withdrawn (Retraction 1): the stored lift has coefficients in {0,+-1} with integer bounds 6 and 7, every facet functional in the census is rational, and Q(sqrt2) is not among the eighteen canonical arithmetic fields. Certificate: d4_arithmetic_profile.py. WHERE THE EVIDENCE IS THIN, STATED IN THE PAPER. Two sweeps quoted here drew no positive instances at all: the d=4 half of the 2,100-family equivalence test, and the 6,500-trial false-certificate sweep, which draws no contextual family at any of d=2,4,8 and therefore establishes the absence of false certificates only vacuously. Both are disclosed where they appear. Theorem 2 is labelled machine-validated rather than proved: the closed form is established end to end for the deletion families treated, while the general closed-triple d=2 statement in compressed coordinates remains open and is recorded as open in the verification ledger. HARDWARE CAVEAT, STATED UP FRONT. The quoted significances, about 56 sigma for the ray-level Wigner-friend holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented witness model and conditional on compatibility and nondisturbance assumptions. They are not systematics-aware and neither measurement is loophole-free; a roughly 3.5 sigma preparation offset on one strand is itself evidence of unmodelled systematics. We also record that the pinned value S = 4.6125 cannot be recomputed from the stored counts (a naive recomputation gives 4.5662, a gap of about 2.7 standard errors); the archived value 4.558 +- 0.018 is the one an independent reader can reproduce from the deposited data. Read these as consistency checks on real hardware, not as precision measurements or certifications. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. It was held back from the first publication batch and released only after three adversarial review passes; what each pass found, and how each item was closed, is recorded in verification/INDEX.md rather than quietly fixed. One defect found there is NOT closed and belongs to the companion Paper B, which cites a false-certificate artifact that is not in fact in the repository; it is recorded rather than left for a reader to discover. 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 . Note: https://doi.org/10.5281/zenodo.21630739 . Code archive: https://doi.org/10.5281/zenodo.21498498 AI-ASSISTANCE DISCLOSURE. Large-language-model assistants (Anthropic Claude) were used substantially in drafting, in developing the verification scripts, in literature search and in proposing proofs. Every load-bearing claim is machine-verified independently of that assistance by the scripts named in the text, and the author takes full responsibility for the results, including any errors. VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
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
Scope label (load-bearing). Genuinely interacting quantum field theory in flat 1+1 Minkowski space. No gravity: not dynamical, not backreacting, not quantum. This is Exit (a) of Proposition 2 — the coupling axis, isolated from the gravity axis. Archived as Phase VII (with its certification Phase VII-b); not merged into the free-field Minkowski corpus of Phases IV–V, nor into the fixed-curved-background Phase VI. Phase VI closed the fixed-background branch with a structural obstruction (Proposition 2): for a free field on a fixed classical background the state is a functional of the background data, hence so is every modular observable, and grade (ii) is the ceiling — a genuine positive is structurally unreachable there. Exactly two exits survive: (a) genuine interaction, and (b) dynamical gravity. This paper attacks Exit (a), the minimal scope extension: still flat space, no gravity, only the coupling switched on. The object is the interval entanglement Hamiltonian K_A = −log ρ_A in the DMRG/MPS ground state of the mixed-field Ising chain — genuinely interacting, non-integrable, gapped, non-conformal — and the reference is the model's own interacting Bisognano–Wichmann family (identity plus a freely weighted local energy density plus first descendants), never the free stress tensor. The same structural logic caps the attainable outcome at a distinction inside grade (ii): REDUCE (the third verdict extends to coupling) versus IRREDUCIBLE (the first crack of the enclosure). Both were preregistered as publishable and hash-frozen before any production run. Phase VII returned a substantive but uncertifiable result: all four target residuals sit 5–30× below the controls, the residual anti-tracks the coupling, and the co-primary spectral reconstruction echoes a correlation-length ordering — yet the frozen multiplicative threshold (θ = 10 × floor = 1.62) exceeded the maximum response of any bounded foil (≈ 0.45), because the free-control floor was dominated by Jordan–Wigner representation mismatch, an instrument bias ~30× the target signals. The teeth precondition failed by arithmetic, not by physics, and the verdict was left with an asterisk. Phase VII-b removes it: an independently frozen rerun in the model's natural variables (the fermionic Jordan–Wigner-bilinear BW family, whose free-control residual is exactly zero at full range — the calibration the earlier instrument lacked), an additive threshold, and satisfiable contrast teeth. Teeth pass; all four targets lie 8–200× below the certified threshold and below every control, in both representations. Verdict: COLLAPSE (Exit (a)), certified. The interacting entanglement Hamiltonian reduces to the local Bisognano–Wichmann energy density; the reduction is representation-independent, and increasing the coupling makes K_A more BW-local, not less. The strong-coupling axis carries no grade-(ii)-irreducible modular orientation. No grade-(i) claim is made or implied (Proposition 2 forbids it for a fixed-Hamiltonian ground state). The genuine positive, if it exists, is pushed onto Exit (b) — dynamical geometry — named and out of scope here. Preregistration and reproducibility. Both investigations were governed by preregistrations frozen and hashed before any production run — Phase VII: SHA-256(§1–§6) = 5c53a0c0…fc09f (frozen 2026-06-30 22:45:34 UTC); Phase VII-b: SHA-256(§1–§6) = c63f8a10…39d46 — with append-only deviation logs (DEV-1…DEV-6 and DEV-1…DEV-4(VII-b)) below the hash boundary, and cautionary records of the two failed instruments preserved rather than discarded. Code, preregistrations, per-claim ledgers, and all emitted CSV/JSON data: https://github.com/PauDD/Simulador-Fase-VII Continues Phase IV (10.5281/zenodo.21261576), Phase V (10.5281/zenodo.21302338) and Phase VI (10.5281/zenodo.21321084) of the programme Rigidez de la Incidencia Geométrica (Geometric Incidence Rigidity).
What this note does. Guérin, Baumann, Del Santo and Brukner (Commun. Phys. 4, 93 (2021)) proved that, except for two special choices of Wigner's measurement basis, no joint probability distribution consistent with unitary quantum mechanics describes Wigner's friend's perceived outcomes before and after Wigner's measurement. Their theorem is exact and binary: it asks whether two effective perception observables commute. This note asks how much the friend's records must degrade before the obstruction disappears, and answers in closed form. Writing Wigner's basis parameter as c = |a² − b²| and smearing both perception observables to visibility η, a persistent-reality description exists if and only if η ≤ 2/(√(1−c²) + √(1+3c²)). The curve equals 1 exactly at the two compatible cases of the qualitative theorem and is minimized at √3/2 ≈ 0.866 when c² = 2/3. What is new, and what is not. Stated plainly, because each ingredient is due to someone else. The scenario, the assumptions P1–P3 and the two effective perception POVMs are from Guérin et al. The equivalence between a linear two-time distribution and a joint POVM is established in the proof of their Theorem III.1 and is used as stated there, not re-proved here. The joint-measurability criterion for unbiased qubit observables is Busch's (Phys. Rev. D 33, 2253 (1986)) and is standard. Given the Bloch vectors, the threshold follows from that criterion in two lines; this note does not present the computation as difficult. The contribution is the robustness question, the closed-form answer, the worst-case basis, and an elementary observation about the single-time claim. A clarification the note also records. The frequently repeated claim that no single global density operator reproduces both agents' descriptions is false in its single-time operational form: the two states agree on the friend's entire record algebra, differing only in coherences she cannot access, so Wigner's own state satisfies both agents' operational constraints. The claim becomes a theorem only through the two-time persistence requirement. This is elementary and expected to be folklore among specialists; it is recorded because the inference is common and because it locates where the real obstruction lives. Status and scope. This is a preprint, not a peer-reviewed article. Two honest caveats are stated in the text rather than buried. The noise model is a stipulation on the effective observables, not a decoherence channel derived from a modified unitary model; Del Santo, Manzano and Brukner (Phys. Rev. Research 7, 033279 (2025)) have a physically motivated degradation parameter for the same scenario, and the map between the two is not known here. And smearing the first, sharp observable means degrading the friend's perception of her own outcome, which requires an interpretive commitment some readers will not grant; smearing only the later readout provably achieves nothing, which is why the symmetric family is used. Verification. All algebra was recomputed symbolically and independently: reconstruction of the perception POVMs from the unitary model, reproducing Eqs. (12)–(15) of Guérin et al.; derivation of the threshold and of the minimum at c² = 2/3; and a semidefinite-programming feasibility test of the joint-POVM constraints at five values of c on both sides of the threshold, agreeing with the curve in all ten cases. The three scripts are deposited with the note. Use of AI assistance. This note was prepared with substantial assistance from AI language models, used for symbolic computation, drafting, literature search, and adversarial review of the arguments. Every mathematical claim was independently recomputed symbolically and cross-checked numerically. No specialist in quantum foundations has refereed it. The author is responsible for the content. This disclosure is made unconditionally.