We present a structural, non-parametric test of quantum-error-correction syndrome streams against entire classes of noise models at once, together with a cautionary correction to a natural first version of the test. The test has two stages. Stage one is the sign stage. If a stationary binary stream is generated by a finite hidden-Markov model in Moore form, meaning state-conditional emissions, whose underlying chain is reversible in the detailed-balance sense, then the run statistics m_k = p(1^{k+1}) form a Hamburger moment sequence. Consequently the offset Hankel matrices [m_{i+j}] are positive semidefinite at every order. We prove this by detailed-balance symmetrization. Two scope corrections are essential. First, the n = 0 entry p(1^0) = 1 must be excluded: including it in the naive Hankel falsely rejects legitimate periodic models, as a deterministic two-state alternator shows. Second, the Moore qualifier is essential: a Mealy, or edge-emission, model on a reversible chain is not covered, because the induced Moore model lives on the edge chain, and the edge chain of a reversible chain is not generally reversible. A statistically signed offset Hankel therefore certifies that no Moore-form hidden-Markov model with reversible chain, of any dimension, reproduces the stream. This is a representation-class statement, narrower than an earlier draft's claim and stated exactly. Stage two is the pole stage. Prony analysis of m_k separates the two ways a sign can arise: real or rational pole structure, compatible with non-reversible finite models, versus a complex pair at irrational phase on the dominant circle, which by the theory of nonnegatively realizable sequences excludes every finite-state model. The dominance qualifier is essential, since subdominant complex pairs are unconstrained, and the protocol tests it explicitly. The pole stage requires order selection, namely numerical Hankel rank before Prony; fixed-order fitting provably hallucinates poles, as shown on an exactly solvable model. Applied to Google's 2023 surface-code memory experiment, using public data from 64 stabilizer streams with 50,000 shots each, 64/64 streams nominally sign: decisively for the typical stream, with minimum eigenvalue around -10^{-3}, tight bootstrap intervals at B = 2000, survival under a conservative Bonferroni statement, and signal an order of magnitude above the derived within-shot drift systematic; provisionally for the weakest streams, where the residual concern is bootstrap boundary behavior rather than drift. The order-selected pole stage finds purely real primary poles in 64/64 streams, and the rank scan finds no stream with a resample-stable, dominant complex pair. Thus the clock signature is absent, while an oscillatory control exhibits it at stability and dominance 1.00. The verdict is anchored by an exact model lemma: the standard detection-event mechanism, in which measurement errors fire the same detector in consecutive rounds, is a four-state chain of letter-transfer rank two with exact poles {+0.2836, -0.2336}. It signs the offset Hankel with purely real poles while being distributionally time-reversal invariant and Mealy-realizable on a reversible chain. Therefore the sign certifies the absence of a reversible Moore-form hidden realization, not a temporal arrow in the data and not the absence of all reversible-chain models. The device's syndrome statistics show exactly the pair-mechanism structure documented by the source publication by other means, and no rotation, or "clock", signature that would obstruct finite-state modeling up to the dimension bound finite data can certify. Controls demonstrate instrument power: an i.i.d. stream passes, while a hidden irrational rotation at matched rate is decisively rejected.
We present a structural, non-parametric test of quantum-error-correction syndrome streams against entire classes of noise models at once, together with a cautionary correction to a natural first version of the test. The test has two stages. Stage one is the sign stage. If a stationary binary stream is generated by a finite hidden-Markov model in Moore form, meaning state-conditional emissions, whose underlying chain is reversible in the detailed-balance sense, then the run statistics m_k = p(1^{k+1}) form a Hamburger moment sequence. Consequently the offset Hankel matrices [m_{i+j}] are positive semidefinite at every order. We prove this by detailed-balance symmetrization. Two scope corrections are essential. First, the n = 0 entry p(1^0) = 1 must be excluded: including it in the naive Hankel falsely rejects legitimate periodic models, as a deterministic two-state alternator shows. Second, the Moore qualifier is essential: a Mealy, or edge-emission, model on a reversible chain is not covered, because the induced Moore model lives on the edge chain, and the edge chain of a reversible chain is not generally reversible. A statistically signed offset Hankel therefore certifies that no Moore-form hidden-Markov model with reversible chain, of any dimension, reproduces the stream. This is a representation-class statement, narrower than an earlier draft's claim and stated exactly. Stage two is the pole stage. Prony analysis of m_k separates the two ways a sign can arise: real or rational pole structure, compatible with non-reversible finite models, versus a complex pair at irrational phase on the dominant circle, which by the theory of nonnegatively realizable sequences excludes every finite-state model. The dominance qualifier is essential, since subdominant complex pairs are unconstrained, and the protocol tests it explicitly. The pole stage requires order selection, namely numerical Hankel rank before Prony; fixed-order fitting provably hallucinates poles, as shown on an exactly solvable model. Applied to Google's 2023 surface-code memory experiment, using public data from 64 stabilizer streams with 50,000 shots each, 64/64 streams nominally sign: decisively for the typical stream, with minimum eigenvalue around -10^{-3}, tight bootstrap intervals at B = 2000, survival under a conservative Bonferroni statement, and signal an order of magnitude above the derived within-shot drift systematic; provisionally for the weakest streams, where the residual concern is bootstrap boundary behavior rather than drift. The order-selected pole stage finds purely real primary poles in 64/64 streams, and the rank scan finds no stream with a resample-stable, dominant complex pair. Thus the clock signature is absent, while an oscillatory control exhibits it at stability and dominance 1.00. The verdict is anchored by an exact model lemma: the standard detection-event mechanism, in which measurement errors fire the same detector in consecutive rounds, is a four-state chain of letter-transfer rank two with exact poles {+0.2836, -0.2336}. It signs the offset Hankel with purely real poles while being distributionally time-reversal invariant and Mealy-realizable on a reversible chain. Therefore the sign certifies the absence of a reversible Moore-form hidden realization, not a temporal arrow in the data and not the absence of all reversible-chain models. The device's syndrome statistics show exactly the pair-mechanism structure documented by the source publication by other means, and no rotation, or "clock", signature that would obstruct finite-state modeling up to the dimension bound finite data can certify. Controls demonstrate instrument power: an i.i.d. stream passes, while a hidden irrational rotation at matched rate is decisively rejected.
Abstract Quantum error-correction decoders must convert noisy syndrome records into logical decisions while operating under strict latency and reliability constraints. Minimum-weight perfect matching (MWPM) remains a strong baseline for surface-code decoding because it is fast, interpretable, and exact for its graphlike optimization problem [1–8]. However, the graphlike independent-error approximation can become mismatched when syndrome records contain temporal drift, measurement corruption, crosstalk, bursts, or mixtures of mechanisms [9–18]. We introduce SAGE-QEC, a failure-aware selective decoder that retains nominal PyMatching as its default decision and learns when an observable syndrome structure warrants an alternative candidate. SAGE-QEC uses train-frozen structure thresholds, a candidate ranker, validation-only policy selection, and a paired blind evaluation. Across 45 simulator conditions, SAGE-QEC reduced the aggregate logical error rate from 27.1285% for PyMatching to 24.8320%, corresponding to an 8.47% relative reduction. The campaign used rotated surface-code memory circuits at distances 3, 5, and 7, nominal circuit parameters 0.002, 0.003, and 0.005, five seeds, and four test regimes withheld from training: Burst-3, Temporal Drift, Crosstalk, and Mixed Noise. The test set contained 81,000 paired shots. All twelve distance-by-regime aggregate comparisons favored SAGE-QEC in the executed campaign, with paired bootstrap intervals below zero for SAGE-QEC minus PyMatching. The result is evidence of a reproducible simulator-level improvement, not a claim of universal decoder superiority. SAGE-QEC currently uses logical-output proxy candidates rather than a complete physical correction search, and its intervention rate remains high under distribution shift. It has not yet been compared with a fully calibrated correlated-noise space-time PyMatching baseline or hardware calibration data. We therefore characterize SAGE-QEC as a strong qualification-stage prototype and release a complete audit protocol for the next industrial validation stage.
This preprint studies finite-shot reconstruction of hidden quantum factor structure from global calibration-free sequence statistics without assuming an internal tensor-product cut in advance. A probability-only complex-projective 3-design self-test is used as an imported anchor for the active Hilbert/Jordan geometry. From this anchor, global control maps are reconstructed with explicit confidence bounds, including a weighted estimator for unequal shot counts and missing reference settings whenever the surviving frame remains full rank. The main certification result is a whole-commutant-energy lower bound. For reconstructed controls, the sum of the lowest commutator singular energies yields a basis-free lower bound on the aggregate projective Hilbert–Schmidt distance to every common hidden matrix factor of a specified multiplicity. Combined with exact Choi-to-projective-unitary conversion and finite-shot confidence balls, this produces a one-sided lower bound on distance to the complete common-factor model class. An explicit exact factor witness gives the complementary PROXIMAL-RECOVER certificate; otherwise the procedure returns ABSTAIN. The paper also proves that exact generated-algebra / tensor-product-structure type is not uniformly identifiable from finite samples without a structural separation margin. For the fixed two-qubit 60-state stabilizer benchmark, the paper provides an anchor-inclusive raw-count validation and an exact-rational / outward-rounded one-sided trust path from integer counts through anchor and control confidence radii to factor RECOVER/REJECT. The scope is deliberately operational: the result certifies active factor structure supported by the augmented data and does not claim identification of arbitrary inactive spectator degrees of freedom or a uniquely true microscopic decomposition.
Abstract We study decoder-representation sensitivity in simulated rotated surface-code Z-memory circuits with local spatially correlated XX pair events. At distance 3, ordinary minimum-weight perfect matching (MWPM) produced 4,610 versus 1,260 logical failures at p_corr = 10^-4 and 5,437 versus 2,239 at p_corr = 2 × 10^-4 on the same 500,000-shot samples using original-order versus canonical-sorted detector error models (DEMs). Across 50 additional seeded permutations per condition, failure counts varied widely. Canonical sorting tied for the minimum in this finite tested set; it is not claimed to be universally optimal. The ordering experiment reorders complete error instructions in a flattened DEM, preserving their probabilities and absolute detector and logical targets. PyMatching documents retaining the first-added logical-label set when parallel graph edges are merged; we therefore interpret the findings as a workflow-specific reproducibility result, not a newly discovered general software defect. At distances 5 and 7, correlation-aware MWPM had lower observed failure rates in all eight tested conditions, with six paired contrasts remaining significant after Bonferroni correction. An exact maximum-a-posteriori calculation gave a 0.2367% Bayes risk for the flattened-DEM distribution at p_corr = 10^-4; this is optimal for that modeled distribution only. This bounded classical simulation study proposes no new decoder, estimates no threshold, and provides no hardware evidence. Some historical source-to-result provenance remains incomplete, as disclosed in the manuscript. Code and evidence: https://github.com/tgiwn/QEC-surface-code-correlated-noise/tree/106d32e815c5f6009941afc36d3f65be7ecf35a3 Status: This is a preprint and has not undergone peer review.
This preregistration describes a confirmatory study of an upstream conditioning architecture in a quantum error-correction workflow. The project’s purpose is to test whether an intervention applied prior to the primary decoder produces a real and reproducible decoder-relevant effect, remains compatible with more than one downstream decoder family, generates a measurable exposed-observable statistical footprint, and improves or preserves performance across a preregistered regime rather than only at a single operating point. The study is intentionally limited to architecture-level evaluation, with the public claim set confined to exposed observables, frozen transformations, preregistered statistical tests, explicit negative controls, and bounded interpretation rules. The confirmatory design is organized around five preregistered tests: category existence, decoder compatibility, structural footprint, observable statistical signature, and regime robustness. Across these tests, the central comparison is between a baseline control pipeline and a conditioned pipeline in which the upstream intervention is applied while all non-conditioning settings are held fixed. The study uses frozen observables and frozen execution rules, including matched seeds, shot counts, code distances, physical error rates, geometry, and baseline decoder settings, so that any supported effect can be interpreted as evidence about the architecture under test rather than as a byproduct of post hoc tuning. To preserve a clean-room boundary, the registration restricts primary analysis to exposed, decoder-facing quantities only. These include logical failure, an exposed defect-count summary, and an exposed decoder-difficulty proxy, along with a locked scalar error-load construction derived from control-only standardization. The study does not rely on decoder-internal state variables, hidden confidence traces, or implementation-specific internal diagnostics in its primary confirmatory analyses. This structure is intended to let readers evaluate whether the architecture leaves a reproducible footprint in decoder-facing behavior without disclosing reconstruction-level mechanism details. Expected outcomes are defined in confirmatory rather than speculative terms. If the preregistered hypotheses are supported, the study is expected to provide evidence that an upstream conditioning intervention exists as a real architectural category in QEC, acts before the primary decoder, is compatible with downstream decoding, changes decoder-relevant exposed structure, and produces a reproducible observable statistical footprint in logical-failure behavior. If support is absent, mixed, or null, those outcomes will still be recorded under the frozen rules without rescue through post hoc metric changes, reweighting, or reinterpretation. In either case, the expected result of the registration is a bounded, auditable public record of whether this architecture class shows reproducible category-level behavior under a preregistered confirmatory design. The preregistration is not intended to establish a unique mechanism identity, identify a privileged implementation, disclose implementation-specific reconstruction details, or support claims about exact targeting logic, suppression laws, subset-sizing logic, telemetry-governed control, or broader cross-domain theory narratives. Public-facing interpretation is therefore intentionally limited to category validation and exposed-observable behavior. This is meant to support rigorous public evaluation while preserving strict clean-room limits around protected implementation detail.
Version 4 (2026-08-25). Two additions from the correction campaign, carried as dated in-body correction records. The (2,5) entry, printed as a prediction in v3, is now census-exact -- and it was the wall law's first divergence test. At the constructed maximal-wall stratum point the stiff transverse count is exactly 10, so alpha_stratum(2,5) = 5; a fresh 60k ensemble's calibrated read is consistent with 5, with alpha = 10 (the superseded single-wall count's prediction) excluded at p = 0.000 and demonstrated power ~ 1; and a stratum-conditional paired ladder tracks the exact rank-10 Hessian form to <= 0.002 while a rank-20 comparator separates by >= 2.7 on identical draws. The law m_C(2,d) = 2(d-1) is census-exact at d = 3, 4, 5, now including the first point where it diverges (by 2x) from the superseded count. The (3,4) entry, printed open in v3, is now a PAIR of statements, and neither alone is alpha(3,4). The posted product-wall counting landed census-exact (alpha_stratum(3,4) = 5, so the asymptotic exponent satisfies alpha(3,4) <= 5), while the accessible window at n = 3e4 is steeper (calibrated 90 percent set [5.4, 6.9], with the previously read 4.0-4.1 excluded at power ~ 1): the codim-10 stratum's prefactor has not engaged at reachable depth, and window and asymptote have visibly decoupled. This is the scope lesson of the (d >= 3) x (d' > d) regime -- census plus conditional ladder measure the law, global windows measure the pre-asymptotic shoulder -- and it retro-explains the earlier fresh-seed ladders' instability as shoulder reads. Version 3 (2026-08-20). One SUPERSESSION: the qutrit-qutrit exponent closes. Versions 1 and 2 left alpha(3,3) open, v1 by a small-sample fit reading 3.25 and v2 by the bracket [2.3, 3.0] read off a descending window ladder. Both readings were artifacts of the estimator problem for which the pair-type table was already corrected in v2. The descent is attenuation tracking sample count rather than tail depth: an ensemble drawn from an EXACT alpha = 3.0 law descends by 0.62 across the ladder against the real data's 0.34, so a descending ladder is evidence FOR a constant exponent, not against one. Replacing the window fit with a calibrated Monte-Carlo test and inverting it over candidate exponents gives alpha(3,3) = 3.0 at p = 0.517 with a 90 percent confidence set [2.75, 3.10]; v1's 3.25 is excluded at p = 0.017. Power against alternatives is 0.990 / 0.590 / 0.120 / 0.575 / 0.990 / 1.000 at true alpha = 2.50 / 2.75 / 3.00 / 3.25 / 3.50 / 4.00. An independent re-audit at n = 10^4 reads flat near three on two seeds. Disclosed defect, carried in the paper: the test's own calibration row missed at the low edge (rejection rate 0.207 at a nominal 0.10 when the truth is alpha = 2.50, 4.4 standard errors high), so the lower end of the confidence set is softer than printed. This ensemble separates 3.0 from 3.25 with about 58 percent power and has none to separate 3.0 from 2.95. The (3,3) CARRIER family remains unattributed: the exponent is settled, the stratum that carries the accessible tail there is not. Version 2 (2026-08). Changes from v1: the pair-type exponent table is corrected (v1's alpha(2,4) = 2.08 was a 50-sample order-statistics fluctuation, placed at the 0.15th percentile of its own estimator's sampling distribution; three independent codebases now agree on the wall law alpha(2,d) = d, census-exact at d = 3 and 4); the transverse constant 1/12 is derived in closed form (diagonal cost 1/6, halved by the congruent partner's equal-cost correction); the (2,3) tail's carrier stratum is fully attributed (an isotropic-intertwiner family sharing the exponent 3); the qutrit-qutrit exponent is honestly bracketed open at [2.3, 3.0]; and the dispersion rule (tail-exponent fits print bootstrap dispersion or do not print) is adopted. The v2 ledger appendix carries the correction anatomy. Why is the multipartite certification constant heavy-tailed, where does the tail live, and what kills it? Localization: the credential pencil is exactly block-diagonal over party-subset supports; the tail is the worst pair; geometry statistics reconstruct from pair statistics (14/14 factor-band comparisons). The law: a frame-congruence theorem: whenever the two parties' operation frames subtend equal Bloch angles, the rotation intertwining them is an exact common kernel direction; the zero set is codimension one at generic angles, transverse growth is universally quadratic (mu = (Delta theta)^2/12), and the qubit-pair tail exponent is exactly 1/2 (the previously measured 0.39 is the finite-window slope of this law). The dichotomy: pairs containing a d >= 3 party measure exponents 2.08 to 3.69 because higher-dimensional operation pairs carry many local invariants that must all match: freedom helps the certifier. Engineering: heterogeneous dimension profiles tame the tail; qubit-pair presence splits all measured geometries into two clean classes; screening is a five-minute two-party calculation. Pre-registered; two entry gates that caught wrong conventions and all deaths ledgered.
This paper develops a framework-relative ontology of determinacy. Its core question is not what the world is made of, but what must minimally be accounted for if a stable deter- minate identity is internally self-representing. The primitive and functional core of Version 3.8 is retained: Being, the possibility of distinction, and domain-relative realizability define the sparse primitive basis; coherent self-representation then requires three non-equivalent func- tional questions—Support, Internal Encoding, and Correspondence. Explicit finite witness pairs establish uniform non-determination of each role from the other two in the unrestricted baseline class, while stronger canonical or equivariant subclasses remain open. Version 4.1.1 is a corrective consolidation of Version 4.1 rather than a new upstream on- tology step. It retains the Version 4.0 bridge revision and the Version 4.1 constructional layer. That layer adds the reverse evaluative direction Physics ⇒ Mathematics ⇒ Ontology and records where downstream structures constrain, but do not retroactively constitute, the ontol- ogy. Several previous bridge claims are weakened or rejected. Symmetry classification, tensor factorization, entanglement of a state, and path-dependent dynamics are kept as four distinct mathematical layers. A conditional expectation is treated as a localization map rather than as actualization; a branch instrument defines possible conditional events but does not select one realized branch; and a projection onto admissible spectral sectors is not called conservative dynamics without an independently derived dilation. The causal and propagation bridge is sharpened in two directions. First, a previous can- didate definition of a null relation by vanishing accumulated interval volume is proved degen- erate: every comparable pair admits a chain of links, so that criterion vanishes throughout the causal order. Link ensembles remain useful near-null approximants, but the null sector is therefore a limiting or measure-relative object rather than a pair-local primitive in the de- clared causal-set model. Second, the long-range free-chain calculation at 𝛼 = 2 is separated into two non-commuting limits. The infinite-range spectral symbol has maximal group veloc- ity 𝜋𝐽𝑎, whereas the envelope of finite-cutoff maxima tends to 2𝐽𝑎 Si(𝜋). These are spectral group-velocity statements; a causal signal cone still requires separate Lieb–Robinson-type hy- potheses. Isotropy and a unique physical Lorentz cone remain open. The defect bridge is updated with the completed 𝐾 = 512 data layer of the frozen ratio campaign. All 903 prescribed values of 𝜃 are present with eight branches each; 897 aggregate points are admissible and six lie in a short rejected interval. Neither √ 2 nor 𝜙 is a local or global minimum. The original preregistered primary ratio test nevertheless remains non- evaluable because its 𝐾 = 64 training gate is universally degenerate. Thus 𝐾 = 512 completes a characterization block; it does not retrospectively repair the primary estimator. Provenance registration and cross-platform verification remain pending. Version 4.0 turned Test 28A into an explicit reconstruction audit, and Version 4.1 retains that audit unchanged. For the standard three one-body extractions on ℋ = (C 3 ) ⊗3 , the combined linear map has exact rank 25 and kernel dimension 704. The hidden space splits as 192 two-body plus 512 fully traceless three-body directions; even the full 𝑆3-invariant class retains an exact 156-dimensional hidden sector. The preregistered continuation identifies an exact energy-selected fixed point, the totally antisymmetric state |𝜀⟩, while holonomy and variance objectives yield set-valued argmin correspondences. The historical non-triviality gate is therefore preserved but shown not to be a universal criterion, and no retroactive 𝑉28.4 verdict is declared. A prospectively frozen two-local QPH family provides an exact computer-assisted existence witness: its cycle-phase differential has rank 704/704 on the marginal kernel for the primary family and two preregistered replications, so marginals plus relational cycle phases are locally in- formationally complete in the fixed regularity stratum. Canonical modular-mismatch selectors are then audited rather than assumed. Identical additive qutrit references and every single pure mismatch under exact 𝑆3 protection obey strict capacity/rank no-go bounds. On the protected 156-dimensional domain a physically generated mixed mismatch has sufficient raw capacity but standard phase-only QPH remains incomplete. Exact cumulant analysis explains why order three is the natural next layer: the 𝑆3-hidden sector decomposes as 156 = 36 + 120, and the third connected cumulant is a complete affine coordinate on fibres of fixed proper marginals. A historical preregistered cubic-moment completion is retained only as a delicate T-NUM wit- ness, not as a theorem premise. This is the declared stopping point of the arity/cubic line: selecting one specific cubic observable would require a new independent physical law. Test 28B remains suspended. Version 4.0 added one further macro-level correction, retained in Version 4.1. Causal and conformal structure, transport geometry, stable matter sectors, and quantum correlations are treated as parallel downstream representations of one substrate model, not as a serial matter– space–time chain. A proposed identification of the matter admissibility projector Πadm with spacetime volume is rejected in its literal form: the projector is matter-branch specific, need not be nested under generative updates, and has no canonical finite trace in a type-III con- tinuum. In its place a conditional causal–transport conformal closure theorem is proved. If a causal reconstruction supplies a Lorentzian conformal class and an independent transport limit supplies a positive spatial metric on the same spacelike distribution, the conformal factor is fixed pointwise exactly when the two induced spatial metrics are conformally compatible. A scale-free generalized-eigenvalue defect provides a direct falsifier. The corresponding clock– cone–matter gate is also corrected by conformal weight: frequencies and dimensionful spectral scales have lapse weight one under a pure lapse deformation, whereas spectral ratios, localiza- tion fractions, and dimensionless stability-window coordinates have weight zero. A Tolman– thermal-time comparison is retained only as a relative lapse-profile gate; absolute time units remain open. Version 4.1 introduced a controlled common-substrate realization. Version 4.1.1 corrects its scope: parity alone excludes only an odd or linear mass/source identification with the same signed coordinate; an even law such as 𝑀 ∝ 𝑑 2 is not excluded by parity. On the declared graph Klein–Gordon sector, charge conjugation reverses Noether/gauge-current orientation while leaving mode energy and localization intensity unchanged. A grounded-graph Green- kernel theorem fixes the spatial uniformity of the cross-term sign, while the Coulomb sign itself is conditional on realizing a non-dynamical 𝐴0-type constraint sector; the same kernel in a dynamical scalar sector gives the opposite sign. A separate no-go proves that matter Dirichlet energy alone cannot select a nontrivial interior geometry. A state-selected positive geometry Hessian yields the conditional linear response 𝑦 = 𝐾 −1 𝐸 𝜏 , so weak 𝐶-even stress sources add while 𝐶-odd currents can cancel. The principal new bridge is a conditional stationary common causal–transport–matter con- struction. If one protected center supplies a common base, the transport branch supplies a positive spatial metric ℎ, and several modular/physical clocks agree on one relative lapse 𝑁, then 𝑔CTM = −𝑐 2 *𝑁2𝑑𝑇2 + ℎ has one timelike sign, predicts the same null front for all canonically normalized matter sectors, and fixes its stationary volume element without an additional scalar measure. Different masses and opposite 𝑈(1) representation weights remain lower-order data and do not alter the characteristic cone. The independently reconstructed HSMI conformal class remains a held-out test rather than an input to this construction. A second independent Version 4.1 result supplies a conditional physical law selecting com- plex rank two. A nonzero-Chern line cannot be closed under conjugation at rank one on 𝑆 2 , whereas 𝐿 ⊕ 𝐿¯ is the minimal conjugation-closed carrier; independently, ClC 2 ≃ 𝑀2(C) has minimal irreducible complex module dimension two. The existing odd-Chern defect-link con struction realizes this pair. If its Clifford algebra is physically admissible, the local carrier has 𝑀2(C) qubit kinematics. This is not an assertion that opposite electric charges form a coherent qubit, nor that every particle is a qubit. The resulting Version 4.1.1 is a constrained foundational proposal with a frozen primitive core, stronger positive and negative bridge results, a first common stationary geometry can- didate, an independently motivated minimal rank-two carrier, and a reproducibility-oriented ledger for every step from ontological determinacy toward physics. It also makes the external spin-sign, soft-graviton, equivalence-principle, and mass-budget inputs explicit without treat- ing them as evidence for the ontology.