This release presents PooleQ/P Capture v5.6, a channel-resolved local-geometry framework for analyzing measured binary fields, p-bit samples, readout histories, and quantum syndrome-event data. The method preserves the Poole birth, survival, over-support, and strain channels rather than collapsing them into a single cellular-automaton update. The v5.6 amendment reframes PooleQ/P as a local-geometry spectrometer. It defines a decomposed signature vector[\mathcal S_{\rm Poole}(X)=(R_B,R_H,R_\psi),]where (R_B) measures birth-window or boundary geometry, (R_H) measures high-support geometry, and (R_\psi) measures support-strain geometry. The normalized spectrum (\Sigma_{\rm Poole}) identifies which local Poole geometry carries the measured structure. The included benchmark uses exact active-density matching, IID null controls, and same-density shuffled controls. Because shuffling preserves active-cell count while destroying local geometry, the results support the paper-safe claim that PooleQ/P detects structured local correlation beyond active density alone. This work does not claim to reconstruct unknown quantum states, clone qubits, or demonstrate quantum decoder superiority. It is presented as an interpretable measurement-side feature transform and diagnostic layer for structured binary data.
This release presents PooleQ/P Capture v5.6, a channel-resolved local-geometry framework for analyzing measured binary fields, p-bit samples, readout histories, and quantum syndrome-event data. The method preserves the Poole birth, survival, over-support, and strain channels rather than collapsing them into a single cellular-automaton update. The v5.6 amendment reframes PooleQ/P as a local-geometry spectrometer. It defines a decomposed signature vector[\mathcal S_{\rm Poole}(X)=(R_B,R_H,R_\psi),]where (R_B) measures birth-window or boundary geometry, (R_H) measures high-support geometry, and (R_\psi) measures support-strain geometry. The normalized spectrum (\Sigma_{\rm Poole}) identifies which local Poole geometry carries the measured structure. The included benchmark uses exact active-density matching, IID null controls, and same-density shuffled controls. Because shuffling preserves active-cell count while destroying local geometry, the results support the paper-safe claim that PooleQ/P detects structured local correlation beyond active density alone. This work does not claim to reconstruct unknown quantum states, clone qubits, or demonstrate quantum decoder superiority. It is presented as an interpretable measurement-side feature transform and diagnostic layer for structured binary data.
Matched quantum readouts often contain more structure than their local marginals display.The experiments studied here show a recurring pattern: some implemented-history squarescarry a stable non-additive component, while matched branch, key, retained-marker, Borncompatible, and separable controls collapse. History-selected geometric readout (HSGR) isintroduced as the geometry that summarizes this pattern. It keeps standard Born probabilitiesinside each specified operational channel, but assigns a relational scalar to the implementedhistory coordinate that survives presentation effects. The elementary coordinate is KHSGR =12(pAB + pBA − pAA − pBB), the mixed Walsh-Hadamard component of a four-cell probabilitytable. It cancels common bias, additive leakage, branch-separable response, matched-depth offsets,and separable analyzer effects. Superconducting, photonic, and raw-count quantum data motivateand test the construction. Tuna-9 gives selected mixed coordinates, orientation-odd signedholonomy, history-key nulls, and a retained-marker veto. Photonic mode-count data give signalcontrol screens, closed-holonomy fringes, coherent-key recovery, and lock-shadow-antilock controls.IBM count reductions give local-null decompression, phase-holonomy transport, quantum-eraserrecoverability, Born-compatible nulls, and backflow controls. The same geometry then gives arelational kernel for a hard CMV-B7 carrier-closure assay. A four-state RPHERNGFTVL/HLAB*07:02 kernel is selected from 3072 candidate protocols, with exactly one kernel satisfying thecarrier rules. A high-count Tuna-9 block measures the sixteen history cells at 6144 shots per cell.The hard-reference endpoint is positive, ΓRPH = 0.063070, with model-based SEind = 0.012351and zind = 5.11. Pooling with the earlier completed 2048-shot block gives ΓRPH = 0.065674,model-based SEind = 0.010712, and zind = 6.13. The result is a single carrier-kernel signal: a nonadditive antigenic relation is recovered by the connected history coordinate after local biologicalsimilarity, support-swap, pHLA-swap, raw-maximum, and separable zero-HSGR reductions fail,while strict subcell projections are reported as partial shadows of the implemented-historycoordinate
This paper reframes logical-qubit benchmarking from a scalar error-suppression problem into a branch-resolved logical-state maintenance problem. Conventional quantum error-correction reporting focuses on logical error rates, better-than-physical comparisons, code-distance scaling, decoder performance, and accepted-stream outcomes. These metrics are essential, but they do not by themselves reveal which stabilization mechanism produced the improvement, whether the result depends on active correction or detection-assisted filtering, how much acceptance overhead was paid, or which branches remain underdetermined because raw timing, reset, syndrome, leakage, or feed-forward records are unavailable. The central contribution is QHOME-RETROFIT, a branch-resolved diagnostic framework that operationalizes the Quantum-State Homeostasis condition of Paper 22 on published quantum error-correction records. The framework converts logical-state maintenance into normalized engineering margins, evidence-status labels, tiered verdicts, limiting-branch reports, and a reproducible CSV-first evaluation workflow. It separates restoration capacity, logical-basis sharpness, protected-mode occupation, source-sink coupling, logical gain, acceptance overhead, and repeated-round stability instead of collapsing them into a single logical-error-rate claim. QHOME-RETROFIT is not a new quantum processor, error-correcting code, decoder, or threshold theorem. It does not claim raw shot-level access where such records are not publicly available, and it does not treat detection-assisted post-selection as equivalent to full real-time source-sink closure. The core operating rule is: score only the branch supported by the released evidence, label what is weakly proxied, and leave underdetermined what the public record cannot decide. The manuscript is a systems-code and reproducibility-layer paper, not a hardware demonstration. It defines a diagnostic grammar, evidence classes, tier gates, reproducibility plans, raw-record replay boundaries, and package-level audit artifacts. Its companion package provides fixed CSV inputs, generated outputs, dashboards, tests, and manifest checks so that the branch verdicts can be inspected rather than accepted as prose claims. Before scaling claims about fault-tolerant quantum computing, this paper argues, researchers should test logical-state maintenance: whether a reported improvement is correction-driven, detection-assisted, acceptance-limited, repeated-round stable, source-sink supported, and sufficiently evidenced to justify the engineering claim being made. Keywords: QHOME-RETROFIT, quantum error correction, logical qubits, fault-tolerant quantum computing, logical-state maintenance, branch-resolved diagnostics, source-sink architecture, post-selection, accepted-stream filtering, reproducibility, systems code, evidence-status labels, tiered verdicts, logical error suppression.
We introduce the Quantum Measurement Timeline Framework (QMTF): an operational, target-relative account of quantum measurement that is timeline-complete and probability-correct. Core idea Declare a measurement target explicitly: what is registered, where it is registered, and when it is admitted as “the measurement,” at stated finite resolutions. Treat “measurement” as a localized quantum instrument, not as “anything that interacts.” Pipeline Target frame: 𝒟* = { (x_i, t_j) } (declared spacetime bins on which the measurement is admitted). Pre-measurement output: a sub-normalized joint spacetime support f_xt(x_i,t_j) = Tr(ρ E_(x_i,t_j)) p_surv = Σ_(x,t)∈𝒟* f_xt(x,t) Prediction layers (explicitly separated): Per-run (unconditional): P_abs over 𝒟* ∪ {∅} Conditional (given survival): P_cond defined only when p_surv > 0 Null handling (explicit): Includes a null outcome ∅ and a null decomposition (missed target vs reporting shortfall). Formal guarantees (in Appendix A) Formation→detection plane equivalence (“timeline equivalence”): evaluate at a formation plane and propagate, or evaluate directly at detection—predictions agree (up to discretization). No-signalling for localized instruments (operational locality). Finite-resolution stability via coarse-graining: predictions are stable under binning and converge under refinement. Worked constructions + artifacts Double slit benchmark (standard screen statistics) with a resolution-aware recombination/formation plane. Which-slit variant using an explicit instrument, with a tunable decoherence factor. Photon baseline (no intervening interactions) to show the same target logic in the simplest case. Runnable computational artifacts are released alongside the manuscript, with quality gates for verification. Positioning QMTF is interpretation-neutral: it does not assume any ontology for ψ. It is compatible with time-of-event POVMs and dilation (as an optional compatibility note, not a required ingredient).
Abstract We study whether a fixed qutrit feature geometry built from classical time-series derivatives and residual variability supports compact readouts that remain meaningful across heterogeneous cohorts. The eight special-unitary-group SU(3) Gell-Mann coordinates are derived analytically as deterministic functions of the four classical inputs, making the representation's inductive structure explicit. We then separate representation, candidate readout subspace, fitted direction, target detectability, and predictive utility under participant-separated evaluation. Human Activities and Postural Transitions (HAPT) data repeatedly select the gauge-fixed sector {λ₆, λ₈}. On Daphnet freezing-of-gait data, this core reaches pooled area under the receiver operating characteristic curve (AUROC) 0.72572 with participant-cluster jackknife 95% interval [0.63792, 0.81352], close to 0.72872 for the full eight-coordinate qutrit representation (Q3). A prospectively frozen FoG-STAR lower-back test fails its empirical detectability screen: the best pre-specified model has AUROC 0.50977 [0.45615, 0.56339]. A post-hoc event-level audit using archived fold-specific thresholds finds high nominal event sensitivity but 4.06 false alarms per minute on Daphnet and 27.69 on FoG-STAR primary, excluding a practical detector interpretation. Local encoder perturbations do not rescue the failed primary transfer. Same-information classical interaction features match or exceed reconstructed Q3 on several external settings. Thus neither quantum advantage nor SU(3)-specific predictive gain is supported. The contribution is a falsification-oriented, gauge-aware framework for testing whether compact operator readouts survive cohort, sensor, and task shifts.
Paper-5 develops a reproducible symmetry-resolved method for analyzing the internal structure of fixed-order many-body quantum correlator fields using Johnson-harmonic decomposition. Instead of compressing a large collection of labelled correlators into a single overall number, the method keeps the subset structure of the data and separates the centered correlator field into different harmonic layers. This makes it possible to see how correlations are organized inside a quantum system, not only how large the total correlation is. J742_Paper5_Main_Manuscript_DOI… This work is part of the broader QDL five-paper progression: Paper-1 — Exact Permutation Moments: develops exact finite-sample mean, variance, and covariance formulas for Walsh interaction-order energies under permutation. Paper-2 — Exact Distribution Laws: extends the framework to structured exact distributions, Krawtchouk-based reductions, computational-complexity boundaries, and continuation-horizon classification. Paper-3 — Exact Certified Tail Computation: develops certified deterministic counting methods for difficult exact tail probabilities in a structured finite Walsh/Clebsch problem. Paper-4 — Identifiability, Contrast Closure, and Frozen External Testing: studies restricted four-variable log-linear interaction models, rank, identifiability, contrast closure, and a frozen external statistical test. Paper-5 — Johnson-Harmonic Correlator Profiles: applies a symmetry-resolved framework to complete labelled quantum correlator fields and studies how their internal correlation structure is distributed across Johnson-harmonic layers. The central challenge in Paper-5 is that a many-body experiment can produce hundreds or thousands of labelled correlators. If these are reduced to one aggregate norm, important structural information can be lost. Paper-5 preserves the full labelled subset geometry and resolves the correlator field into interpretable harmonic components. What Paper-5 does: reconstructs complete fixed-order labelled correlator fields from public experimental data; removes the common-mode component and decomposes the remaining structure into Johnson-harmonic layers; computes layer energies and normalized structural statistics; uses exact finite-population projector calibration; preserves subset-label information instead of reducing everything to a single total norm; propagates uncertainty using source-native randomized experimental replicates; applies an exact finite-shot bias correction to quadratic layer energies; compares the physical signal with a source-defined noise-reference cohort; provides a reproducible computational route through QDL Research Suite v1.3.0. The mathematical Johnson/slice decomposition itself is established mathematics; the contribution of Paper-5 is the combined experimental-analysis workflow and its application to two independent public quantum datasets. J742_Paper5_Main_Manuscript_DOI… Main locked results: For the six-qubit tomography dataset, each setting contains 20 three-body correlators with harmonic dimensions 20 = 1 + 5 + 9 + 5. Across 28 source measurement settings, the pooled centered correlation structure is: H1 = 48.4133% H2 = 36.7277% H3 = 14.8590% This shows a distributed harmonic profile rather than concentration in a single layer. J742_Paper5_Main_Manuscript_DOI… For the independent 32-qubit hardware dataset, each seed contains 4,960 three-body correlators, decomposed as 4,960 = 1 + 31 + 464 + 4,464. Across nine frozen seeds, the pooled profile is: H1 = 0.341937% H2 = 0.123369% H3 = 99.534694% showing an extremely strong H3-dominant structure. J742_Paper5_Main_Manuscript_DOI… The H3-dominant result remains stable across 675 source-randomized physical twirls. A seed-blocked bootstrap gives a pooled H3 95% interval of approximately: 99.5301% – 99.5388%. J742_Paper5_Main_Manuscript_DOI… After exact finite-shot correction, the pooled H3 fraction changes only from approximately 99.53469% → 99.53486%, showing that ordinary finite-shot sampling bias is extremely small relative to the observed structure. J742_Paper5_Main_Manuscript_DOI… A source-defined noise-renormalization reference cohort gives the opposite profile: Physical corrected H3: 99.534860% Noise-reference corrected H3: 0.138145% providing a strong diagnostic contrast between the physical cohort and the source-defined reference data. J742_Paper5_Main_Manuscript_DOI… How Paper-5 connects to the earlier papers:Paper-1 provides exact permutation-moment tools. Paper-2 studies structured exact distributions. Paper-3 develops certified exact-tail computation. Paper-4 focuses on identifiability and restricted interaction models. Paper-5 moves to a different but related application layer: it uses structured mathematical tools to analyze the internal organization of many-body quantum correlation fields. Why it is useful:The method is useful when a quantum experiment produces many labelled multi-qubit or many-body correlators and researchers want to understand where the structure is located inside that large correlation field. Potential applications include: quantum-state tomography; randomized-measurement analysis; many-body quantum experiments; multi-qubit correlation analysis; quantum-hardware characterization; comparison of correlation structures across devices or experiments; finite-shot robustness checks; structured analysis of subset-indexed data; reproducibility and independent verification of quantum experiments. Rather than asking only: “How much correlation is present?” Paper-5 also asks: “How is that correlation organized across different symmetry layers?” This makes the method useful as a structure scanner for complex quantum correlation data. Reproducibility:The computational implementation for Paper-5 is included in QDL Research Suite v1.3.0, DOI 10.5281/zenodo.22972830. The software provides the Paper-5 computational reproduction route while preserving the original public datasets as the source authority. J742_Paper5_Main_Manuscript_DOI… Paper-5 Preprint DOI:10.5281/zenodo.22974172 J742_Paper5_Main_Manuscript_DOI… Scope:Paper-5 provides a structural and statistical diagnostic workflow. The Johnson decomposition itself is established mathematics. The paper does not claim a new universal Johnson theorem, Bell nonlocality, neutrino thermalization from the H3 statistic, a new physical mechanism, causation, retrocausality, future-state prediction, or a nonzero physical intervention parameter. J742_Paper5_Main_Manuscript_DOI… In simple terms:Paper-5 takes a large set of quantum correlations and breaks it into meaningful symmetry layers. Instead of giving only one total correlation number, it shows where the correlation structure lives inside the data. In the six-qubit experiment, the structure is spread across several layers. In the 32-qubit dataset, almost all of the centered structure appears in the highest Johnson layer, and this pattern remains stable after randomized-twirl analysis and finite-shot correction. In one sentence:Paper-5 is a reproducible structure-analysis framework for complex quantum correlation data that shows not only how much correlation exists, but how that correlation is organized inside the system.
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.