Finite-time return measurements can assign the same stability label to different dynamical responses. We document this ambiguity in a periodically kicked Ising chain initialized in a Neel product state, and replace an earlier numerical claim with a reproducible finite-model benchmark. For ten spins, even-period return highlights identity-like pulse settings as well as a period-doubled cycle. Signed odd-period and Fourier diagnostics distinguish these cases. At the perfect-pulse point, diagonal phase perturbations preserve the basis-state cycle exactly. Under fresh Gaussian transverse rotations, the alternating ensemble-mean local correlation has envelope exp(-2σ²n), independently of the diagonal Ising coupling. Independent local channels also give an elementary product expression for the ensemble cycle fidelity; a shared pulse-angle fluctuation has the same local mean but can have a different fidelity. These ensemble identities do not determine nonlinear per-realization scores, whose averaging order must be retained. All simulation results derive from one newly seeded state-vector dataset with raw traces and source hashes; analytic controls are evaluated separately. The resulting shelves and sampled noise crossings describe a specified preparation, channel, diagnostic and observation window. They supply no evidence for a universal discreteness mechanism, interaction protection from these exact-center ensemble observables, or a thermodynamic time-crystal phase. Corrective release with the corrected manuscript, code, data and figure pipeline. Related Research Square record: https://www.researchsquare.com/article/rs-8790240 . This version replaces the earlier audit bundle with the reviewed reproducibility package. Archived claims are retained for provenance and are not endorsed. This preprint is not peer reviewed.
Finite-time return measurements can assign the same stability label to different dynamical responses. We document this ambiguity in a periodically kicked Ising chain initialized in a Neel product state, and replace an earlier numerical claim with a reproducible finite-model benchmark. For ten spins, even-period return highlights identity-like pulse settings as well as a period-doubled cycle. Signed odd-period and Fourier diagnostics distinguish these cases. At the perfect-pulse point, diagonal phase perturbations preserve the basis-state cycle exactly. Under fresh Gaussian transverse rotations, the alternating ensemble-mean local correlation has envelope exp(-2σ²n), independently of the diagonal Ising coupling. Independent local channels also give an elementary product expression for the ensemble cycle fidelity; a shared pulse-angle fluctuation has the same local mean but can have a different fidelity. These ensemble identities do not determine nonlinear per-realization scores, whose averaging order must be retained. All simulation results derive from one newly seeded state-vector dataset with raw traces and source hashes; analytic controls are evaluated separately. The resulting shelves and sampled noise crossings describe a specified preparation, channel, diagnostic and observation window. They supply no evidence for a universal discreteness mechanism, interaction protection from these exact-center ensemble observables, or a thermodynamic time-crystal phase. Corrective release with the corrected manuscript, code, data and figure pipeline. Related Research Square record: https://www.researchsquare.com/article/rs-8790240 . This version replaces the earlier audit bundle with the reviewed reproducibility package. Archived claims are retained for provenance and are not endorsed. This preprint is not peer reviewed.
This repository contains the complete reproducibility bundle for PAC–DTC–001-R1F, an independent secondary analysis of the quantum-processor discrete time-crystal experiment reported by Mi et al. in Nature 601, 531–536 (2022). The study evaluates whether the certification architecture of the PAC–(\mu^8) framework can be translated into an explicit, auditable analysis of established experimental evidence. Rather than treating a subharmonic peak or period-doubled oscillation as sufficient evidence of time-crystalline order, the analysis applies a non-compensatory, multi-witness structure involving temporal persistence, echo-based separation of external decoherence from internal thermalization, initial-state typicality, effective-energy independence, localization of perturbations, and finite-size spin-glass order. A reconstruction of the published finite-size trends yields an estimated crossing point [\widehat g_{\mathrm{cross}}=0.8688,] with a Monte Carlo interval of (0.8663)–(0.8710) when only figure-digitization uncertainty is propagated. Because this interval does not include hardware systematics, finite-time effects, finite-size drift, or model-selection uncertainty, the study adopts the more conservative range [g_{\mathrm{cross}}\simeq0.86\text{–}0.88,] which is compatible with the finite-system critical region reported in the original experiment. The multi-witness stress test also shows that a criterion based only on subharmonic response can falsely accept a long-lived prethermal response associated with special initial states. The PAC-style hard-gate analysis rejects this comparator because it fails additional tests of state typicality, energy independence, and localization. This result supports the operational usefulness of a non-compensatory certification architecture, but it does not establish new Floquet or many-body-localization dynamics. The present release is designated R1F, where “F” denotes figure-level reconstruction. It uses digitized published figures and numerical facts explicitly reported in the original paper. It is not presented as a byte-level reproduction from the official Zenodo CSV archive, and no new physical experiment was performed. The current evidence level is classified as E2-FL: published experimental conclusions are reconstructed at figure level, and the PAC–(\mu^8) certification interface is shown to be computationally operational. The release does not claim that PAC–(\mu^8) outperforms the original collaboration’s multi-witness physical analysis, validates a universal value of (\mu_*), or experimentally proves the broader ontology of the PAC–(\mu^8) framework. The archive includes: English and Chinese technical reports; the English LaTeX source; analysis and reproduction code; digitized finite-size data with provenance records; witness and mechanism-comparison tables; Monte Carlo uncertainty results; reconstructed figures; machine-readable result summaries; analysis-lock and claim-registry files; source-audit records and integrity checks; unit tests and reproducibility instructions. This release is intended as a transparent methodological benchmark for connecting PAC–(\mu^8) concepts—protocol, record, witness, certification, failure vector, and object status—to publicly reported experimental evidence while preserving clear boundaries between external experimental facts, secondary reconstruction, framework-specific interpretation, and untested conjecture.
For pure state unitary dynamics, the Mandelstam Tamm (MT) lower-bound functional compares the endpoint Fubini Study return angle with path averaged energy dispersion. Their distinct size and temporal dependences obscure the origin of period two MT structure in discrete time crystal (DTC) like dynamics and its relation to the spin response. For binary Floquet drives, we derive an exact segment resolved MT expression without assuming commuting segment Hamiltonians and apply it to a disordered Floquet Ising chain. Absolute and uniform summability of connected covariances of local energy terms implies an O(L) upper bound on the path-averaged energy dispersion. Endpoint data for four system sizes are consistent with this leading behavior and support the corresponding rescaling of the MT functional. At a representative point in the finite-size region with a locked spin response, odd and even rescaled MT branches remain separated throughout the 102 period observation window. The return angle alternates strongly, whereas the size-normalized path-averaged energy dispersion shows little discernible parity dependence, indicating that endpoint geometry is the main source of the branch splitting. Across the interacting parameter grid, the period-two MT component has a strong partial Spearman rank correlation with the locked spin response after controlling for pulse error and interaction strength. The rescaled MT functional characterizes the global return geometry of finite-size period-two dynamics and quantifies its association with the locked spin response.
We give a self-contained explicit counterexample for the existential unregularized bounded-region fermion question on printed page 371 of Oberwolfach Report 7/2025, with pointwise operator-norm topology distinguished from strong-operator topology on page 365. In dimension three, one fixed smooth nonnegative radial compactly supported pair potential and one fixed interaction ball give a fixed smooth normalized annihilation mode whose Heisenberg norm differences tend to the maximal value 2. Explicit packed finite-particle Slaters and times pi/(2N+1-kappa) witness the same vector-norm limit, a stronger vector asymptotic, and changing normal-state values tending to 4. Both diagonal-density and normal-ordered interactions are covered with ordered-pair coefficient 1 and no ultraviolet smearing. A fixed smooth-cutoff commutator, Slater second moment and two-sector Duhamel comparison give error O(N^(-1/6)+N^(-1/3)). The kinetic energy acts on all of R³. Continuity on every fixed vector and in every fixed normal state remains valid. Siebert's arXiv:2609.34402v1, submitted 28 September 2026 before the original 7 October candidate, supplies the earlier high-density cluster and localized phase mechanism. Its stated theorem concerns full-space difference potentials, but its proof directly adapts to this bounded symmetric cutoff kernel and yields the qualitative existential conclusion. Its Proposition 2.6 explicitly gives maximal norm 2 for the full-space constant-number reference. The present note gives an explicit free-Slater transfer to the fixed spatial cutoff. A separately checked audit-time energy bootstrap also recovers the cutoff maximal limit through the earlier localized phase mechanism. These cutoff implications are deductions made in the audit, not literal cutoff theorems attributed to the prior paper. No first solution, first quantitative refinement, historically certified novelty, or continued open status through October 2026 is claimed. The bounded primary-source priority audit records access and indexing limitations. This five-page unrefereed research note is accompanied by its identical authored PDF/LaTeX source, unchanged 26-file historical candidate and independently authored analytic, operator-algebra, computational, source/model, priority and priority-mapping audits. The fresh computational family has 2,668 exact finite predicates and 558 floating diagnostics; finite tests supplement the universal written proof, and numerical diagnostics are not rigorous interval enclosures or formal proof certificates. Historical optimized-assertion and inventory weaknesses are repaired by externally pinned closed regular-file validation and isolated nonoptimized checker execution, while all original bytes and the original 1/5 candidate count are preserved. Historical result outputs are not claimed byte-identical to current replays, and runtime source-byte checks are explicitly omitted. AI tools were used extensively in development, verification, adversarial review and writing. Independent AI-assisted review is not human or journal peer review; neither is claimed. No copied third-party source bodies are distributed. No all-potential, all-region, dimension-one/two, fixed-density/energy, thermodynamic, fixed-state-discontinuity or CAR-invariance result is asserted.
Replication Data and Code for: "Capturing the Universality Class of the 2D Ising Model via Symmetry-Corrected Machine Learning and Finite-Size Scaling" This repository contains the complete source code, simulation datasets, and analysis scripts required to reproduce all findings presented in the associated manuscript. The study introduces a symmetry-corrected machine learning pipeline (Gauge-Fixed PCA + Logistic Regression) to identify phase transitions and estimate critical temperatures with high precision, validated on the two-dimensional Ising model. Repository Contents: 01_generate_data.py — Generates 2D Ising model spin configurations using the Wolff cluster algorithm. Produces equilibrium datasets for lattice sizes L∈{32,48,64,96}L \in \{32, 48, 64, 96\} L∈{32,48,64,96} with 10,000 independent configurations per temperature point. 02_analysis_pipeline_v2.py — Core analysis script: performs gauge fixing (σ′=σ⋅sgn(m)\sigma' = \sigma \cdot \mathrm{sgn}(m) σ′=σ⋅sgn(m)), PCA dimensionality reduction (d=16d = 16 d=16, cross-validated), confusion-scheme classification with parabolic sub-grid interpolation, bootstrap uncertainty quantification (Nboot=50N_{\rm boot} = 50 Nboot=50), and pFMp_{\rm FM} pFM computation with isotonic calibration. Outputs summary_ml_v2.json. 03_plot_main_figures.py — Reproduces Figures 1–6 of the main manuscript. 04_plot_supplementary_v2.py — Reproduces Supplementary Figures S1–S5 and Table 1. ablation_preprocessing_S5.py — Standalone preprocessing ablation script: runs raw and ∣m∣|m| ∣m∣-only comparisons and generates Supplementary Figure S5. Does not modify main results. summary_ml_v2.json — Pre-computed results (gauge-fixed pipeline) for immediate reproduction of all main figures without re-running Monte Carlo simulations. summary_ml_v2_raw.json — Pre-computed ablation results: raw (no gauge fixing) preprocessing, L∈{32,64,96}L \in \{32, 64, 96\} L∈{32,64,96}. summary_ml_v2_absm.json — Pre-computed ablation results: ∣m∣|m| ∣m∣-only preprocessing, L∈{32,64,96}L \in \{32, 64, 96\} L∈{32,64,96}. Table1_Tc_Comparison.tex — LaTeX source for Table 1. requirements.txt — Python dependencies. README.txt — Step-by-step reproduction instructions. Methodology Highlights: System sizes: L∈{32,48,64,96}L \in \{32, 48, 64, 96\} L∈{32,48,64,96} 10,000 independent configurations per temperature point; Wolff cluster algorithm with 10410^4 104 thermalization steps Symmetry correction: global Z2\mathbb{Z}_2 Z2 gauge fixing prior to PCA Confusion scheme: validation cross-entropy minimization over T0∈[2.10,2.45]T_0 \in [2.10, 2.45] T0∈[2.10,2.45] (60 candidate values, band Δ=0.05\Delta = 0.05 Δ=0.05, 5-fold CV) Bootstrap: 50 configuration-level resamples; parabolic sub-grid interpolation for discretization bias reduction Key result: Tc≈2.2717(8)T_c \approx 2.2717(8) Tc≈2.2717(8) for L=96L = 96 L=96 (0.6%0.6\% 0.6% from Onsager); universality class confirmed via FSS data collapse with ν=1\nu = 1 ν=1
Broad response regions in a reaction-rate ratio do not by themselves identify a biological transduction mechanism. This correction audits the earlier quantum-biological transduction preprint, distinguishes its original and later model versions, and checks selected outputs from a related corrected radical-pair study. Nondimensionalization and explicit two-point error bounds show why a fixed recombination-rate ratio does not generally preserve the absolute response when magnetic frequencies remain fixed. A classical two-stage success probability has a broad interior peak and exact rate-scale invariance; this establishes the non-specificity of curve shape, without reproducing magnetic anisotropy. The earlier pumped two-level model also lacks a specified finite readout: its unweighted population integral diverges when its stationary excited population is positive. Reaction generators, normalization, environmental channels and spectral overlap weights therefore require explicit treatment. Original figure producers and the advertised later source archive remain unrecovered. The numerical examples are attributed, known-target secondary evidence; no new spin simulation or biological experiment is reported. Claims of general formalism robustness, isotope catastrophe, cross-species ratio invariance and a physiological explanation are withdrawn. The retained contribution is an auditable correction and a set of model-comparison requirements. A matched-observable mechanism test and a demonstrated biological pathway remain absent. Corrective release containing the revised manuscript and audit supplement. Related Research Square record: https://www.researchsquare.com/article/rs-8800376 . Earlier unsupported interpretations are withdrawn as detailed in the manuscript. This preprint is not peer reviewed.
We construct an effective carrier model within the Worldline–Residue–Resource–Action framework. Two conditionally independent registers encode prime-factor multiplicities. A label-symmetric equality projector controls a common source coupled to two supplied particle-pair channels. One pulse generates the earlier collision-statistic probabilities without address-dependent interaction strength. A restricted single-register obstruction and a classification of diagonal permutation-invariant effects specify the construction’s resource assumptions. The implementation reproduces species probabilities, but not the preceding interface’s coherent output channel. Bare-energy conservation holds at the calibrated reference volume; detuning away from resonance requires interaction energy and switching work. A response identity relates the reference pressure-volume moment to the logarithmic-volume derivative of mean pulse work. Composition with the implemented muon-decay kernel recovers energy and pressure histories at full conversion. This is an executable effective interaction candidate and compatibility analysis; lepton identities, weak interactions, and the full fifteen-channel carrier are not derived from arithmetic alone. Version 0.2, editorial revision of 9 October 2026. Includes the English manuscript, Korean guide, and reproducibility archive. The 123 carrier-level checks are internal consistency checks, not experimental validation or external journal peer review. The manuscript was prepared before this deposit; its preparation-time statement that no public DOI had been assigned is superseded by this record. Preceding WRRA records: r11, https://doi.org/10.5281/zenodo.23237629; particle interface v0.2, https://doi.org/10.5281/zenodo.23241511; dynamic decays v0.2, https://doi.org/10.5281/zenodo.23246308. Correction release 0.2-r1 (9 October 2026): Table 3 now states that the hot electron branch has a positive pressure-volume moment; the antielectron-neutrino overbar in Section 6.2 is correctly rendered in the PDF. The scientific model, reproduction code and numerical results are unchanged. The manuscript retains its v0.2 designation and filenames; 0.2-r1 identifies this corrected deposit. A third Astra medium AI internal review and post-correction check examined the final files. Both required corrections were resolved, with no further mandatory technical corrections identified. The review report is included. This is not external journal peer review or acceptance. Earlier statements in the guide/review about two review rounds describe the historical pre-correction state.