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.
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.
This Zenodo collection brings together three coordinated studies from the PAC–(\mu^8) research programme. The papers address three distinct but connected questions: [\text{What qualifies as a physical object?}] [\text{Under what dynamical conditions does a complex structure emerge on a real state space?}] [\text{Can an experimental certification framework transfer across physically different realizations of time-crystalline order?}] The collection is organized as a progression from philosophical reconstruction, through mathematical audit, to public-data and cross-platform empirical assessment. 1. PAC–OBJ–001 From Position to Certified Object: A Historical and Modal Reconstruction of Physical Objecthood This paper reconstructs the development of physical objecthood from geometrical position and the Newtonian material point to relativistic events and worldlines, field modes, spectral packets, experimental records, and certified object classes. Its central proposal is that physical objecthood should not be treated as a primitive visual or spatial fact. Instead, an object may be understood as a process-generated structure that remains identifiable through persistence, invariant relations, recordability, separability from background, and robustness under admissible perturbations and changes of protocol. The paper introduces the PAC distinction between: [\text{field existence},\qquad\text{mode existence},\qquad\text{certified object status}.] It does not claim that observation creates physical reality, nor that all objects are periodic resonances. Its narrower thesis is that public and scientifically warranted object reference depends on stable relations among dynamics, boundaries, records, reconstruction, and certification. 2. PAC–MAT–001 Complex Structure from Real Reversible Dynamics: A Domain, Kernel, Uniqueness, Irreducibility, Spectral-Support, and Positive-Energy Audit This paper provides a mathematical audit of the claim that an orthogonal complex structure can arise from real reversible dynamics. For a strongly continuous orthogonal one-parameter group on a real Hilbert space, the skew-adjoint generator (A) admits a polar decomposition on the closed dynamical support (\ker A)^\perp \overline{\operatorname{Ran}|A|},] of the form [A=J_A|A|,] where [J_A^*=-J_A,\qquadJ_A^2=-I,\qquad[J_A,|A|]=0.] The audit shows that: mere invertibility is insufficient; norm-preserving orthogonal dynamics are required; the complex structure is canonically selected only on the non-stationary dynamical support; the kernel of (A) does not acquire a preferred complex structure without additional choices; positive energy is not required for the mathematical existence of (J_A); a positive-energy and future-time convention selects the Schrödinger orientation and the positive Hamiltonian[H=\hbar|A|;] the positive operator[K=|A|^2]does not by itself determine phase orientation; irreducibility and a spectral gap are not required for existence, although they can matter for uniqueness under larger symmetry algebras and for perturbative stability. The paper therefore narrows the legitimate claim: the imaginary unit may represent the quarter-turn structure canonically associated with oriented real orthogonal dynamics on their dynamical support. It does not claim that this construction alone derives the Born rule, quantum measurement, relativistic quantum field theory, particle content, gauge groups, or the Standard Model. 3. PAC–DTC–002–R1M Cross-Platform Transfer Audit of Multi-Witness Certification in a Room-Temperature Prethermal Time Crystal This study examines whether the multi-witness certification architecture developed for a many-body-localized discrete time crystal on a superconducting quantum processor can be transferred literally to a physically different realization: a room-temperature prethermal discrete time crystal in a three-dimensional dipolar (^{13}\mathrm C) nuclear-spin ensemble in diamond. The literal transfer fails at the level of witness availability and physical mechanism. The original MBL-DTC protocol relies on observables such as processor echo, localization, programmable initial-state testing, and finite-size spin-glass order. These measurements do not transfer directly to a prethermal NMR ensemble governed by different stabilization and failure mechanisms. Under the frozen literal witness set, the direct evidence coverage is only [\kappa_{\mathrm{direct}}^{\mathrm{literal}}=25%,] or [\kappa_{\mathrm{augmented}}^{\mathrm{literal}}=37.5%] when partial literature-level evidence is included. The appropriate formal output is therefore [\mathsf{INDETERMINATE},] rather than PASS or FAIL. The study then identifies a more general transfer principle: [\boxed{\text{cross-platform certification should preserve evidence roles and failure logic,}\newline\text{not necessarily identical experimental observables.}}] For the prethermal time-crystal platform, relevant evidence roles include subharmonic locking, persistence, perturbation rigidity, interaction dependence, mechanism controls, separation from alternative phases, initial-state robustness, and collective order. Because this evidence-role map was constructed after inspection of the target experiment, the result is classified as a retrospective interface reconstruction rather than a prospective cross-platform validation. The current evidence level is therefore reported as [\mathrm{E2!-!META},] not E4. Unified Contribution Taken together, the three studies establish a disciplined sequence: [\boxed{\begin{aligned}\text{process and record}&\longrightarrow\text{qualified physical objecthood},\\text{real reversible dynamics}&\longrightarrow\text{complex phase structure on dynamical support},\\text{platform-specific observables}&\longrightarrow\text{common evidence roles and controlled certification}.\end{aligned}}] The collection develops PAC–(\mu^8) primarily as a framework for philosophical clarification, mathematical interface analysis, and auditable public-data research. It emphasizes explicit assumptions, domain restrictions, carrier separation, evidence coverage, negative results, and the formal possibility of an INDETERMINATE outcome. The collection does not claim that: PAC–(\mu^8) has been experimentally verified as a whole; the three papers constitute a completed unified physical theory; complex structure alone derives all of quantum mechanics; time-crystal experiments validate a universal value of (\mu_*); many-body localization and prethermalization are the same physical mechanism; all physical objects are resonances; public-data reconstruction is equivalent to performing a new experiment. No new physical experiment was conducted in these studies. The empirical component consists of independent secondary analysis and methodological comparison based on published experimental results and publicly described data products. The collection is intended to demonstrate a more modest but testable research standard: [\boxed{\text{a PAC claim should be accepted only after its assumptions, carrier, records,}\newline\text{evidence role, uncertainty, and failure conditions have been made explicit.}}] Suggested Keywords PAC–(\mu^8); physical objecthood; certified object; process ontology; complex structure; real Hilbert space; skew-adjoint generator; polar decomposition; imaginary unit; reversible dynamics; positive energy; discrete time crystal; prethermal time crystal; many-body localization; cross-platform certification; public-data research; evidence-role mapping; mathematical audit; philosophy of physics
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.
A timing signature is not physics until its reference operator survives a representation audit. CV⋆=FR2,UT⋆=1−FR2,CV⋆+UT⋆=1 This framework separates three objects that must not be merged: a completed historical event, the record support still accessible to a laboratory, and a separately calibrated timing observable. Standard quantum theory closes the optimized coherent-recovery envelope. QTT adds a distinct, falsifiable timing complement only after a physical intertwining certificate proves that the laboratory record operator and the central timing projector are the same physical object in two representations. A public 11,009-trace test of explanatory burden Version 1.4 executes the complete usable public archive associated with Gosling et al., Probing the memory of a superconducting qubit environment. Every trace is split chronologically into training, a discarded guard interval, and held-out testing. The ordinary one-TLS Solomon camera learns two rates per trace, while the memoryless comparator learns one. median(RMSE0RMSE0−RMSETLS)=0.36015,P(TLSwins)=11,00910,169=0.92370 The fitted TLS camera is therefore a successful held-out effective model. Its resolved trajectory is not a parameter-free derivation: the values of Γq and Γqt are learned from each target-bearing trace's training segment. Version 1.4 makes that distinction machine-auditable through the target-fit burden vector BM=(Nc,Nd,Nw,Nn,Nu,Nh),BM=0⟹the fitted output is not derived parameter-free. The QTT result A public QTT source statement from 12 November 2025, before the Gosling preprint, already required complete reset to erase distributed record support beyond the visible carrier. That statement contains no Gosling-fitted rate, hidden-mode count, target window, or trajectory coefficient. The resulting comparative verdict is QTT-ZERO-FIT-SOURCE-EXPLANATORY-VICTORY/TRAJECTORY-VERDICT-OPEN. This is a scientific victory at the source/ontology layer, not a claim that QTT has already predicted the same resolved qubit trajectory. The stronger same-observable verdict remains locked because the public archive does not independently provide the residual record fidelity Fres, leakage diagnostic D, timing complement UT, or physical intertwiner W. The paper prints the exact next experiment that would close or falsify that bridge. Reproducibility 11,009 row-level held-out results are included. The 840 traces favoring or tying the memoryless camera are retained. No false significance is assigned to correlated sweep windows. All three official archive objects pass their published MD5 checks. The release verifier passes 30/30 scientific and provenance checks. Three adversarial reviews cover observable equality, leakage and selection, chronology, and claim scope. Version: 1.4 Concept DOI: 10.5281/zenodo.21902886 Author: Ali Attar Website: quantumtraction.org Reader anchors Completed-record timing blind test Dynamic-circuit record-timing extension Observation as Access Quantum Traction Theory: Main Book Gosling public data archive The PDF is the default preview. The reconstruction archive contains the LaTeX source, row-level CSV, public-data integrity receipt, chronology certificate, fit-burden certificate, analysis scripts, exact source checks, adversarial and render audits, metadata, and checksum manifest.
PAC–µ 8 is a unified operator–spectral and audit–protocol framework designed to make physical and mathematical claims simultaneously (i) structurally minimal, (ii) modality-invariant, (iii) falsifiable through pre-registered numerical windows, and (iv) auditable via replayable, machine checkable certificates. Its core is an AV/AQ dual presentation: a positive self-adjoint generator K ≥ 0 with Ω = √ K and Hamiltonian H = ℏΩ, coupled to an explicit boundary interface represented by an edge projector Πedge(∆) and protocol-defined calibration maps. A distinguished universal scale µ∗ ≈ 1.86 × 10−4 (with visibility floor √µ∗ ≈ 1.36%) anchors a universal log– budget J∗ = − 1 2 ln µ∗ used as a common currency across heterogeneous experimental windows. On the AQ side, a generalized Lindblad family is adopted as the canonical “mother equation”, specialized by H = ℏ √ K and boundary-tied Lindblad operators scaled by µ∗. On the verification side, PAC–µ 8 introduces auditable certificate packs (CCP), conformance rules (CR), semantic tests (CTS), and decision transcripts that strictly separate closure failures (non-replayable / non-conformant) from physics-level falsification. This paper provides a concise, publication-ready definition of PAC–µ 8 , its axioms, its main equations, its phase–arithmetic spectral axis (PAS), and its certification discipline.
This paper develops a mid-level structural layer in the PAC–µ 8 framework by introducing resonance families as the primary certifiable units between spectral dynamics and object-level appearance. The central claim is that physically persistent and observationally identifiable structures are not most naturally modeled as isolated states, but rather as stable families of phase-organized, boundary-compatible, and protocol-certifiable modes. We formalize the basic PAC–µ 8 data as a quintuple P = (H, K, Πedge, µ, Q), where H is a state space, K is a positive spectral generator, Πedge is a boundary projector or boundary protocol, µ is an audit/compression scale, and Q is a class of admissible protocols. On this basis we define resonance seeds, resonance families, protocol records, certification functionals, objectification thresholds, and inter-family coupling kernels. We formulate theorem-level principles linking local spectral organization to family formation, family certification to event bundles and objecthood, measurement to family-sector stabilization, and large-scale geometry to the coupling graph on family space. The framework is then illustrated through sharpened worked realizations on quantum graphs and topological edge sectors, together with a broader discussion of non-Hermitian skin phenomena and quasicrystalline order. The resulting picture suggests that PAC–µ 8 is most coherently interpreted not as a universe of isolated objects, but as a universe of generated, filtered, coupled, and certified resonance families.
Here is a polished description suitable for Zenodo, repository metadata, or the front matter of the revised paper: This verified v2 audit examines a supplied manuscript attributed to Wen et al. reporting the reconstruction of 1,419,857 discretized single-photon paths from 85 complex propagator measurements obtained across 17 spatial sites and five time steps. The analysis independently checks the manuscript’s arithmetic and physical quantities, corrects interpretations that extend beyond what the reported experiment establishes, and applies the Scretching Quantum Chain (SQC) and Maxwell–Scretching Chain (MSC) only at interfaces where their use is physically and mathematically appropriate. The revised edition additionally verifies the manuscript against the indexed primary publication: PMC13510607; PMID 42647606; Science Advances 12(35), eaeh1011; DOI 10.1126/sciadv.aeh1011. Quantities and performance measures that could not previously be independently reproduced are reconciled directly with the published Results and Materials and Methods sections. The reported path count is confirmed exactly as 17⁵ = 1,419,857. Using λ = 795 nm and a propagation step of 15 mm, independent recalculation gives a photon frequency of ν = 3.7709743 × 10¹⁴ Hz, photon energy Eγ = 2.4986740 × 10⁻¹⁹ J = 1.55955 eV, paraxial effective mass m_eff = h/(λc) = 2.78015 × 10⁻³⁶ kg, and propagation time Δt = 5.00346 × 10⁻¹¹ s. These values reproduce the prior audit and agree with the physical parameters of the primary report to the stated precision. The spatial-grid spacing inferred from the ±48.72 μm range is 6.09 μm and is independently confirmed by the published coordinate interval x_k ∈ [−0.0487 mm, 0.0487 mm]. Performance figures previously retained as provisional are also confirmed against the primary Results section: propagator fidelity of 98.5%, Postulate I fidelity of 94.4%, Postulate II fidelity of 94.7%, Postulate I mean absolute percentage error of 4.45%, propagator MAPE of 8.17 ± 3.50%, and Postulate II MAPE of 17.4%. A further source-level discrepancy is identified. The published Abstract reports a Postulate I fidelity of 94.9%, whereas the Results section reports and computes 94.4%. The resulting 0.5-percentage-point difference originates in the primary publication itself rather than in the supplied manuscript or the present audit. Overall, the v2 report strengthens the verification status of the reconstructed-path analysis by distinguishing exact combinatorial results, independently reproducible physical quantities, source-confirmed experimental metrics, and interpretation-dependent extensions. It also clarifies the proper roles of the SQC and MSC as cross-domain conversion and consistency frameworks rather than replacements for the underlying quantum-optical propagation model.