Major revision, 19 October 2026. Existing single-particle continuous-time walk calculations on the planar 4.8.8 graph show several echo minima and two fitted arrival-time branches. We retain these numerical observations and their square- and honeycomb-graph controls, while correcting the spectral comparison and time units. The fitted values 0.81 and 0.60 are graph hops per echo step. The later full eight-band calculation reports velocity scales near 0.78 and 1/sqrt(2) in cell units per natural evolution time; neither the original ratio 1.42 nor its intermediate replacement 1.28 is retained. A quantitative branch-by-branch reconciliation remains open. The graph is a standalone walk model, not a current representation of the framework's three-dimensional substrate or a calculation of physical photon birefringence. Changes from earlier versions: The revision corrects hop/step versus cell/natural-time units. The revision reports the final full-band scales near 0.78 and 0.707 separately from echo fits; it withdraws both the original 1.42 and intermediate 1.28 spectral comparisons. The revision removes native-lattice, photon-birefringence and speed-unification claims. Identify the measured quantity as a single-particle probability echo rather than proof of many-body scrambling; correct the edge-family description. Retained result: Saved echo minima, finite-size controls and two fitted arrival branches on the standalone 4.8.8 graph. Previously titled: Lattice Birefringence: A Bifurcated Operator-Spreading Light Cone on the 4.8.8 Walk Graph. The preceding version and earlier versions remain available. This is a revised preprint, not an independently peer-reviewed result. It uses existing evidence; no new scientific calculations were run and research branches remain frozen. AI assistance is acknowledged in the manuscript. Revision guide for all twelve papers. The attached PUBLICATION_UPDATES.csv provides old and new titles, DOIs and replacement descriptions for catalogue and website updates.
Major revision, 19 October 2026. Existing single-particle continuous-time walk calculations on the planar 4.8.8 graph show several echo minima and two fitted arrival-time branches. We retain these numerical observations and their square- and honeycomb-graph controls, while correcting the spectral comparison and time units. The fitted values 0.81 and 0.60 are graph hops per echo step. The later full eight-band calculation reports velocity scales near 0.78 and 1/sqrt(2) in cell units per natural evolution time; neither the original ratio 1.42 nor its intermediate replacement 1.28 is retained. A quantitative branch-by-branch reconciliation remains open. The graph is a standalone walk model, not a current representation of the framework's three-dimensional substrate or a calculation of physical photon birefringence. Changes from earlier versions: The revision corrects hop/step versus cell/natural-time units. The revision reports the final full-band scales near 0.78 and 0.707 separately from echo fits; it withdraws both the original 1.42 and intermediate 1.28 spectral comparisons. The revision removes native-lattice, photon-birefringence and speed-unification claims. Identify the measured quantity as a single-particle probability echo rather than proof of many-body scrambling; correct the edge-family description. Retained result: Saved echo minima, finite-size controls and two fitted arrival branches on the standalone 4.8.8 graph. Previously titled: Lattice Birefringence: A Bifurcated Operator-Spreading Light Cone on the 4.8.8 Walk Graph. The preceding version and earlier versions remain available. This is a revised preprint, not an independently peer-reviewed result. It uses existing evidence; no new scientific calculations were run and research branches remain frozen. AI assistance is acknowledged in the manuscript. Revision guide for all twelve papers. The attached PUBLICATION_UPDATES.csv provides old and new titles, DOIs and replacement descriptions for catalogue and website updates.
Major revision, 19 October 2026. This revision separates three objects previously conflated: a classical [8,4,4] code, its one-code CSS stabilizer state, and a nonlinear set of 48 allowed eight-bit register words. The register admits a 32+16 partition by one generation bit. A declared evolution preserves that partition if its operators commute with the corresponding parity. This elementary conservation statement is retained; it does not establish a concatenated quantum code, a noise threshold or topological protection. The channel-friction ansatz, golden-ratio fixed point and XOR bookkeeping are given their proper conditional scope. Claims of CKM predictions and a derived particle-mass mechanism are withdrawn, as is the claim that the legacy walk is native to the corrected geometry. Changes from earlier versions: The revision removes concatenated-code/topological-protection claims and CKM/mass predictions unsupported by the declared register and retired transport law. The revision separates 16 codewords, a one-dimensional CSS stabilizer space and 48 allowed register words; the latter has Hamming distance one. The revision corrects the geodesic/line-graph count. The revision states a real recovery criterion and the hypotheses of the commutation argument. Retained result: Classical code facts, the nonlinear register count, a conditional sector-conservation proposition and explicitly conditional scalar/graph identities. Previously titled: A Concatenated Quantum Code with Topologically-Protected Outer Structure on the Q3 Hypercube: Channel-Friction Semantics and Applications to Particle Physics. The preceding version and earlier versions remain available. This is a revised preprint, not an independently peer-reviewed result. It uses existing evidence; no new scientific calculations were run and research branches remain frozen. AI assistance is acknowledged in the manuscript. Revision guide for all twelve papers. The attached PUBLICATION_UPDATES.csv provides old and new titles, DOIs and replacement descriptions for catalogue and website updates.
WITHDRAWAL NOTICE (18 October 2026). This paper is withdrawn and should no longer be cited as a result. It is built on a lattice geometry — the 4.8.8 tiling ("circlette") — that the framework retired between June and September 2026. The theorems and mechanisms tied to that geometry were withdrawn [G81, G84]. Its matrix element is a band velocity, not a gauge coupling, and fixes no interaction [K8, G84]; the velocity unification it supports was withdrawn [K7]. The research programme was concluded in October 2026; its review found the framework's Standard-Model content assigned rather than derived. The original description is kept below for the record. Original description (kept for the record): We analyse the symmetry structure of the continuous-time quantum walk on the 4.8.8 (truncated square) Archimedean tiling, whose bifurcated band structure was recently char- acterised via OTOC echo protocols [1]. Decomposing the 8 ×8 Bloch Hamiltonian into irreducible representations of the C4v point group at the Γ point, we show that the gapped slow branch transforms as the fully symmetric scalar representation A1, while the gapless fast branches transform as the two-dimensional vector representation E. At Γ, the Wigner-Eckart theorem enforces strict orthogonality between these sectors: ⟨A1|H|E⟩= 0. Away from Γ, symmetry reduction C4v →Cs breaks this selection rule. We compute the inter-branch matrix element exactly and find M=− i 2 sin kx for the Ex component, yielding a momentum- linear vertex M∝i(k·E) that is structurally identical to the p·A minimal coupling of quantum electrodynamics. We then promote the tight-binding hopping amplitudes to dy- namical U(1) link variables in a Wilson lattice gauge theory, demonstrate via a weak-field expansion that the gauge-covariant Hamiltonian reproduces the same vertex, and identify a two-coupling structure (β4,β8) rigorously locked by the tiling geometry. We formulate the velocity-unification conjecture—that renormalisation group flow drives the distinct bare group velocities toward a common infrared fixed point—as a concrete numerical programme for lattice Monte Carlo simulation.
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.
Reproducibility package for the paper "Number-projected coherent-state kernels for variational Bose-field dynamics" submitted to New Journal of Physics (2026). Contains the LaTeX manuscript source, Python benchmark scripts, numerical data (CSV), and publication-quality figures. Scripts reproduce all results (Figs. 1–5) for two-, three-, and four-mode Bose-Hubbard models using number-projected coherent states with fixed-basis Galerkin and moving-basis TDVP methods. Requirements: Python 3.8+, NumPy, SciPy, Matplotlib.
Major revision, 19 October 2026. A total ordering of tensor-product sites permits the standard Jordan-Wigner construction of anticommuting dressed operators. We retain the explicit exchange-sign calculation and the finite K_3 colour-label matrix identity, while separating both from particle statistics and colour confinement. An ordering-dependent parity string does not by itself select a physical fermionic algebra or local transport law. The earlier same-register product of orthogonal colour projectors is not a baryon creation operator, and the symmetric vector of a three-colour label space is not an SU(3) singlet. Fermionic matter remains an explicit premise in the later framework; the calculation is a conditional representation of exchange algebra, not a derivation of the spin-statistics connection. Changes from earlier versions: The revision withdraws derivation of baryon statistics, local fermion transport and colour confinement from XOR closure. The revision distinguishes Hermitian Majorana-like operators from nilpotent creation operators; a product of orthogonal same-register colour projectors is zero. A symmetric three-colour vector is not an SU(3) singlet; an anti-Hermitian square is not an energy argument. Retained result: Finite Jordan-Wigner anticommutation calculation and K3 matrix identities. Previously titled: Pauli Antisymmetry from F2 XOR-Closure: A Discrete-Geometric Derivation of Composite Baryon Statistics. The preceding version and earlier versions remain available. This is a revised preprint, not an independently peer-reviewed result. It uses existing evidence; no new scientific calculations were run and research branches remain frozen. AI assistance is acknowledged in the manuscript. Revision guide for all twelve papers. The attached PUBLICATION_UPDATES.csv provides old and new titles, DOIs and replacement descriptions for catalogue and website updates.