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.
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.
Here is a polished version suitable for Zenodo, manuscript front matter, or a research-paper description: This work extends the Scretching Quantum Chain (SQC) into a new experimentally grounded domain: directly measured complex propagators rather than solely tabulated transition observables. The strongest defensible extension is a local phase-action reconstruction, Ŝₖ = ℏ Arg(Kₖ), followed by additive path closure, Ŝⱼ = Σₖ Ŝₖ mod 2πℏ. This construction permits experimentally measured propagator phases to be translated into local and path-integrated quantum-action quantities while preserving the phase periodicity inherent in complex amplitudes. The Maxwell–Scretching Chain (MSC) can be incorporated when calibrated optical transmission or absorption measurements are available, allowing attenuation to be related to absorption cross-section, extinction coefficient, and dielectric loss. The present free-space experiment, however, does not independently determine molecular molar absorptivity and therefore does not by itself identify a direct ε → f molecular conversion chain. The underlying experiment, attributed to Wen et al., reports the reconstruction of 1,419,857 discretized single-photon paths from 85 measured complex propagators distributed across 17 spatial sites and five time steps. The present analysis independently checks the internally testable arithmetic and physical quantities, limits interpretations to what the experiment actually establishes, and applies the SQC and MSC only where the relevant physical observables are measured. The combinatorial path count is confirmed exactly: 17⁵ = 1,419,857. For λ = 795 nm and a 15 mm propagation interval, independent calculation gives ν = 3.7709743 × 10¹⁴ Hz, Eγ = 2.4986740 × 10⁻¹⁹ J = 1.55955 eV, m_eff = h/(λc) = 2.78015 × 10⁻³⁶ kg, and Δt = 5.00346 × 10⁻¹¹ s. The spatial interval implied by the reported ±48.72 μm range is 6.09 μm. Within the paraxial effective-particle representation, a transverse displacement of one grid interval contributes ΔS/ℏ = 0.00977071 rad per 15 mm propagation slice. The experiment provides direct support for coherent multiplication and summation of complex transition amplitudes within the tested discrete paraxial optical system. This constitutes a meaningful experimental interface for the SQC because both propagator magnitude and phase are available for reconstruction. It does not, however, establish that individual mathematical paths possess independent ontological reality, validate unrestricted interacting-particle path integrals, or independently confirm molecular Maxwell–Scretching relations not measured in the experiment. Several falsifiable extensions follow from the combined framework. These include an SQC action-closure residual for testing phase consistency across reconstructed paths; a gauge-invariant loop-phase observable; multiplicative uncertainty propagation for chains of measured complex propagators; explicit separation of phase evolution from attenuation in lossy propagators; and a combined absorption–action tomography experiment in which complex propagation and calibrated optical loss are measured simultaneously. Such an experiment would provide a direct interface between SQC phase/action reconstruction and MSC attenuation, cross-section, extinction, and dielectric-loss transformations. The resulting framework therefore does not replace the underlying quantum-optical propagator formalism. Instead, it adds a measurement-linked conversion architecture in which complex propagators can be translated into experimentally testable action relations, while optical-loss measurements can independently activate the Maxwell–Scretching branch. Six falsifiable applications and a dedicated validation protocol are developed to distinguish numerical closure, phase consistency, attenuation physics, and genuinely independent experimental confirmation.
Yong-Li Wen et al. (2026) experimentally test Feynman’s two path-integral postulates with single photons by measuring complex propagators and reconstructing 17^5 = 1,419,857 discrete path skeletons. This record accepts that experimental result within its declared paraxial domain and asks a different question: when a measurement architecture maps a richer source space into a reduced readout, which distinctions are actually measured, which are generated by deterministic composition, and which remain outside the jurisdiction of the declared task? ORIGAS Cabin 1/2 Device IX v9.5 formalizes this question as a measurement-architecture boundary. It develops task-relative representational jurisdiction, fibre-based sufficiency criteria, closure under intervention, covariance-aware model-manifold tests, frozen provenance, and independent null/recovery protocols. The public Wen/Dryad dataset is used as the empirical baseline; reconstruction depth is explicitly distinguished from independent source width and from representational completeness. The record freezes prospective tests rather than retrospectively fitting them: the P9-C/Q5/Q7 photon closure programme, a Point-0 balance prediction centered on an operationally definedμ = 1/2, +t/−t, K × T OFF/ON/recovery law, and the previously frozen Double RingCross outer-Solar-System prediction as a chronologically independent external adjudicator. A separate author-frozen layer records sociotechnical and AI-jurisdiction predictions, including the France 2026–2027 case study. These are explicitly separated from the empirical Wen photon results.** No Device IX calculation is presented as a measured validation of a physical World B, Complete EPR, +t/−t, K, T, or the Double RingCross. Bell/Aspect, Connes and Wen are treated as valid within their declared tasks. The narrower claim is that success of a reduced representation for one task does not establish injectivity, sufficiency, or closure for every enlarged task. Device IX is therefore experimentally adjudicable, but its prospective physical branches remain open until independently tested. The central methodological rule is: a reduction may be valid without being complete; the relevant question is whether the representation preserves the distinctions required by the task.Direct experimental test of Feynman’s path integral postulates with single photons | Science Advances
This paper verifies the Maxwell–Scretching Chain (MSC) and the Scretching Quantum Chain (SQC) as closed mathematical transformation chains. The MSC begins with measured absorbance and derives the linked optical quantities Aλ, ελ, α_abs, κ, εᵣ″, σ, and f_eff. The SQC begins with frequency, wavelength, oscillator strength, and transition dipole strength, then derives photon energy, |μ₂₁|², A₂₁, and τ. The hydrogen atom is used as the control example because it provides a fully known physical system in which the major links of the chain can be checked directly. Maxwell electrodynamics supplies the Coulomb field of the proton, Schrödinger wave mechanics supplies the bound-state eigenfunctions and quantized energy levels, and the Planck–Einstein relation supplies the emitted-photon condition: ΔE = ℏω. When these components are combined, the final chain recovers the Bohr radii, Schrödinger hydrogen energy levels, Rydberg spectral wavelengths, and standard spontaneous-emission scaling. The result is a verified derived framework that organizes known physics into a closed transformation chain. It is not presented as an independent replacement for Maxwell electrodynamics, Schrödinger wave mechanics, Dirac theory, or quantum electrodynamics, but as a structured bridge connecting classical optics, quantum transition theory, and hydrogen spectral validation.
This paper applies the corrected Scretching–Schrödinger Equation (SSE) to the complete bound-state hydrogen atom spectrum. The ordinary Coulomb hydrogen Hamiltonian is retained as the exact benchmark operator, while the Scretching Quantum Chain (SQC) and Maxwell–Scretching Chain (MSC) are imposed as spectroscopic closure relations that connect quantum wavefunction matrix elements to measurable optical quantities, including oscillator strengths, molar absorptivity, Einstein coefficients, and transition frequencies. Using CODATA 2022 constants and the corrected hydrogen 1s→2p1s\rightarrow2p1s→2p radial transition integral, the Lyman-alpha transition is numerically verified with Kν=7.42165600145×10−22 s,K_{\nu}=7.42165600145\times10^{-22}\ \mathrm{s},Kν=7.42165600145×10−22 s, KSSE=7.50174281×10−13 m2 s,K_{\mathrm{SSE}}=7.50174281\times10^{-13}\ \mathrm{m^{2}\,s},KSSE=7.50174281×10−13 m2s, ∣μ∣SQC=3.2804 D,|\mu|_{\mathrm{SQC}}=3.2804\ \mathrm{D},∣μ∣SQC=3.2804 D, and A21=6.26169×108 s−1.A_{21}=6.26169\times10^{8}\ \mathrm{s^{-1}}.A21=6.26169×108 s−1. The corrected analytic hydrogen dipole moment is ∣μ∣analytic=3.2795 D,|\mu|_{\mathrm{analytic}}=3.2795\ \mathrm{D},∣μ∣analytic=3.2795 D, which removes the previously reported 13% discrepancy and confirms close agreement between the SQC closure value and the standard hydrogenic quantum-mechanical result. The paper then extends the corrected SSE framework across the full bound-state hydrogen spectrum by generating the Lyman, Balmer, Paschen, Brackett, Pfund, and Humphreys series from the reduced-mass Rydberg formula. In this application, the SSE does not replace the ordinary Schrödinger solution for hydrogen; instead, it constrains and verifies the standard Coulomb spectrum through spectroscopic closure. Because the hydrogen Coulomb Hamiltonian already reproduces the bound-state spectrum exactly within nonrelativistic quantum mechanics, the SQC correction term is effectively null for hydrogen, VSQC(H)≈0.V_{\mathrm{SQC}}(H)\approx 0.VSQC(H)≈0. Thus, for the hydrogen atom, the Scretching–Schrödinger Equation reduces to the ordinary Schrödinger equation while preserving the SQC and MSC spectroscopic chains as verification layers linking wavefunctions, transition moments, oscillator strengths, Einstein coefficients, and observed spectral frequencies [1–4,12].
This paper applies the Scretching–Schrödinger Equation (SSE), the Scretching Quantum Chain (SQC), and the Maxwell–Scretching Chain (MSC) to Shamshiri’s Photon-Field Interactions: A Relativistic and Quantum Approach. Shamshiri’s formulation introduces an effective photon potential, Φγ = pc, defines the electric-field relation E = −∇(pc), develops modified Maxwell equations, proposes a fourth-order photon-field equation, and uses Lorenz-system boundary conditions to describe quasi-stable photon-field dynamics [1]. The present work extends that model by embedding the Scretching spectroscopic-closure operator, V_SQC, into the photon potential, source current, wave vector, refractive index, fourth-order photon-field equation, and stability conditions. This Scretching–Shamshiri extension does not replace the relativistic photon-field framework; rather, it adds a deterministic spectroscopic layer that connects photon-field dynamics to experimentally measurable optical and molecular parameters. The resulting framework links Φγ, field gradients, modified Maxwell terms, and photon-field stability to oscillator strength f, transition dipole magnitude |μ|², Einstein spontaneous-emission coefficient A₂₁, molar absorptivity ε(λ), effective bandwidth Δν̃_eff, absorption coefficient α_abs, extinction coefficient κ, absorption cross-section σ, and imaginary relative permittivity ε″_r. By inserting SQC and MSC closure relations into Shamshiri’s photon-field equations, the paper derives new equations for spectroscopically constrained photon potential, SQC-corrected photon current density, refractive-index-linked photon propagation, fourth-order Scretching–Shamshiri field dynamics, and stability criteria governed by measurable absorption and transition parameters. Numerical constants, including Kν and K_SSE, are recalculated using CODATA 2022 values, and dimensional consistency is checked throughout. The paper concludes that Shamshiri’s photon-field interaction model can be extended into a testable Scretching photon-field framework in which relativistic photon dynamics, quantum transition structure, and optical spectroscopy are connected through a unified chain of equations.