Independent Verification of the Identity Thesis between Particles and Spherical Bessel Standing-Wave Solitons: PDG 2026 Full-Spectrum Mass Ordering, Comparison-Convention Calibration, and Applicability Boundaries
Year: 2026
Type: preprint
Abstract: This paper independently verifies the identity thesis between particles and spherical Bessel standing-wave solitons proposed in Refs. [1]–[10], using 378 massive particles selected from the PDG 2026 full spectrum by five transparent rules. The thesis receives independent support at three levels—curve-shape signature, mass-ordering structure, and shell-layer quantitative regularity—while absolute scale, long-range recursion, and mechanism-level extrapolation define its precise applicability boundaries. The thesis asserts that massive particles are spherical Bessel standing-wave solitons in a spherical cavity, and that the mass-ordering structure should be generated, at the relative spectral-order level, by the parameter-free spherical Bessel zero sequence R = μ/K with K = 2l + 2n + 1. The theoretical construction and mechanistic argumentation are completed jointly by Refs. [1]–[10], which form a fixed derivation chain; Ref. [11] is an introductory review of this system, and Refs. [12] and [13] are application extensions (division of labor in Section 1.3). This paper does not repeat those works. The object of verification is the consistency between the computable corollaries of the thesis and experimental data. The verification imposes a prerequisite condition: the curve-shape signatures of the R = μ/K sequence and the Compton-wavelength sequence λ_C must first be shown to agree in overall shape; if this test fails, the two sequences do not agree in curve shape, and subsequent mass calculations based on ordering alignment are invalid. The sample covers leptons, mesons, baryons, charmonium, bottomonium, electroweak gauge bosons, and the Higgs boson, with masses spanning approximately five orders of magnitude—a full-spectrum verification sample for current particle physics. The verification employs four groups of methods: a six-layer criterion system, dual-convention validation, implementation-sensitivity scanning, and quantitative boundary delineation. The verification proceeds layer by layer according to the logical dependencies of the corollaries of the thesis. The curve-shape signature layer is strongly supported: the DTW distance between the normalized R = μ/K and λ_C curves is 1.6740, versus 6.6180 for the sorted random control, giving a discrimination ratio of 4.0; Pearson correlation is 0.987123; the boundary-condition version discrimination between K = 2L + 2N + 1 and the standard spherical-cavity form K = 2L + 2N yields 4.1 after sorting and 57.8 before sorting, with permutation-test z = 29.61. The ordering-structure layer is strongly supported: the median error of 349 pairs is 0.23%, 99.1% of paired errors are below 5%, and the shuffle-test signal ratio is 71.4. The shell-layer quantitative layer is supported: the median error of 335 pairs is 2.47%, 78.2% are below 5%, and the shuffle-test signal ratio is 5.3. The absolute-scale layer is not supported: the log–log slope is −4.07 and R² = 0.649. The stability-boundary layer is locally supported: the derivative-DTW discrimination ratio falls to 1.0, the 5% error threshold is reached after an average of 22.1 steps, and long-range recursion fails. The 66.5-fold discrimination ratio reported in the original thesis comes from the 300-element subset in Chapter 22 of the original monograph (PDG 2025/2024 dataset, unsorted convention). Recomputing on the PDG 2026 350-element set (378 particles with 14 removed from each end) gives 57.8 under the unsorted convention, the same order of magnitude as 66.5, and 4.0 under the sorted convention. The order-of-magnitude difference between 66.5 and 4.0 is mainly due to the comparison convention; changing the dataset does not change the order of magnitude under the unsorted convention, and there is no numerical contradiction between the two. Judgment details: the curve-shape signature layer and the ordering-structure layer are both strongly supported; the shell-layer quantitative layer is supported; specificity—the degree to which the true pairing can be distinguished from control pairings—is confirmed by three independent checks: the sorted random control, the shuffle test, and the permutation test. Data, code, and random seeds are publicly available, and the results are independently reproducible.
Author: Xu, shiwei
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225777834
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