BKT-83-EN Relational tomography of baryon transitions as an anchor for the LOM–GTSFC–USC–GTCW programme.

Relational tomography of baryon transitions as an anchor for the LOM–GTSFC–USC–GTCW programme Form factors, multichannel stability and restricted transfer from proton structure to observables Robert Kupski | BKT-83 | Edition 2.11 | 14 September 2026 Independent research programme LOM–GTSFC–USC–GTCW This article presents a mathematical and physical analysis of baryon transitions as a domain for testing the Law of One Mechanism (LOM; PJM in Polish). The central question is whether a single restricted coupling rule can describe several observables, rather than fitting each independently. Within LOM, relationality denotes postulated geometric, topological and curvature-based conditions governing the organisation of structures. The Universal Structural Code (USC) describes coupling-admissibility rules; shared rules do not imply identical parameter values or tolerance bands in all channels. The direct empirical basis is the BESIII Collaboration publication “Exploring baryon semileptonic decays through polarization and entanglement”, Nature 657, 92–97 (2026), DOI: 10.1038/s41586-026-10818-8. Its results concern the electron decay Λ → pe⁻ν̄e, where ν̄e denotes the electron antineutrino. BKT-83 also includes a separately published measurement of the muon channel. The analysis combines these experimental summaries with form factors calculated in lattice quantum chromodynamics (LQCD), checks of approximations and specified sectoral LOM hypotheses. Tomography here means a parametric reconstruction of transition structure, not a direct image of the proton interior. The study is not a refit of the original BESIII events. Combining the published electron and muon branching fractions gives the decay-rate ratio Rμe = 0.18137 ± 0.02817, assuming zero covariance between the results of the two publications. The central LQCD reference is R₀ = 0.16638. For specified, unmeasured parameters A = 0.3 and bΛ = 0.5, the common spectral-deformation model H2-R gives Rμe = 0.151022, whereas H2-M, which preserves the mean squared four-momentum transfer in the electron channel, gives 0.165627. The comparison also includes higher moments and angular structure, so agreement in a single rate does not replace a test of the full distribution. A central formal result is the relation between electron- and muon-channel observables within the class of a common positive weight: Rμe ⟨O⟩μ = ⟨r₀ O⟩e. Here O is an integrable function of the normalised squared four-momentum transfer, brackets denote expectations with respect to the relevant spectra, and r₀ is determined by the reference spectra and their rate ratio. This relation allows the common-weight hypothesis to be tested without first determining its exponent. Centred conditional moments complement this test by separating changes in the momentum-transfer spectrum from changes in relative angular structure. The analysis also specifies how finite bins, correlations and detector response affect the scope of these tests. A second part of the study connects local stability, susceptibility and channel-specific tolerances through a reduced energy Hessian. Specified models demonstrate that stability of every pair of modes does not guarantee stability of the complete cycle, and that internal stability does not ensure stability under every coupling to the environment. For a positive, undamped linear response with three active frequencies, the seventh expansion coefficient is predicted from the preceding six. These results constrain models; they do not measure the number of modes or internal proton angles. A separate anchor is provided by converting Compton-polarisability data into an electric stiffness projection without equating it with the weak current. The study also uses results from the standalone geometric Annex BKT-83.E. A fixed proton-profile model calibrated on the radius and curvature of the electric form factor gives a Friar moment of 2.177425 fm³, compared with the source value of 2.246 fm³, a difference of −3.053%. The third quantity is not used to retune the model, but shares source data with the calibration; the comparison therefore does not provide independent confirmation. Standard atomic transfer maps this difference to +0.62584 μeV in one elastic contribution to the muonic-hydrogen 2S energy level, not to the complete Lamb shift. The contribution to the LOM programme is a transition from a general relational interpretation to specified operator relations, conditional predictions and criteria for rejecting individual realisations. The study also develops an effective-current description, identifiability after profiling nuisance parameters and precision design that distinguishes median sensitivity from test power. Its contribution to physics is a coherent comparative framework connecting rates, spectra, angles, stability and restricted transfer from structure to observables. The results establish neither empirical superiority over the Standard Model nor complete USC microphysics. The operational response exponent βcodeᵒᵖ, amplitude exponent bF, shape exponent bΛ, environmental normalisation κenv and activation scale Eact remain empirically undetermined. The historical calibration 0.25 ± 0.06 is explicitly withdrawn. Interpretation preserves the distinction between data, numerical transformations, model examples and limitations arising from incomplete LQCD systematics and joint covariances. Accompanying materials comprise complete Polish and English editions, LaTeX sources for recompilation in Overleaf, computational code, explicit inputs, tables and figures. Annexes A–D form an integral part of the article; Annex BKT-83.E remains a separate work. Keywords: LOM; PJM; Law of One Mechanism; USC; baryon transitions; hyperon semileptonic decays; BESIII; lattice QCD; form factors; identifiability; cross-channel transfer; multichannel stability; tolerance tensor; proton geometry; Friar moment; effective currents