Neutrinos as an Access Channel to Structural-Informational Physics Rank-2 Structure and Majorana Projection as a Modal Closure Test in the USC Formalism

Short description This appendix presents the neutrino sector as a test channel for the hypothesis of a structural informational layer of physics within the GTWSSF USC GTCW programme. In the rank 2 variant of normal mass ordering, under the assumption m₁ = 0, the dimensionless observable R₂₃ᵒˢᶜ = m₂ / m₃ = √(Δm²₂₁ / Δm²₃₁) is derived. For the benchmark based on JUNO and NuFIT data, the result is R₂₃ᵒˢᶜ = 0.17221 ± 0.00155 and ln R₂₃ᵒˢᶜ = −1.75905 ± 0.00901. In standard neutrino physics, this quantity is derived from oscillation data. In the USC formalism, it additionally serves as a numerical test anchor for the operator projection of a modal structure onto the effective Majorana mass matrix. The work defines the comparison between the oscillation observable R₂₃ᵒˢᶜ and the modal prediction R̂₂₃ᵁˢᶜ = C₂ᵁˢᶜ / C₃ᵁˢᶜ, then formulates the statistic zᴿ and the PASS / INCONCLUSIVE / FAIL criterion. The document does not claim a complete solution to the problem of neutrino masses. It builds a falsifiable comparison channel between known oscillation physics and the hypothesis of a relational informational USC layer. It includes the mathematical and physical apparatus, Takagi factorization, MasterData, numerical results, physical interpretation, model limitations and a programme for further validation. introduction This appendix presents the neutrino sector as one of the most precise test channels for the hypothesis of a structural informational layer of physics within the GTWSSF USC GTCW programme. The starting point is the rank 2 variant of normal neutrino mass ordering, in which the lightest mass satisfies the condition m₁ = 0, while the two remaining masses are determined by the oscillation splittings Δm²₂₁ and Δm²₃₁. The main result of the work is the derivation of the dimensionless observable: R₂₃ᵒˢᶜ = m₂ / m₃ = √(Δm²₂₁ / Δm²₃₁) For the adopted benchmark, based on JUNO oscillation data and the NuFIT global analysis, the result is: R₂₃ᵒˢᶜ = 0.17221 ± 0.00155 and: ln R₂₃ᵒˢᶜ = −1.75905 ± 0.00901 In standard neutrino physics, this quantity is a derived observable from oscillation data. In the USC formalism, the Universal Structural Code, it plays an additional role. It becomes a numerical test anchor for the operator projection of a modal structure onto the effective Majorana mass matrix. As a result, the neutrino sector is written as a verifiable sequence: USC operator → mass projection → Majorana matrix → Takagi values → neutrino masses → observable R₂₃ The purpose of the appendix is not to claim a complete solution to the problem of neutrino masses. Its purpose is to formulate a sharp, falsifiable comparison channel between the standard oscillation observable and the modal prediction of the USC layer: R̂₂₃ᵁˢᶜ = C₂ᵁˢᶜ / C₃ᵁˢᶜ The comparison between both quantities leads to the test statistic: zᴿ = (ln R̂₂₃ᵁˢᶜ − ln R₂₃ᵒˢᶜ) / σₗₙR and to an explicit PASS / INCONCLUSIVE / FAIL criterion. This means that the structural informational hypothesis is not presented as a metaphor, but as a testable programme. If the modal USC prediction reproduces the oscillation observable within the defined uncertainty, the channel remains compatible with the data. If it does not, the corresponding model variant is constrained or rejected. The significance of the work lies in showing that the abstract concept of the Universal Structural Code can be reduced to a concrete mathematical and physical apparatus: operator, projection, spectrum, observable, uncertainty and falsification criterion. The appendix does not reject the Standard Model or standard neutrino oscillation physics. On the contrary, it uses them as the empirical layer on which an additional hypothesis about a deeper relational informational order of mass structure can be tested. In the broader context of the GTWSSF USC GTCW programme, the work indicates a method for moving from general ideas of informational physics to numerical and verifiable research channels. The neutrino sector is particularly valuable because relations between masses are accessible through precise oscillation data, while remaining independent of complete knowledge of the absolute mass scale. For this reason, the observable R₂₃ᵒˢᶜ can serve as a first sharp test anchor for the hypothesis of modal closure in the neutrino sector. The document has the status of a scientific appendix and technical supplement. It includes formal assumptions, a mathematical and physical apparatus, Takagi factorization, the definition of mass projection, the MasterData table, numerical results, physical interpretation, model limitations and PASS / FAIL criteria for further validation. Keywords GTWSSF, USC, GTCW, LOM, neutrinos, Majorana mass, rank 2, normal mass ordering, Takagi factorization, informational physics, Universal Structural Code, metafield, neutrino oscillations, JUNO, NuFIT, KATRIN, MasterData, PASS FAIL, structural informational physics.