A parameter-free derivation of the neutrino mass-squared ratio Δm²₃₁/Δm²₂₁ = 4π² cos²(π/8) in Quantum Traction Theory

This article derives the active-neutrino mass-squared ratio R ≡ Δm²₃₁ / Δm²₂₁ = 4π² cos² (π/8) = 33. 69694… from two structural inputs of Quantum Traction Theory (QTT): the canonical π/4 refoliation between the absolute substrate clock T and the laboratory clock τ fixed by axiom A1, and the minimal-holonomy mass-spectrum proposition fixed by axioms A6–A7. The metaplectic half-angle laboratory readout of the π/4 refoliation gives the two-clock projection constant Iclk = cos (π/8), and the minimal-holonomy proposition forces the Takagi singular values (0, m₀/ρ, m₀) with ρ ≡ 2π Iclk. The capacity-scale normalization m₀ cancels from R. No continuous coupling, mixing angle, or normalization is introduced. **Cross-paper coherence within the QTT corpus. ** The same Iclk = cos (π/8) projection independently appears in five other QTT papers as the same projection of the same A1+A5 substrate: - the magic-state T-gate overlap modulus and the symmetric CHSH variational optimum (π/8 paper, doi: 10. 5281/zenodo. 19979595, mathematical identity) ;- the Hubble branch-saturation endpoint Hₗate/Hₑarly = sec (π/8) ≈ 1. 0824 (omega-baryon paper, doi: 10. 5281/zenodo. 20042421), matching the local-vs-CMB Hubble ratio at 0. 1σ;- the same A1+A5 visible-factor projection that forces the V−A weak-interaction current in the chirality paper (doi: 10. 5281/zenodo. 20051962), which re-derives the present mass spectrum inline as a cross-check;- the dyad/triad partition labels mapping to SU (2) and SU (3) gauge factors (SM charge-ledger paper, doi: 10. 5281/zenodo. 20045141) ;- the parameter-free Newton constant G = ℓ̃²c³/ℏ used in the orientation-level capacity-scale estimate (EH endurance paper, doi: 10. 5281/zenodo. 20042844). A reader who engages with the cross-paper coherence treats the present article as one face of a five-face structural identity, not as an isolated number-match. **Comparison with data. ** Using the last fully published NuFIT 6. 0 global fit and a deliberately conservative uncorrelated-error propagation, Rdata = 33. 55 ± 0. 92, giving a 0. 16σ diagnostic residual against Rₚred = 33. 69694. The data are consistent with the prediction but do not yet strongly confirm it. **Limitations and falsifiers. ** The spectrum is intrinsically normal-ordered with m₁ = 0. The strict ratio R = ρ² requires all-order protection of m₁ = 0 from axiom A6's convex equal-share rule. Six concrete falsifiers are listed in §9, including a Δχ²R ≥ 9 post-JUNO/DUNE profile-likelihood departure of R from 33. 6969, a confirmed inverted ordering, a robustly nonzero m₁ above ~1. 4 meV, a clean positive 0νββ signal far above m_ββ ∈ 1. 4, 3. 6 meV, the discovery of a fundamental low-energy elementary gauge sector beyond the dyad/triad share lattice, and failure of the cross-paper coherence with independent QTT predictions in unrelated observational sectors. **Three-layer audit. ** Every load-bearing equation is classified as standard mathematics/established physics (S), QTT postulate inherited from the framework manuscript (P), or QTT consequence conditional on P (C). The load-bearing new content of the present article is the four C entries: the two-clock projection constant Iclk, the lab-visible loop factor ρ, the holonomy weights, and the ratio prediction. **Use of AI assistance. ** The author used AI assistance (Anthropic Claude) in the preparation of this manuscript for: generating and verifying Python code for numerical and symbolic checks; translating conceptual content from the underlying QTT framework into precise mathematical formulations, including derivations and equation development; testing claims through symbolic and numerical computation; and literature search and bibliography cross-referencing. All physics decisions, structural choices, derivations, and final text were reviewed and approved by the author, who takes full responsibility for the content. **Version note. ** v4. 0 (May 2026) supersedes v3. 6 with bolder framing, removal of the "conditional" hedge from title and abstract, full QTT corpus integration with seven cross-cited papers, a three-layer audit table, a six-falsifier table, a reviewer firewall, and the standard Use-of-AI-Assistance disclosure following the QTT submission workflow standing policy. Mathematical content (derivations, theorems, numerical values) is unchanged from v3. 6. The cross-paper coherence section is new.