Discrete Topological Torsion Theory: The Standard Model Mass Spectrum from Trefoil T(2,3) Cosserat Substrate Topology (DTTT BATCH-3.4 MASS-SPECTRUM)

MASS-SPECTRUM is the Layer-11 matter-framework paper of the Discrete Topological Torsion Theory (DTTT) research program. It derives the full Standard Model mass spectrum — proton, electron, six quarks, generation count, charged-lepton ratios, and the W/Z/Higgs gauge boson masses (the last three cross-referenced through siblings \dttSMTallyZ and \dttHiggsMassZ) — from the topology of the trefoil knot T(2,3) on a geometrically nonlinear Cosserat micropolar substrate with ω∈H (quaternionic-valued microrotation), using the W-boson mass MW as the sole dimensional input. Per-particle tier-stratified results. The headline results are stratified honestly per V5 Methodology Ch. 8 tier-discipline (THEOREM / DERIVED / DERIVED-WITH-MARGIN / STRONG-CONJ / HN / Observation), with no auto-uniform-tier-promotion claim. DERIVED tier: mp=(9/4)α2π4⋅MW=938.11 MeV at 174 ppm (two independent routes, F-576 overdetermination signature); the six quark masses mu,md,ms,mc,mb,mt with three topology-exact ratios md/mu=p=2, mc/ms=Φ6(nT)=13, mbLO/mc=q=3 (each ratio at machine precision); generation count Ngen=η(T(2,3),Ad)=3 from the Callias index theorem. DERIVED-WITH-MARGIN tier: me=(3α2/8π)⋅MW at 270 ppm via Beasley-Witten localisation on the orbifold solid torus D2(2,3)×S1; primary home cross-referenced to \dttElectronMassZ per D-013. STRONG-CONJ tier: the W/Planck hierarchy MW/MP=exp(−c3π2)=exp(−4π2) at +8.7% bare (D-010 fold-in; two explicitly disclosed weak links and a factor-62 scale gap preserved openly); mH=e4/9⋅MW=125.245 GeV at 0.09% (Form-A locked; cross-referenced to \dttHiggsMassZ). HN (Honest Negative) tier: mμ/me as a derivation (the F-458 integer pattern c32Ntot=208 at 0.6% retained at Observation only); three neutrino masses mνi individually; the Peter-Weyl spin-J lepton-internal mass-ratio programme (not built); independent MZ derivation (currently overdetermined through the sin2θW=3/13 consistency route in \dttWeinbergZ). Substrate axiom and inheritance. The substrate axiom (Cosserat micropolar continuum with ω∈H quaternionic microrotation field, geometrically nonlinear; trefoil T(2,3) identified with the proton ground state), 5-tuple operator algebra finality on the Hurwitz closure on H, 14-layer hierarchy, and α-assembly identity are inherited from BATCH-1.1 FOUNDATIONS-SYNTHESIS (\dttFoundationsZ); the axiom statement and Hurwitz-closure finality argument are inherited from BATCH-1.2 AXIOMS (\dttAxiomsZ); the publication-cascade convention is inherited from BATCH-1.3 MANIFESTO (\dttManifestoZ); the substrate-derivation of α−1=4π3+π2+π flows into the α2 factor of every DERIVED-tier mass formula via \dttAlphaZ; the corpus-wide SM-26 overdetermination scorecard is in \dttSMTallyZ. All cross-paper references are by DOI macro, not by paper number, per Block 44.202 LOCK-1. Predictions and falsifiers. The paper carries three load-bearing forward predictions (LOCK-3 Option C; \dttPredictionsCatalogZ): P1 — the full SM mass spectrum (12 charged fermions + 3 neutrinos + W/Z/H) is substrate-derivable at the explicitly stated per-particle tier (DERIVED / DERIVED-WITH-MARGIN / STRONG-CONJ / HN), with no auto-uniform-tier-promotion; falsifier = any DERIVED-tier entry shifts > 3$\sigma$ from current PDG without a substrate-correction term being identified, OR the stratification itself is shown to depend on a hidden uniform-tier assumption. P2 — SM mass ratios md/mu=2, mc/ms=13, mbLO/mc=3 (plus the lepton ratio mτ/mμ=c32(1+Qα) STRONG-CONJ from charged-lepton-hierarchy paper) carry exact topological integer/cyclotomic structure not visible in the absolute mass values, and new cyclotomic-family ratios are predicted; falsifier = any of the three exact quark ratios shifts beyond its band at > 3$\sigma$. P3 — HN-classified masses (the five listed in P1) reach binary outcome by end of BATCH-3+ window: either an explicit substrate-derivation route with L41 discrimination step is found and the entry promotes under §A.14 user-reserved promotion, or the entry is permanently catalogued as HN in the HONEST-NEGATIVES casebook (BATCH-4.7) with a disclosed reason; falsifier = any HN entry quietly migrates to a higher tier without an accompanying explicit derivation chain. Honest residue (preserved openly). Residue items inherited from the Block 39 Phase C consolidation and the Anchor §7 corpus-wide residue list: (i) the Peter-Weyl lepton-internal-ratio programme remains OPEN (this paper derives absolute masses + generation count but not mμ/me or mτ/mμ); (ii) F-458 mμ/me integer pattern (~208 vs observed 206.768) is Observation tier with explicit 0.6% deviation-flag, not eligible for STRONG-CONJ without an identified correction term; (iii) source-internal 169 vs 174 ppm proton figure discrepancy (canonical figure 174 ppm); (iv) gauge-hierarchy STRONG-CONJ with two disclosed weak links + factor-62 scale gap; (v) SHC R-1 PDE-analytic residue (load-bearing for α2 in DERIVED-tier formulas through the α-assembly chain); (vi) Wolfenstein A 3.18$\sigma$ tension cross-referenced through \dttCKMPMNSZ; (vii) T8 external-LLM audit pending (user-side cross-validation). Status. Tier-β (Block 44.202 publication-phase classification): canonical paper source (14 TeX files, 5 PDFs, 38 MD notes, 12 Python verifiers including verify_mass_spectrum.py at 50-digit precision, 6 JSON metadata files, 2 figures present) is content-complete with the 174 ppm proton, 270 ppm electron, three topology-exact quark ratios, and Ngen=3 each independently re-verified 2026-06-02 at 50-digit mpmath precision. Figures column partially populated (2 of the typically-expected 3-4 figures): fig4_mass_spectrum.png (quark mass spectrum DTTT-vs-PDG, HM-ORG-03 recovered asset) and fig2_alexander_tower.png (CS propagator taxonomy mapped onto Alexander tower). Recommended additional figure dispatch (see STATUS.md): SM mass tier-stratification chart with per-particle confidence label visualization; trefoil-derived ratio identity diagram. Citation TIER-0 baseline cleared. Honest-residue register reconciled. T8 external-LLM audit pending.