Publication history: 2026-08-29

Summary

The DET16 finite-cluster hit, the two neutrino-texture structural nulls, the master scaling-limit theorem SEAM.MMST.TYPEIII.CHARGED.01, the gauge-stiffness step-scaling divergence, and the holomorphic-KMS document; suite 994 \to 996, ledger 1168 \to 1171: three new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1001). (1) v1002_ spin10_ mirror_ projector.py (39/39): DET16 rank-one projector on the full 2^{16} cluster — \Omega^\dagger\Omega=P_{16}, \Omega\Omega^\dagger=P_0, defect 0; P_\phi hermitian idempotent 2.8{\times}10^{-18}, rank 1; h_{\mathrm{mir}} spectrum \{0^1,1^{65535}\}, gap exactly 1; all 45 \mathfrak{so}(10) Fock commutators =0 (\det\rho_{16}=1); parity commutator 0; \lvert0\rangle and \lvert F\rangle singlets. Hopping stability on the 4-mode analogue: gap 0.90 (2 clusters) / 0.86 (3 clusters) at t=0.2; spectators untouched. NEW ledger row CHIRAL4D.MIRROR.DET16.01 Candidate [C](exact finite-cluster gapping; open: dynamical gauge fields, domain-wall geometry, 4D volume theorem). (2) the Casimir kill, permanent. Number-preserving Casimir projector uniqueness fails at every cluster size: one 16=\{N{=}0{:}1,\,N{=}16{:}1\} (none at N{=}8); k{=}2 half-filling multiplicity 27; k{=}3{:}1463 (exact Weyl alternation, |W(D_5)|{=}1920). Ledger note on CHIRAL4D.NOMIRROR.01: number-preserving Casimir projector route excluded; display stays [O]. (3) v1003_ nu_ structural_ nulls.py (24/24): charged-sector data h=(1,1,1), d=(64,60,64) [E]; Schur-texture NULL — all 8 preregistered (K,B) fail, D4 reflection forces \lambda_1=\lambda_3, hierarchy (\varepsilon,2\varepsilon,3) structurally unreachable from D4-even seam data, required K\sim[3536.998,1768.499,1/3] matches none of 9 comparators; orientation-doubling structure theorem — \mathrm{sgn}\,J odd sector generically lifts the degeneracy (exact rational witness); scale NULL — 12/12 fail, required cancellation 1-\lvert c/a\rvert=1.885{\times}10^{-4} not supplied, \eta-branches isospectral. NEW ledger row FLAV.NU.TEXTURE.MECHANISM.01 [O]: both nulls are binding constraints (mechanism must be D4-odd AND supply a \sim2{\times}10^{-4} even-odd cancellation; pure seam data excluded [X]-typed). FLAV.NUSCALE.05/.06 notes only; candidates unmoved. (4) registrations (no marker moves). NEW SEAM.MMST.TYPEIII.CHARGED.01 [O]: ONE scaling-limit theorem \Psi_{\lambda,N}\to\Psi_\lambda strongly on the finite-energy core + crossed-product continuity, from which B\cong(E_8)_1, \mu=1, type III_1, unique rotational KMS, unique CE, deck equidistribution and modular invariance follow as corollaries; children SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.STATE.RPMIXING.01 continuum, ALPHA.QUILLEN.EXACT.01 rigidity, AX.P1.01 reading (listed on the parent, not back). Cited document articles/2026-08-29/holomorphic_kms_extension_en.tex (13 pp): unconditional rotational-KMS uniqueness via KLM + Longo–Tanimoto GIVEN the identification; P1 = theorem-conditional on seam identification + \beta_{\mathrm{angle}}=2\pi; axiom typing UNCHANGED. GAUGE.DETLINE.FIXPOINT.01: mechanism executed at fixed volume (unique fixed point, contraction -0.632, exact q^2 and SU(2) Dynkin ratio 4.0) BUT the preregistered thermodynamic step-scaling L=2{..}8 is DIVERGENT (g_\star oscillates 0.65{..}1.69, \lvert R'\rvert>1 at L=4,5,8); typed hurdle: the 1{+}1D toy has no plaquette self-interaction, the real contract needs \ge2{+}1D; display stays [O]. v_{\mathrm{geo}} boundary note: unit choice closed; dimensionless hierarchies (M_{\mathrm{Pl}}/v_{\mathrm{EW}},\,M_R/M_{\mathrm{scal}},\,\Lambda_{\mathrm{QCD}}/v_{\mathrm{EW}},\,T_{\mathrm{reh}}/M_{\mathrm{scal}}) remain predictive obligations. Surfaces: tfpt_research_contracts (new sections MIRROR.DET16, TYPEIII.CHARGED, NU.TEXTURE.MECHANISM; DETLINE stiffness update; NOMIRROR Casimir kill); tfpt_4_frontier wave-5 paragraph; tfpt_2 (texture-mechanism note); introduction status card v_{\mathrm{geo}} hierarchy sentence.

Summary

Two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v997). (1) v998_ seam_ modular_ closure.py (14/14): two-edge HS remainder bounded by 2.11 on the frozen plateau N_x\in(16,24,32,48,64,96); lattice character \theta_{E_8}/\eta^8 EXACT four orders [1,0,248,0,4124,0,34752]; \Theta_{E_8}(\tau)=E_4(\tau) as Eisenstein series, q-expansion match to \ge8 orders exact (Jacobi identity; the reviewer's C7 sharpening); j^{1/3} numeric transform at 60 digits with S-weight bookkeeping. Ledger notes on SEAM.EQUIV.MMST.01 and SEAM.SIMPLECURRENT.GENERATOR.01: C7 arithmetic shadow now exact; net-level C7 stays cited/open. (2) v999_ weak_ collision_ hp.py (14/14): the continuous-time dilation leg — generator extraction Richardson 1.098\times10^{-10}; \operatorname{diag}L_{\mathrm{GKSL}}=Q=\log B symbolic; e^{Q}=B exact; GNS splitting defect 0; locality 1.355\times10^{-20}; strong-collision singularity contrast rank 9/81. DYN.UNITARY.DILATION.01: the finite ladder is now COMPLETE (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time); open = the thermodynamic field limit only; contract stays [O]. (3) v1000_ spin2_ sk_ witnesses.py (26/26): lattice graviton — positivity exact, 2 TT helicities at all 5852 momenta (N=6..12), \omega=k-k^3/24 exact; SK — KMS/FDT \sim10^{-17}, \rho_0-dependence contrast 3.550\times10^{-3} vs static 10^{-16}, saddle 5-fold degenerate with 3\pi/5 unique in the \mu_4 lift [C]. GRAV.SPIN2.EMERGENCE.01 quadratic Hamiltonian half executed; FTRANSFER.SK.RHO0.01 mechanism executed; both contracts stay [O]. (4) v1001_ nu_ pentagon_ chain.py (14/14): U_e=I inventory theorem; misalignment U=U_{v9}R_{13}(\theta,\phi); pentagon double hit \phi=288^\circ=4(2\pi/5) frozen, all three measured angles \le0.56\sigma (honest max pull 0.557) at \theta=2\pi/35, unique LEE survivor 2.7\%; v3 chain SHA-16 a4c28732fa687620 with \Sigma=0.0599 eV, m_\beta=9.0 meV, m_{\beta\beta}\in[1.5,3.8] meV, \delta_{\mathrm{CP}}=287.66^\circ; v270–\theta_{23} tension 1.85\sigma TYPED; census null 0/1607. NEW ledger row FLAV.NUSCALE.06 Candidate [C](pentagon-class misalignment; mechanism = the Q_+-to-flavor operator [O]; kills DESI/DUNE 287.7 vs 240/JUNO). NO seesaw closure; FLAV.NUSCALE.05 unmoved. (5) Amendments (typed; no marker moves). QFT4D.LATTICE.FUNDAMENTAL.01: a single finite box is not a world — the fundamental object is the quasilocal consistent family \{H_\Lambda\} with \tau_t=\lim e^{itH_\Lambda}A e^{-itH_\Lambda}; continuum (a\to0) optional, thermodynamic limit and controlled IR universality mandatory (dated 2026-08-29). ANCHOR.VGEO.01/.02: display retyped from open-physics/primitive phrasing to CLOSED METROLOGY STRUCTURE (\mathbb{R}_+ unit torsor; one dimensionful calibration necessary by dimensional analysis — No-Unit v153/v725); display stays [O], no physical [E]. ALPHA.QUILLEN.EXACT.01: the correct object is the relative determinant Q(A)=\log[\det'\Delta_A/\det'\Delta_{A_0}]+8\,b_1\,c_3^6\log\varphi(A); BFK 2^{-4} is A/\tau/\alpha-independent at fixed cut number so \delta\log 2^{-4}=0 — no physical compensation (consistent with COMPENSATION_INTERNAL). NEW master contract TFPT.TOE.COMPLETE.01 [O]: eight gates T1–T8 with the binding separation \mathrm{TOE}_{\mathrm{Complete}}:=\mathrm{AND}(\mathrm{T1}{..}\mathrm{T8}) vs \mathrm{TOE}_{\mathrm{Validated}}:=\mathrm{Complete} AND independent holdouts; every existing 4D/dilation/detline/SK/flavor/gravity contract is a child of one gate. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, DILATION, GRAV.SPIN2, SK.RHO0; new sections TOE.COMPLETE and NUSCALE.06; lattice-fundamental amendment; ALPHA relative-det note); tfpt_4_frontier + introduction status card / v_{\mathrm{geo}} row; tfpt_2 (NUSCALE.06 candidate paragraph).