Original ledger status
SEAM.EQUIV.APPLICABILITY.01
The applicability ledger (2026-06-30) -- a hypothesis-by-hypothesis audit of the THREE external theorems the seam keystone cites (MMST scaling limit, NPW26 (LTO-RP), Adamo-Giorgetti-Tanimoto covariance), isolating the SINGLE genuinely-imported analytic fact. Answers the reviewer worry that the cited theorems may carry hidden hypotheses, by classifying every hypothesis as either a TFPT-internal computed fact (with its establishing vN) or a genuinely external analytic assumption. [E] MMST HYPOTHESES: D=16 Majoranas (=2^{g_car-1}), c=8 (=g_car+N_fam), rank E8=8, range rank<=c<=D reads 8<=8<=16 (in range, saturating rank=c=8), gapped (6 ln(3/2)>0), quasi-free CAR -- all internal computed facts. [E] NPW26 HYPOTHESES: (LTO-RP)=u_Theta=J, gap, Z2 reflection, mu4 clock, [rho,K]=0 internal (v424/v426/v440); the seam is invertible |det Cartan E8|=1 + beta=1 KMS, OUTSIDE NPW26's topological/trace bucket (worked |det|=4) -- NPW26 used as a TEMPLATE, its theorem not directly imported. [E] ADAMO-GIORGETTI-TANIMOTO (arXiv:2508.07109): DHR reps of nets extending loop-group/Virasoro are AUTOMATICALLY positive-energy + diff-covariant; the seam net extends (D5)_1 x (A3)_1 (v154), so geometric covariance is a CONSEQUENCE -- the 'BW presupposes covariance' circularity (v215) is defused; covariance downgraded ASSUMPTION->[E]. [E] THE SINGLE IMPORTED FACT: of 12 audited hypotheses, 11 are TFPT-internal computed facts and exactly 1 is external -- the continuum EXISTENCE of the chiral massless scaling limit (MMST/v336, Lean FORM.SEAM.MMST.01). [C]/[O] VERDICT: the keystone's external dependence is pinned to ONE analytic fact; covariance is an Adamo consequence, not an input; SEAM.EQUIV.01 stays [O] -- that one fact is the honest closure ceiling.
Recorded status: Applicability ledger [E]/[C]: a hypothesis-by-hypothesis audit of MMST/NPW26/Adamo finds 11 of 12 hypotheses are TFPT-internal computed facts and exactly 1 is external -- the continuum existence of the chiral massless scaling limit; covariance is an Adamo consequence (defuses v215), not an input. SEAM.EQUIV.01's external dependence is pinned to ONE analytic fact; stays [O]
Dependencies, status detail and source
Canonical status: Numerical
Dependencies: SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.LTORP.01; SEAM.EQUIV.LTORP.KMS.01; v424; v426; v440; v336; v154; v215
Scripts: v441_seam_applicability_ledger.py
Location: tfpt_research_contracts
Original CSV, line 499Original ledger status
SEAM.EQUIV.MMST.01
THE MMST ROUTE OF THE SEAM EQUIVALENCE TARGET (2026-07-22 route split, carved out of SEAM.EQUIV.01 -- an ID restructuring, NO status change in substance; this row carries exactly the statement previously attached to 'SEAM.EQUIV.01 closed modulo a cited theorem'): the conditional scaling-limit route. The explicit lattice model (v367/v368) and the S3 closure stack -- central charge c = 8 (v376), the (E8)_1 character with 248 currents and one primary (v377), torus GSD = 1 (v378), reflection positivity (v379), the ground-state witnesses c_- = 8 (v489) and mu_pre = 4 (v490) -- pin the target at every computable level; the continuum leg is checked hypothesis-by-hypothesis (v356/v366: D = 16 Majoranas, rank <= c <= D reads 8 <= 8 <= 16, gap 6 ln(3/2) > 0 derived, v302); the whole route is Lean-formalised as FORM.SEAM.MMST.01 (collar hypotheses kernel-proved; the scaling-limit theorem (Osborne-Stottmeister, arXiv:2107.13834, CMP 398 (2023) 219, on the MMST OAR framework arXiv:2010.11121) and the AMT OS/holomorphy selector as NAMED cited axioms; #print axioms clean); the 128-spinor extension leg is crossed-product-certified on peer-reviewed theorems with the realisation input reduced to invariant level (v469). STATUS AS DOCUMENTED (typing taken verbatim from the pre-split rows/prose): CLOSED MODULO CITED THEOREMS -- [C] conditional; the ONLY residual that stays [O] is the abstract continuum existence of the scaling limit (the cited MMST/OS theorems, v336). The parent SEAM.EQUIV.01 stays [O] as an unconditional claim. UPDATED 2026-08-27 (v973): the cited-theorem coverage is CARVED EXACTLY -- OS23 COVERS the bilinear half (the so(16)_1 fermion-bilinear current algebra with STRONG convergence on the finite-particle core, Thm 5.1 + Eq. 229 incl. Majorana algebras; Virasoro/Koo-Saleur Thms A/4.11/4.16; correlators Thms B/C; polynomial error estimates Error^2 <= C 2^(-2 delta N), delta in [0,2]) and does NOT cover four NAMED items: N1 the mu4/GSO extension SO(16)_1 -> (E8)_1 as a NET statement (the 128 spinor currents are not bilinears), N2 the twist/spin-field sector (deferred by the paper), N3 the one-sided chiral edge net of a 2+1D bulk, N4 the OS/holomorphy selector det K = 1 vs 4; NEW MEASUREMENT: the collar edge-correlator convergence rate p = 3.48 (Richardson 3.1-4.2) lies inside the preregistered band [0.5, 4.0] consistent with the cited polynomial form (HONEST: the ratio observable superconverges past delta_max = 2 -- the band's upper edge is calibration-informed); the M = 3 control does not converge (min rel dev 0.836). The [O] residual is now the NAMED list N1-N4 instead of an unstructured 'cited continuum existence'; status UNCHANGED [C]/[O] residual. EXECUTED UPDATE (2026-08-28, completeness wave, v994): 5 of 7 MMST identification criteria executed [E-measured] -- measured c = 8.005 (16 Majorana copies), conformal edge spectrum [0.506, 1.516, 2.523, 3.524] with degeneracies [1,0,1,1,2], current normalisation k = 1.000000000000, sector collapse det D8 = 4 -> det E8 = 1, and mu4/GSO-projected lattice character sums reproduce the (E8)_1 vacuum character coefficients [1, 0, 248, 0, 4124, 0, 34752] three orders deep. C6 = the quasi-free convergence theorem is now WRITTEN OUT in articles/2026-08-28/psi_lambda_convergence_theorem_en.tex (analytic log coefficient 2/pi^2 = 0.20264 vs measured 0.203, 0.18%); C7 modular invariance stays cited/open. Display UNCHANGED [C]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-29, review wave 4, v998): C7 ARITHMETIC SHADOW now exact -- two-edge HS remainder bounded by 2.11 (plateau Nx in (16,24,32,48,64,96)); lattice character theta_E8/eta^8 EXACT four orders [1,0,248,0,4124,0,34752]; Theta_E8(tau)=E4(tau) q-expansion match to >= 8 orders exact (Eisenstein; Jacobi identity); j^{1/3} numeric transform at 60 digits with S-weight bookkeeping. Net-level C7 modular covariance of the completed extension stays cited/open. Display stays [C]/[O] as booked; no marker move.
Recorded status: Conditional [C] (closed modulo cited theorems: the MMST/OS continuum existence, v336; every computable level pinned [E]; Lean FORM.SEAM.MMST.01)
Dependencies, status detail and source
Canonical status: [C] closed modulo cited theorems (the MMST route of SEAM.EQUIV.01; route split 2026-07-22, no status change in substance); residual [O] = the cited continuum existence (v336) EXECUTED UPDATE (2026-08-28, v994): 5/7 identification criteria [E-measured]; C6 written-out [C] (psi_lambda_convergence_theorem_en.tex; 2/pi^2=0.20264 vs 0.203); C7 cited [O]; status UNCHANGED [C]. | 2026-08-29 v998: C7 arithmetic shadow exact (HS bound 2.11, Theta_E8=E4 through q^8, character four orders, 60-digit S); net-level C7 stays cited. Display unmoved.
Dependencies: SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.CONTINUUM.03; SEAM.S3.LATTICE.01; SEAM.S3.INFLOW.01; SEAM.S3.CENTRALCHARGE.01; SEAM.S3.E8CHARACTER.01; SEAM.S3.MODULAR.01; SEAM.S3.RP.01; SEAM.CCC.01; SEAM.MU.01; FORM.SEAM.MMST.01
Scripts: v366_mmst_seam_collar.py, v994_mmst_criteria_battery.py, v998_seam_modular_closure.py
Location: tfpt_research_contracts;introduction;tfpt_1;tfpt_3;tfpt_4
Original CSV, line 583