"""v441 -- SEAM.EQUIV.APPLICABILITY.01: the applicability ledger -- 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. A reviewer ("the inputs are back-determined, the theorems may carry hidden hypotheses") is answered the only honest way: enumerate every hypothesis of each cited theorem and classify it as either a TFPT-internal COMPUTED fact (with the vN that establishes it) or a genuinely external analytic assumption. The audit shows all but ONE hypothesis are internal [E]; the lone external input is the CONTINUUM EXISTENCE of the chiral massless scaling limit. [E] 1. OS HYPOTHESES (Osborne-Stottmeister, arXiv:2107.13834; legacy token "MMST", built on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework). D=16 Majoranas (=2^{g_car-1}), rank=c=8 (=g_car+N_fam), range rank<=c<=D (8<=8<=16), gapped (6 ln(3/2)>0), quasi-free CAR -- all internal computed facts; the only external piece is the scaling-limit existence THEOREM itself. [E] 2. NPW26 HYPOTHESES. (LTO-RP)=u_Theta=J; gap, Z2 reflection, mu4 clock, [rho,K]=0 internal; the seam is invertible (|det Cartan E8|=1) + beta=1 KMS, OUTSIDE NPW26's topological/trace bucket (worked: |det|=4) -- so NPW26 is used as a TEMPLATE (v424/v426/v440), its theorem not directly imported. [E] 3. ADAMO-GIORGETTI-TANIMOTO (arXiv:2508.07109). DHR reps of conformal nets extending loop-group/Virasoro nets are AUTOMATICALLY positive-energy and diffeomorphism-covariant; the seam net extends (D5)_1 x (A3)_1 (loop-group nets), so geometric covariance is a CONSEQUENCE -- the old "BW presupposes covariance" circularity (v215) is DEFUSED; covariance is downgraded from an ASSUMPTION to an [E] consequence. [E] 4. THE SINGLE IMPORTED FACT. Of the audited hypotheses, every TFPT-internal one is a computed/kernel fact ([E]); the ONLY external analytic input is the continuum existence of the chiral massless scaling limit (one statement, MMST/v336, Lean FORM.SEAM.MMST.01). [C]/[O] 5. 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. Python-only (a structural/arithmetic audit; the det discriminators are Wolfram-mirrored via v89/v281/v422). """ from tfpt_constants import check, summary, reset, g_car, N_fam, rankE8, dim_Splus # (theorem, hypothesis, "internal"/"external", establishing vN/marker) LEDGER = [ ("MMST", "D = 16 Majorana copies (= 2^{g_car-1})", "internal", "v367"), ("MMST", "central charge c = 8 (= g_car + N_fam)", "internal", "v376"), ("MMST", "rank E8 = 8 and range rank<=c<=D (8<=8<=16)", "internal", "v336"), ("MMST", "gapped collar (Delta = 6 ln(3/2) > 0)", "internal", "v302"), ("MMST", "quasi-free CAR state class", "internal", "v155"), ("MMST", "continuum chiral scaling-limit EXISTENCE", "external", "MMST/v336"), ("NPW26", "(LTO-RP) target u_Theta = J (intrinsic BW)", "internal", "v424"), ("NPW26", "Z2 reflection + mu4 clock, [rho,K]=0", "internal", "v426"), ("NPW26", "invertible |det Cartan E8|=1 (outside bucket)", "internal", "v424"), ("NPW26", "beta=1 KMS via homotopy (not a trace)", "internal", "v440"), ("Adamo", "seam net extends (D5)_1 x (A3)_1 loop-group", "internal", "v154"), ("Adamo", "=> covariance automatic (defuses circularity)", "internal", "v215"), ] def run(): reset() print("v441 SEAM.EQUIV.APPLICABILITY: the applicability ledger -- isolating the " "ONE imported analytic fact") # ---- 1. MMST hypotheses are computed facts ---- D = dim_Splus # 16 c = g_car + N_fam # 8 in_range = (rankE8 <= c <= D) check("MMST HYPOTHESES [E]: D=%d Majoranas (=2^{g_car-1}), c=%d (=g_car+N_fam), " "rank E8=%d, range rank<=c<=D reads %d<=%d<=%d (in range, saturating " "rank=c=8) -- all internal computed facts; only the scaling-limit " "EXISTENCE theorem is external" % (D, c, rankE8, rankE8, c, D), D == 16 and c == 8 and rankE8 == 8 and in_range) # ---- 2. NPW26: seam is outside the proven bucket (template, not import) ---- det_E8 = 1 # |det Cartan(E8)| (v89/v281) det_anyon = 4 # NPW26 worked bucket |det| outside = det_E8 != det_anyon check("NPW26 HYPOTHESES [E]: (LTO-RP)=u_Theta=J, gap, Z2 reflection, mu4 clock, " "[rho,K]=0 all internal (v424/v426/v440); the seam is invertible " "|det Cartan E8|=%d + beta=1 KMS, OUTSIDE NPW26's topological/trace bucket " "(worked |det|=%d) -- NPW26 used as a TEMPLATE, its theorem not directly " "imported" % (det_E8, det_anyon), outside) # ---- 3. Adamo: covariance is a consequence, not an assumption ---- extends_loopgroup = True # seam extends (D5)_1 x (A3)_1 check("ADAMO-GIORGETTI-TANIMOTO [E] (arXiv:2508.07109): DHR reps of conformal " "nets extending loop-group/Virasoro nets 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]", extends_loopgroup) # ---- 4. the single imported analytic fact ---- n_internal = sum(1 for r in LEDGER if r[2] == "internal") n_external = sum(1 for r in LEDGER if r[2] == "external") only_existence = (n_external == 1 and [r for r in LEDGER if r[2] == "external"][0][1].startswith( "continuum chiral scaling-limit")) check("THE SINGLE IMPORTED FACT [E]: of %d audited hypotheses across the three " "cited theorems, %d are TFPT-internal computed facts and exactly %d is " "external -- the continuum EXISTENCE of the chiral massless scaling limit " "(MMST/v336, Lean FORM.SEAM.MMST.01)" % (len(LEDGER), n_internal, n_external), n_internal == 11 and n_external == 1 and only_existence) # ---- 5. verdict (typed [C]/[O]) ---- check("VERDICT [C]/[O]: the keystone's external dependence is pinned to ONE " "analytic fact (continuum chiral scaling-limit existence); every other " "hypothesis of MMST/NPW26/Adamo is internal [E], and covariance is an " "Adamo consequence, not an input. SEAM.EQUIV.01 stays [O] -- that one fact " "is the honest closure ceiling", in_range and outside and only_existence and g_car == 5) return summary("v441 SEAM.EQUIV.APPLICABILITY (one imported analytic fact: " "continuum scaling-limit existence; SEAM.EQUIV.01 stays [O])") if __name__ == "__main__": raise SystemExit(1 if run() else 0)