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Original ledger classification: Scaling-limit convergence evidence [E] (the finite-size central charge converges to c=8 and Richardson-extrapolates there -- the existence-relevant observable) + the abstract existence stays [O] (cited MMST v336); an honest attack that strengthens, does not close
Recorded statement: An HONEST attack on the one open lemma of SEAM.EQUIV.01 -- the continuum scaling-limit existence (2026-06-24). It does NOT close v336 (the abstract existence is the cited MMST theorem); it STRENGTHENS the case with the existence-relevant…
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Paper context: Research contracts
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SEAM.S3.SCALINGLIMIT.01
Original ledger classification: Scaling-limit convergence evidence [E] (the finite-size central charge converges to c=8 and Richardson-extrapolates there -- the existence-relevant observable) + the abstract existence stays [O] (cited MMST v336); an honest attack that strengthens, does not close
Original claim text
An HONEST attack on the one open lemma of SEAM.EQUIV.01 -- the continuum scaling-limit existence (2026-06-24). It does NOT close v336 (the abstract existence is the cited MMST theorem); it STRENGTHENS the case with the existence-relevant observable v376 did not test: that the finite-size data CONVERGE (a divergent/drifting sequence would have no continuum limit). [E] MULTI-SIZE CONVERGENCE: the Calabrese-Cardy correlation-matrix EE slope c1(L) at L=66,130,258,386,514 is a monotone sequence approaching 1, with |c1(L)-1| strictly decreasing from 4.6e-4 to 7.1e-6. [E] RICHARDSON EXTRAPOLATION: a 1/L fit gives c1(inf)~0.9999, so the 16-Majorana (=8 complex mode) collar has c=8*c1(inf)~7.9993~8=g_car+N_fam -- the (E8)_1/SO(16)_1 continuum value reached IN the limit. [E] CAUCHY SIGNATURE: the successive differences |c1(L_{k+1})-c1(L_k)| are themselves strictly decreasing and tiny -- a numerical Cauchy sequence (necessary, not sufficient, for existence). [O] convergent finite-size DATA are strong evidence but NOT a proof that the continuum limit exists (the cited MMST theorem, v336), and do not pin (E8)_1 over the same-c SO(16)_1 (the holomorphy det K=1 discriminator, v377/v378). Strengthens the residual, does NOT close it -- SEAM.EQUIV.01 stays closed modulo the cited theorem.
Original classification detail
[E] the multi-size convergence (monotone Cauchy-like c1(L)->1) + the Richardson extrapolation to c=8 + the decreasing successive differences (numerical evidence the scaling limit exists and gives c=8); [O] the abstract continuum existence (cited MMST v336) and the (E8)_1-vs-SO(16)_1 holomorphy discriminator (v377/v378) stay open. Extends v376 from the value (two sizes) to the convergence (five sizes); strengthens v336's residual, does not close it.
Dependencies as recorded
SEAM.EQUIV.CONTINUUM.01; v336; v367; v368; v376; v377; v378
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- Research contracts
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- 2026-06-24 (Attacking the last open lemma: v392 the scaling-limit central charge converges)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v392_seam_s3_scalinglimit.pyRegistered verification module · core
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SEAM.S3.SCALINGLIMIT.01: an HONEST attack on the one open lemma of SEAM.EQUIV.01 (the continuum scaling-limit existence, v336) -- does NOT close it (the abstract existence is the cited MMST theorem); STRENGTHENS the case with the existence-relevant observable v376 did not test: that the finite-size data CONVERGE. [E] the Calabrese-Cardy EE slope c1(L) at L=66..514 is a monotone Cauchy-like sequence approaching 1 (|c1(L)-1| strictly decreasing). [E] a 1/L Richardson fit gives c1(inf)~1.000 so the 16-Majorana collar c=8*c1~8.00 = g_car+N_fam is reached IN the limit. [E] the successive differences are strictly decreasing (numerical Cauchy, necessary for existence). [O] convergent data are evidence, not a proof of existence (MMST v336), and do not pin (E8)_1 vs SO(16)_1 (holomorphy v377/v378). Strengthens the residual, does NOT close it.
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