Original ledger status
SEAM.EQUIV.CONTINUUM.02
SEAM.EQUIV.CONTINUUM.02
THE CONTINUUM REALISATION SHARPENED BY THE BOOTSTRAP (2026-06-22): the 'c=8 ambiguity' flagged open in v277/v344 (E8 vs SO(16) both have c=8) is RESOLVED, non-circularly, by the seam's ORDER-4 mu4 clock; so the continuum residual of SEAM.EQUIV.01 is no longer 'which c=8 net?' but PURELY the existence of the chiral edge / massless scaling limit. [E] two c=8 lattices: E8 (det Cartan 1, holomorphic, 1 primary) and D8=SO(16) (det Cartan 4, 4 primaries). [E] the order-4 clock resolves it: the seam clock is mu4 (order 4, forced by the four Gauss-Bonnet marks |mu4|=4=h(A3), v216); the index-4 simple-current extension of D5(+)A3 is E8 (v154), the index-2 would be D8=SO(16); so the order-4 clock selects E8 (full mu4 condensation 16->4->1, det 1) NOT SO(16) (partial Z2 16->4, det 4, v281) -- the order (4 not 2) is the discriminator, non-circular (marks are Gauss-Bonnet). [E] the bootstrap agrees: h(E8)=30 (max prime 5=g_car, Coxeter-match v6/v350) vs h(D8)=14 (max prime 7); SO(16) fails the carrier bootstrap. [E] so the which-net ambiguity is RESOLVED (c=8 + the order-4 clock pin E8; det K=1/holomorphy is then a CONSEQUENCE, not an extra open input). [O] the residual is PURELY existence: does the gapped quasi-free collar HAVE a chiral edge / massless scaling limit (the bulk-edge correspondence: a gapped E8 bulk has a chiral c=8 edge)? -- the literature-anchored continuum leg (Morinelli-Stottmeister, Adamo OS; v336). The net and the holomorphy are pinned; only existence remains.
Recorded status: Sharpening [E]/[O] (the order-4 clock + Coxeter-match pin E8 over SO(16); the residual is purely the chiral-edge existence)
Dependencies, status detail and source
Canonical status: [E] the order-4 clock + Coxeter-match jointly pin E8 over SO(16), resolving the which-net ambiguity non-circularly; [O] the chiral-edge/scaling-limit existence (v336) is the remaining residual. A sharpening; does NOT close SEAM.EQUIV.01.
Dependencies: SEAM.EQUIV.GEOM.01; v277; v344; v216; v154; v281; v336
Scripts: v351_continuum_realisation_sharpened.py
Location: origin_theory
Original CSV, line 71