A registered result in its source context
Original ledger classification: Sharpening [E]/[O] (the order-4 clock + Coxeter-match pin E8 over SO(16); the residual is purely the chiral-edge existence)
Recorded statement: 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…
Statement, assumptions and sources
Paper context: Origin Theory
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SEAM.EQUIV.CONTINUUM.02
Original ledger classification: Sharpening [E]/[O] (the order-4 clock + Coxeter-match pin E8 over SO(16); the residual is purely the chiral-edge existence)
Original claim text
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.
Original classification detail
[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 as recorded
SEAM.EQUIV.GEOM.01; v277; v344; v216; v154; v281; v336
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- Origin Theory
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- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- 2026-06-30 ( v445 — the rigidity FORCING converse: commuting with the order- [formula in source] clock is exactly [formula in source] -block-diagonality, upgrading the rigidity step from ``permit'' to ``force'')Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (Track 1 — the S3 input made CONCRETE: an explicit gapped chiral-Majorana ( [formula in source] ) lattice model with numerical Chern [formula in source] realises the [formula in source] edge ( v367), and a strip shows the chiral edge exists by anomaly inflow ( v368))Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-23 (Directions 3 \& 7 — the two hard functional-analysis residuals ADVANCED: the QG measure as one-loop fluctuations around the parameter-free saddle ( v365), and the seam collar verified IN MMST's free-fermion class so the scaling limit is [formula in source] ( v366))Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (the two frontier walls attacked directly: Direction A assembles the continuum chain of SEAM.EQUIV.01 theorem-by-theorem and ties its residual to the seam one-sidedness; Direction B was found ALREADY closed by v40 (harmonic metric [formula in source] finite linear algebra, not a PDE): v356)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
All 16 linked sections
- Front matter / support
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Research Contract 1 — [formula in source]
- 2026-06-22 (the bird's-eye rethink: TFPT is a unique self-consistent LOOP with ZERO free dials, not a linear axiom system; [formula in source] is a fixed geometric constant, not a dial; the one residual is the continuum closure: v353)
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- The unique attractor: a gapped transport selects ONE fixed point
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
Registered verification modules
- v351_continuum_realisation_sharpened.pyRegistered verification module · core
Read the description recorded in the module registry
The continuum realisation sharpened -- 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. [E] E8 (det 1, holomorphic) vs D8=SO(16) (det 4). [E] the order-4 clock (the four Gauss-Bonnet marks, |mu4|=4=h(A3), v216): index-4 extension D5(+)A3 = E8 (v154), index-2 = SO(16); so order-4 selects E8 (16->4->1) not SO(16) (16->4) -- the order (4 not 2) is the discriminator. [E] bootstrap agrees: h(E8)=30 (max prime 5) vs h(D8)=14 (max prime 7). [E] which-net ambiguity RESOLVED (det K=1 is then a consequence). [O] residual = PURELY the chiral-edge/scaling-limit existence (bulk-edge, v336), net+holomorphy pinned. Does NOT close SEAM.EQUIV.01.
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