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Original ledger classification: one-particle rigidity + scaling limit [E]/[C]: via Araki self-dual CAR (state<->symbol P, cited) the gapped ground state is the UNIQUE quasi-free realisation (P^2=P), its kernel is Cauchy (~1/N, limit exists), and the limit is the c=1 Dirac CFT (EE c-fit ~1 => c_-=16*1/2=8); Shale-Stinespring makes the Bogoliubov map implementable, upgrading R1 from a bald axiom to an audited [C]; with v463 the residual is entirely certification, zero open internal mechanism; SEAM.EQUIV.01 stays [O]
Recorded statement: The one-particle RIGIDITY + scaling limit attacking R1 (2026-06-30, A of the A+B round) -- the REALISATION input of SEAM.EQUIV.01. The seam is quasi-free (v113/v160/v161), so by Araki self-dual CAR the whole net is the second quantisation…
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Paper context: Research contracts
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SEAM.EQUIV.ONEPARTICLE.01
Original ledger classification: one-particle rigidity + scaling limit [E]/[C]: via Araki self-dual CAR (state<->symbol P, cited) the gapped ground state is the UNIQUE quasi-free realisation (P^2=P), its kernel is Cauchy (~1/N, limit exists), and the limit is the c=1 Dirac CFT (EE c-fit ~1 => c_-=16*1/2=8); Shale-Stinespring makes the Bogoliubov map implementable, upgrading R1 from a bald axiom to an audited [C]; with v463 the residual is entirely certification, zero open internal mechanism; SEAM.EQUIV.01 stays [O]
Original claim text
The one-particle RIGIDITY + scaling limit attacking R1 (2026-06-30, A of the A+B round) -- the REALISATION input of SEAM.EQUIV.01. The seam is quasi-free (v113/v160/v161), so by Araki self-dual CAR the whole net is the second quantisation of its one-particle symbol P, and R1 collapses to a finite-per-mode statement about P. [C] ARAKI SELF-DUAL CAR: a gauge-invariant quasi-free state <-> its symbol P (0<=P<=1) bijectively (Araki 1971; Shale-Stinespring 1965), so a realisation is fully determined by P. [E] RIGIDITY: the gapped ground state is the UNIQUE quasi-free state with P=projection onto K<0 (P^2=P, hermitian to <1e-12), K fixed by gap+chirality+reflection (v426) -- no second realisation. [E] ONE-PARTICLE SCALING LIMIT EXISTS: the real-space kernel is Cauchy on a fixed window (max|P_2N-P_N|~1/N -> 0), so P_inf exists (Gaussianity is why a computation reaches it). [E] LIMIT IS c=1 DIRAC (c_-=8): entanglement S(L)=(c/3)ln L gives c -> 1 (per Majorana 1/2; Peschel/Calabrese-Cardy, ties v450), 16 copies -> c_-=8. [C] Shale-Stinespring: gauge-invariant => no pairing block => the Bogoliubov map is implementable, GNS reps quasi-equivalent. R1 upgraded from a bald axiom to 'the unique quasi-free realisation, one-particle limit exhibited, modulo the named Araki/Shale-Stinespring functor'; with v463 the SEAM.EQUIV.01 residual is now entirely certification, zero open internal mechanism -- closed modulo cited theorems. SEAM.EQUIV.01 stays [O].
Original classification detail
Numerical
Dependencies as recorded
SEAM.EQUIV.01; SEAM.S3.LOCALITY.01; v113; v160; v161; v426; v450; v463
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- Research contracts
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- 2026-06-30 ( v463/ v464 + Lean + Wolfram — the [formula in source] holomorphic-uniqueness pin and the one-particle realisation rigidity: the SEAM.EQUIV.01 residual reduced to entirely certification on both halves)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
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v464_seam_oneparticle_rigidity.pyRegistered verification module · frontier
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SEAM.EQUIV.ONEPARTICLE.01: the one-particle RIGIDITY + scaling limit attacking R1, the REALISATION input of SEAM.EQUIV.01 (A of the A+B round). The seam is quasi-free (v113/v160/v161), so by Araki self-dual CAR the whole net is the second quantisation of its one-particle symbol P. [C] ARAKI: state <-> symbol P bijectively. [E] RIGIDITY: the gapped ground state is the UNIQUE quasi-free state with P=projection onto K<0 (P^2=P), K fixed by gap+chirality+reflection (v426). [E] ONE-PARTICLE SCALING LIMIT EXISTS: kernel Cauchy on a fixed window (~1/N). [E] LIMIT IS c=1 DIRAC: entanglement S=(c/3)ln L gives c->1, 16 copies -> c_-=8 (ties v450). [C] Shale-Stinespring: implementable Bogoliubov map; R1 upgraded from a bald axiom to an audited [C]; with v463 the SEAM.EQUIV.01 residual is entirely certification, zero open internal mechanism. SEAM.EQUIV.01 stays [O]. Python-only (numpy).
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