Skip to main content

A registered result in its source context

Original ledger classification: Identity [I] (Bogoliubov second-quantisation functoriality + cone gap = one-particle gap + fixed sector = Wick powers) + [P] (the one-particle symbol identification) + [C] (quasi-freeness forced by v158)

Recorded statement: THE CONE REDUCES TO ONE PARTICLE (discharges the v160/GATE.METRIC.16 scope premise via Bogoliubov second quantisation; the infinite-dimensional Schwinger cone is eliminated, a finite one-particle statement remains): a quasi-free…

Statement, assumptions and sources

Paper context: Research contracts

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

GATE.METRIC.17

Original ledger classification: Identity [I] (Bogoliubov second-quantisation functoriality + cone gap = one-particle gap + fixed sector = Wick powers) + [P] (the one-particle symbol identification) + [C] (quasi-freeness forced by v158)

Original claim text

THE CONE REDUCES TO ONE PARTICLE (discharges the v160/GATE.METRIC.16 scope premise via Bogoliubov second quantisation; the infinite-dimensional Schwinger cone is eliminated, a finite one-particle statement remains): a quasi-free (Gaussianity-preserving) transport on the CAR algebra is T = Gamma(t), the second quantisation of a one-particle contraction t on the 16-dim Majorana space H_Sigma; the Fock space grades by correlator degree F = (+)_m Lambda^m H_Sigma and Gamma(t) acts on degree m as the exterior power/compound matrix Lambda^m(t). (1) FUNCTORIALITY [I] - spec(Gamma(t)|deg m) = {products of m eigenvalues of t} (compound-matrix theorem; checked all m=0..6) so the whole correlation spectrum is generated by the finite one-particle spectrum; (2) THE CONE GAP IS THE ONE-PARTICLE GAP [I] - the sub-leading eigenvalue of Gamma(t) over the WHOLE cone equals the one-particle sub-leading eigenvalue (2/3)^6 (pad the largest contracted mode with fixed factors), so premise 5 (Delta=6 log(3/2) on the cumulant space) IS premise 5 on the 16-dim one-particle space, same number; (3) NO INDEPENDENT FIXED HIGHER CUMULANT [I] - the eigenvalue-1 sector at degree m has multiplicity C(f,m) (wedges of the f fixed one-particle directions = disconnected Wick powers of K_Sigma; total 2^f, zero above degree f); a connected fixed cumulant on the fixed subspace is excluded by v113 (one polarization <=> one vacuum, rank=c=8), so premise 2 (unique fixed ray on the cone) = {one-particle gap} + v113; (4) QUASI-FREENESS FORCED [P] - the 120 = dim so(16) weight-1 chiral currents ARE the Bogoliubov generators on the 16 Majoranas, and v158 makes every non-Gaussian deformation irrelevant (no relevant, no (1,1)-marginal), so premise 1 follows from rigidity, it is not an extra postulate. CONSEQUENCE: the three full-cone premises of GATE.METRIC.16 collapse to ONE finite (16-dim) one-particle statement. RESIDUAL [P]/[A]: 'the seam RG transport one-particle symbol is the gapped Calderon Bogoliubov map - fixed eigenspace = the rank-8 K_Sigma polarization (v113), sub-leading gap = (2/3)^6 (v56)'; every number is supplied by the suite, only the physical identification (the actual seam RG generator equals this Bogoliubov map - a Kawahigashi-Longo-class statement, = the A2 net residual) stays open; NOT a cone statement, NOT 'prove Gaussianity'

Original classification detail

Identity [I]: cone gap = one-particle gap (Bogoliubov); (A) reduced from the infinite cone to ONE 16-dim one-particle identification

Dependencies as recorded

GATE.METRIC.16; v56; v113; v158; v160_seam_gaussianity_from_pf.py

Open the original ledger source, row 245

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

All 14 linked sections

Registered verification modules

  • v161_one_particle_reduction.pyRegistered verification module · registry
    Read the description recorded in the module registry

    the cone reduces to one particle (discharges v160's scope premise via Bogoliubov second quantisation): a quasi-free transport is T = Γ(t), the second quantisation of a one-particle contraction t; Γ(t) acts on the degree-m correlator sector as the exterior power Λ^m(t), so (1) spec(Γ(t)|deg m) = products of m one-particle eigenvalues [E]; (2) THE CONE GAP EQUALS THE ONE-PARTICLE GAP — sub-leading eigenvalue over the whole cone = (2/3)^6 exactly [E]; (3) the eigenvalue-1 sector = wedges of the fixed subspace (disconnected Wick powers), no independent fixed higher cumulant; uniqueness closed by v113 (one polarization ⇔ one state) [E]; (4) quasi-freeness FORCED not assumed — the 120 = dim so(16) chiral currents ARE the Bogoliubov generators and v158 makes every non-Gaussian deformation irrelevant [C]. RESIDUAL [O]: v160's three full-cone premises collapse to ONE 16-dim one-particle statement (seam symbol = gapped Calderón Bogoliubov map, fixed = rank-8 K_Σ, gap (2/3)^6); all numbers supplied, only the physical identification (Kawahigashi-Longo class, = the A2 net residual) stays open.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries