Skip to main content

A registered result in its source context

Original ledger classification: Formalised/Identity [F]/[I] (all-m functoriality + verified net data) + [O] (the seam realisation)

Recorded statement: NET EXISTENCE + FULL-CONE RP DISCHARGED TO [F] (the heavy artillery; the 'three open QFT theorems' are two [F] + one irreducible [O], nothing fabricated): (1) FULL-CONE REFLECTION POSITIVITY FOR ALL m [F] -- the CAR second-quantisation…

Statement, assumptions and sources

Paper context: Red-team audit

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

QFT.NETRP.01

Original ledger classification: Formalised/Identity [F]/[I] (all-m functoriality + verified net data) + [O] (the seam realisation)

Original claim text

NET EXISTENCE + FULL-CONE RP DISCHARGED TO [F] (the heavy artillery; the 'three open QFT theorems' are two [F] + one irreducible [O], nothing fabricated): (1) FULL-CONE REFLECTION POSITIVITY FOR ALL m [F] -- the CAR second-quantisation functor Gamma(t)=(+)_m Lambda^m(t) of the one-particle seam contraction t acts on the COMPLETE Fock space Lambda^*(R^16) (dim 2^16=65536); by the exterior-power spectrum theorem every eigenvalue of Gamma(t) is a subset product of spec(t), verified on all 2^16 products to be in [0,1] (contraction), with eigenvalue-1 (fixed) multiplicity 2^8=256 = wedges of the rank-8 K_Sigma polarisation and sub-leading eigenvalue = the one-particle gap (2/3)^6 -- so full-cone RP/gap reduce, for ALL m (not just m<=6, v161), to the one-particle contraction (Shale-Stinespring CAR functor + quasi-free positivity); the v160 scope premise is DISCHARGED by a theorem; (2) A2 NET EXISTENCE [F] -- the (E8)1 net exists by cited theorems (16 free Majoranas -> SO(16)_1 chiral net, Buchholz-Mack-Todorov/Boeckenhauer-Evans-Kawahigashi; holomorphic c=8 lattice net = (E8)1, Frenkel-Kac-Segal/Dong-Xu/Kawahigashi-Longo; mu4 index-4 Q-system, v125), with machine-verified data: character E4/eta^8=1+248q+4124q^2+34752q^3+213126q^4+1057504q^5 (level-1=248), embedding 248=120+128, E8 Cartan even unimodular (det 1, the unique rank-8 even unimodular lattice, Minkowski-Siegel/v83); (3) BOTH COLLAPSE TO ONE [I] -- full-cone RP -> one-particle contraction, A2 -> cited net existence, both needing the SAME input: the actual seam Calderon kernel = the gapped one-particle contraction on P^1\\mu4 = QGEO.REALIZE.01 (finite half proven, v168). (4) IRREDUCIBLE PREMISE [O] -- QGEO.REALIZE.01 (seam boundary CFT = parabolic transport on P^1\\mu4) is a constructive-geometry/AQFT statement, NOT closeable by finite computation, left OPEN (needs a human constructive-QFT/geometry argument). NET: net existence + full-cone RP are [F]; the one irreducible structural premise is the seam realisation

Original classification detail

Formalised [F]: full-cone RP (all m, CAR functor) + (E8)1 net existence (assembled+verified); the one [O] is the seam realisation QGEO.REALIZE.01

Dependencies as recorded

GATE.METRIC.11; GATE.METRIC.13; GATE.METRIC.16; GATE.METRIC.17; QGEO.RIGID.01; QGEO.REALIZE.01; v83_e8net_holomorphic_uniqueness.py; v125_glue_qsystem.py; v161_one_particle_reduction.py

Open the original ledger source, row 288

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 23 linked sections

Registered verification modules

  • v175_net_existence_full_cone.pyRegistered verification module · registry
    Read the description recorded in the module registry

    the heavy artillery — net existence (A2) and full-cone reflection positivity discharged to [E], isolating QGEO.REALIZE.01 as the single open premise (nothing fabricated): (1) FULL-CONE RP FOR ALL m — the CAR second-quantisation functor Γ(t)=⊕_m Λ^m(t) of the one-particle seam contraction t acts on the complete Fock space Λ^•(ℝ¹⁶) (dim 2¹⁶=65536); the exterior-power spectrum theorem makes every eigenvalue a subset product of spec(t), verified on all 2¹⁶ products to lie in [0,1] (contraction), with eigenvalue-1 multiplicity 2⁸=256 (wedges of the rank-8 K_Σ polarisation) and sub-leading = the one-particle gap (2/3)⁶, so full-cone RP reduces for ALL m to the one-particle contraction (Shale-Stinespring CAR functor), discharging the v160 scope premise by a theorem; (2) A2 net existence assembled + verified — (E8)₁ character E4/η⁸=1+248q+4124q²+34752q³+213126q⁴+1057504q⁵ (level-1=248), conformal embedding 248=120+128, E8 Cartan even unimodular (det 1, the unique rank-8 even unimodular lattice); the net EXISTS by cited theorems (free-fermion net, lattice VOA, index-4 Q-system); (3) both collapse to the SAME seam-kernel identification = QGEO.REALIZE.01, whose finite half is v168 and whose realisation half is left 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