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A registered result in its source context

Original ledger classification: Identity/Lattice [I]/[L] (DtN + character identity exact) + [P]/[A] (free-bulk premise + net existence)

Recorded statement: THE SEAM-NET CONSTRUCTION (Route 3 carried to its exact verifiable endpoint; B=(E8)1 turned from assertion into checked computation): (1) DtN = FREE CHIRAL DISPERSION [I] - the Dirichlet-to-Neumann (Calderon) operator of the 2d Laplacian…

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Paper context: Origin Theory

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GATE.METRIC.13

Original ledger classification: Identity/Lattice [I]/[L] (DtN + character identity exact) + [P]/[A] (free-bulk premise + net existence)

Original claim text

THE SEAM-NET CONSTRUCTION (Route 3 carried to its exact verifiable endpoint; B=(E8)1 turned from assertion into checked computation): (1) DtN = FREE CHIRAL DISPERSION [I] - the Dirichlet-to-Neumann (Calderon) operator of the 2d Laplacian on the half-space acts on a boundary mode e^{ikx} via the harmonic extension e^{ikx-|k|y} by -d_n u|_0 = |k| u, so the seam-Calderon operator for a free bulk is omega_k = |k|, the massless chiral free-field dispersion defining the free-fermion net on S^1; (2) 16 FREE MAJORANAS c=8 [I]: c=16/2=8=c(D5)_1+c(A3)_1=5+3 (SO(10)xSO(6)=SO(16) carrier grading, conformal embedding coset c=0); (3) E8 CURRENTS 248=120+128 [I]: NS bilinears psi_i psi_j (dim SO(16)=120) + Ramond spinor ground states (2^7=128) = dim E8 (Frenkel-Kac; v148 NS/R split as level-1 current count); (4) THE (E8)1 CHARACTER IDENTITY [I]/[L]: chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+34752q^3+213126q^4+...) = j^{1/3} (q-series to order 4) - the 248 at level 1 is dim E8, so the net IS (E8)1; the GSO/spin-structure sum E4 = (theta3^8+theta4^8)/2 [NS] + theta2^8/2 [R] has level-1 coeff 240 = 112(NS)+128(R) = the 240 E8 roots, 248 = 240+8 (Cartan). RESIDUAL [P]/[A]: exact GIVEN (i) the free-bulk premise (DtN=|k|, v155) and (ii) the operator-algebraic existence/uniqueness of the chiral net from the seam Calderon kernel (Kawahigashi-Longo-type net construction, not a finite computation); Route 3 EXHIBITS and VERIFIES the target net, the irreducible residual is the one premise + the standard net-existence step - where TFPT meets constructive QFT, now sharply located

Original classification detail

Identity/Lattice [I]/[L]: seam net constructed, (E8)1 character verified; residual = free-bulk premise + net existence

Dependencies as recorded

GATE.METRIC.12; GATE.METRIC.11; GATE.METRIC.03; v77; v83; v148; v154; v155

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Registered verification modules

  • v156_seam_net_construction.pyRegistered verification module · registry
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    constructive route (Route 3), exact endpoint: DtN of the 2d Laplacian = |k| (free chiral dispersion); 16 free Majoranas c=8=5+3; E8 currents 248 = 120 (NS bilinears) + 128 (R spinor); the (E8)1 character E4/eta^8 = q^{-1/3}(1+248q+4124q²+...) = j^{1/3} verified to order 4 ⇒ B=(E8)1 CHECKED not asserted; residual = free-bulk premise (v155) + net existence

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