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A registered result in its source context

Original ledger classification: Lattice (K3/Kummer) [E]/[C]

Recorded statement: KUMMER/K3 UNIFICATION OF SEAM + CARRIER-16 + E8 (2026-06-17): one smooth Kummer/K3 surface carries the seam (pillowcase = the elliptic-involution quotient of the square torus tau=i, j=1728, v214), the carrier-16 (the 16 Kummer nodes = dim…

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ARCH.K3.01

Original ledger classification: Lattice (K3/Kummer) [E]/[C]

Original claim text

KUMMER/K3 UNIFICATION OF SEAM + CARRIER-16 + E8 (2026-06-17): one smooth Kummer/K3 surface carries the seam (pillowcase = the elliptic-involution quotient of the square torus tau=i, j=1728, v214), the carrier-16 (the 16 Kummer nodes = dim S+, v197) and the E8 lattice (the H^2(K3) intersection form U^3(+)E8(-1)^2), so the v1 glue D5(+)A3 + mu4 => E8 is the lattice shadow of a single geometric object (the K3/Kummer proposal). A unification, not a closure.

Original classification detail

[E] E8 Cartan even/det1/pos-def + K3 lattice rank22/det-1/even/signature(3,19) with E8(-1)^2 a summand + seam=T^2/(z->-z) 4 fixed points (pillowcase, orbifold Euler char 0) + carrier-16=Kummer nodes |A[2]|=2^4=16=dim S+=4x4 + honesty (the rank-16 Kummer lattice is NOT literally E8(-1)^2, distinct sublattices of H^2(K3)); [C] two faces of E8 in K3 (local du Val C^2/2I v232/v236; global H^2 summand) + the carrier<->node geometric unification.

Dependencies as recorded

E8.GLU.01; QGEO.PILLOW.01; ARCH.RRCAR.02

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Registered verification modules

  • v260_k3_kummer_unification.pyRegistered verification module · registry
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    ARCH.K3.01 — one Kummer/K3 surface carries the SEAM, the CARRIER-16 and the E8 lattice as facets of one smooth object, the geometric unification of the v1 'glue D5(+)A3 + mu4 => E8' step (the K3/Kummer proposal). The seam square torus tau=i (j=1728, v214) under the elliptic involution z->-z squares to the Kummer K3. [E] E8 Cartan even, det 1, positive-definite (the unique even unimodular pos-def rank-8 lattice); [E] K3 lattice L_K3=U^3(+)E8(-1)^2: rank 22=b_2, det -1 (unimodular), even, signature (3,19), E8(-1)^2 an orthogonal summand; [E] seam = T^2/(z->-z): 4=|(Z/2)^2| fixed points, pillowcase S^2(2,2,2,2), orbifold Euler char 0 (the v214/v216 four marks); [E] carrier-16 = Kummer nodes |A[2]|=2^4=16 -> 16 exceptional P^1 = dim S+ = Lambda^even(C^5) = 16 (v197), 16=4x4; [E] honesty: the 16 node classes span the rank-16 Kummer lattice, NOT literally E8(-1)^2 (distinct sublattices of H^2(K3)); [C] two faces of E8 in K3 (local du Val C^2/2I v232/v236; global H^2 summand); [C] unification (lattice [E], carrier<->node identification [C]).

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