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A registered result in its source context

Original ledger classification: Reduction/citation [E]/[C]/[O] (graph->geometry bridge discharged to Kronheimer 1989; finite input data compiler-exact; premise transforms, stays open)

Recorded statement: THE R3 COMBINATORIAL-TO-GEOMETRIC BRIDGE IS KRONHEIMER'S THEOREM (2026-07-14, bird's-eye round): SEAM.DETK.01/v344 named R3's residual 'the rewrite attractor (a graph) IS the du Val singularity' -- that bridge is Kronheimer's ALE…

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SEAM.KRONHEIMER.01

Original ledger classification: Reduction/citation [E]/[C]/[O] (graph->geometry bridge discharged to Kronheimer 1989; finite input data compiler-exact; premise transforms, stays open)

Original claim text

THE R3 COMBINATORIAL-TO-GEOMETRIC BRIDGE IS KRONHEIMER'S THEOREM (2026-07-14, bird's-eye round): SEAM.DETK.01/v344 named R3's residual 'the rewrite attractor (a graph) IS the du Val singularity' -- that bridge is Kronheimer's ALE hyper-Kaehler quotient construction + Torelli classification (J. Diff. Geom. 29 (1989) 665-683 and 685-697), and ALL of its finite input data are already TFPT compiler outputs. [E] MARKS = NULL = PERRON: C_aff delta = 0 and A delta = 2 delta on the affine-E8 McKay graph; multiset {1,2,2,3,3,4,4,5,6} = 2I irrep dims = the v312 rewrite-attractor Perron vector. [E] KRONHEIMER DIMENSION COUNT: dim_R M - 4 dim_R G = 4(sum_edges d_i d_j - sum d_i^2 + 1) = 4 -- the hyper-Kaehler quotient of the marks quiver is 4-real-dimensional (the C^2/Gamma geometry); sum_edges d_i d_j = sum d_i^2 = 120 forced by the null-vector identity. [E] GAUGE DATUM = |2I|: sum delta_i^2 = 120 = |mu4| h(E8) = 4*30, h(E8) = 30 = |Z2| N_fam g_car. [E] RESOLUTION DATA: 8 = rank(E8) exceptional spheres, intersection form -Cartan(E8) with det = 1 and SNF = identity (the Poincare-sphere link = the det K = 1 face, v232/v344); deformation space h (x) R^3, dim 24. [C] the theorems are CITED, not re-proved (same import class as NPW26/MMST/AGT, v424/v336/v459). [O] the residual premise TRANSFORMS, it does not vanish: 'the raw seam supplies ALE hyper-Kaehler data asymptotic to the (2,3,5) cone' = the SAME single arrow as SEAM.EQUIV.01 (v346 L2); the keystone's open content is now reachable from BOTH sides (net-side scaling limit v336/v458; geometry-side Kronheimer datum). No gate closes, no marker moves. Wolfram mirror added to the extension file (counted with the next verified engine run). LEAN: the finite input data are kernel-checked in TfptCarrier/KronheimerMarks.lean (marks = null/Perron vector over Z, sum delta^2 = 120 = 4*30 with 30 = 2*3*5, hyper-Kaehler dimension count = 4; lake build clean, #print axioms = the 3 standard kernel axioms only).

Original classification detail

Reduction [E]/[C]/[O]: R3's combinatorial-to-geometric bridge = Kronheimer's theorem; marks = null/Perron vector, quotient dim 4, |2I| = 120, unimodular -E8 resolution all [E]; premise 'seam supplies the ALE/orbifold datum' stays [O] (= SEAM.EQUIV.01's one arrow)

Dependencies as recorded

SEAM.DETK.01; SEAM.DETK.02; SEAM.EQUIV.01; HYP.INJECT.01; E8.NETWORK.01; CORR round (experiments); v232; v236; v298; v312; v344; v345; v346

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Registered verification modules

  • v479_kronheimer_quiver_bridge.pyRegistered verification module · core
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    SEAM.KRONHEIMER.01: the R3 'combinatorial-to-geometric bridge' of the det K=1 keystone (SEAM.DETK.01/v344) is Kronheimer's theorem (JDG 29 (1989) 665+685) with all finite input data already compiler outputs. [E] Kac marks = null vector of the affine-E8 Cartan AND Perron vector (A delta = 2 delta) = the v312 rewrite-attractor vector; [E] hyper-Kaehler quotient dimension count dim_R X = 4 (the C^2/Gamma geometry), with sum_edges d_i d_j = sum d_i^2 = 120 forced by the null identity; [E] gauge datum = |2I| = 120 = |mu4| h(E8), h(E8) = 30 = 2*3*5; [E] resolution = 8 spheres with unimodular -E8 form (det 1 = Poincare link = the det K=1 face) and 24 = 3*rank deformation parameters. [C] Kronheimer cited, not re-proved (import class of NPW26/MMST/AGT). [O] the residual premise transforms to 'the raw seam supplies the ALE/orbifold datum' -- the same single arrow as SEAM.EQUIV.01; nothing closes.

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