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A registered result in its source context

Original ledger classification: Identity [I] (closures + negative control) + Audit (chi_T fingerprint; dual cuts = presentation)

Recorded statement: SPINE TETRAHEDRON - the compiler microkernel as ONE finite object (review proposal 2026-06-10, validated and typed): the spine T={2,3,4,5}={|Z2|,N_fam,|mu4|,g_car} equals {e3(a),p0(a),e1(a),e2(a)} for the anchor a=(1,1,2), so the…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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ARCH.SPINE.01

Original ledger classification: Identity [I] (closures + negative control) + Audit (chi_T fingerprint; dual cuts = presentation)

Original claim text

SPINE TETRAHEDRON - the compiler microkernel as ONE finite object (review proposal 2026-06-10, validated and typed): the spine T={2,3,4,5}={|Z2|,N_fam,|mu4|,g_car} equals {e3(a),p0(a),e1(a),e2(a)} for the anchor a=(1,1,2), so the tetrahedron is the anchor plus its zeroth moment, not a second structure [I]. Edge products {6,8,10,12,15,20} = {|R+(A3)|/C6, rank E8=h(D5)=det R, A_Lambda=|E(K5)|, |R(A3)|=dim SM gauge, dim A3, det L} [I]; face products {24,30,40,60} = {|W(A3)|, h(E8), |R(D5)|=SumL, cascade start=dim(10,6) block (v89)} [I]; volume 120=|R+(E8)|=5!=sum E8 exponents=Tr_S+ X^2 [I]. Graph reading: |R(E8)|=240=|mu4|*|E(K4)|*|E(K5)| with |E(K4)|=p2(a)=6, |E(K5)|=p3(a)=10, plus negative control: breaks at K6 (|E(K6)|=15 != p4(a)=18) - specific not generic [I]. DISCIPLINE: the dual cuts (node x opposite face, edge x opposite edge, all =120) are TAUTOLOGIES of complementary partitions - typed as presentation raster, never as evidence; the grammar is a SUB-grammar (7, 16, 41, 48, 240, 248 are NOT subset products: the tetrahedron complements the admissibility filter, it does not replace it). chi_T=t^4-14t^3+71t^2-154t+120 (coefficients = node/edge/face sums + volume; 14=dim G2; spine symmetric about 7/2: chi(0)=chi(7)=120, chi(1)=chi(6)=24; scalaron 7=2+5=3+4 = complementary-pair sum = the same 7 as the branch-divisor trace v80/v81) typed AUDIT, not load-bearing

Original classification detail

Identity [I]: spine tetrahedron closures; dual cuts tautological; sub-grammar honestly typed

Dependencies as recorded

ANCHOR.GEN.01; FLAV.PENCIL.05; GATE.METRIC.06 (60=dim(10,6))

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Registered verification modules

  • v91_spine_tetrahedron.pyRegistered verification module · registry
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    Spine tetrahedron {2,3,4,5} = {e₃(a), p₀(a), e₁(a), e₂(a)}: edges {6,8,10,12,15,20}, faces {24,30,40,60}, volume 120 = |R⁺(E₈)| = 5!; 240 = |μ₄|·|E(K₄)|·|E(K₅)| with K₆ negative control; dual cuts typed as tautological presentation; sub-grammar honestly incomplete (7,16,41,48,240,248 outside)

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