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A registered result in its source context

Original ledger classification: Identity/Lattice [I]/[L] (B residual reduced to the half-spinor input)

Recorded statement: Red-team Target B residual REDUCED [I]/[L]: the carrier 'K=2 Pascal truncation' flagged by the red team as a free postulate is NOT free. K=(g-1)/2 is the Pascal-row MIDPOINT: sum_{k<=(g-1)/2} C(g,k) = 2^(g-1) for every odd g (verified…

Statement, assumptions and sources

Paper context: Red-team audit

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CAR.PASCAL.01

Original ledger classification: Identity/Lattice [I]/[L] (B residual reduced to the half-spinor input)

Original claim text

Red-team Target B residual REDUCED [I]/[L]: the carrier 'K=2 Pascal truncation' flagged by the red team as a free postulate is NOT free. K=(g-1)/2 is the Pascal-row MIDPOINT: sum_{k<=(g-1)/2} C(g,k) = 2^(g-1) for every odd g (verified g=3,5,7,9), i.e. the half-spinor split of the 2^g Dirac spinor. Equivalently the carrier is the even Clifford half-spinor Lambda^even(C^g_car): C(5,0)+C(5,2)+C(5,4)=1+10+5=16=2^(g_car-1)=dim S+. So Target-B's residual is not 'why K=2' but the single standard input 'carrier = half-spinor of Spin(2 g_car)', already used in the D5+A3 glue (v1/v15); the Lean arithmetic 2^g=g^2+g+2<=>g=5 stays [F]

Original classification detail

Identity/Lattice [I]/[L]: K=(g-1)/2 is the half-spinor midpoint, not a free truncation; B residual reduced to the standard half-spinor carrier

Dependencies as recorded

REDTEAM.B.01; FORM.CAR.01; CAR.UNIQ.01; v2; v44

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Registered verification modules

  • v83_e8net_holomorphic_uniqueness.pyRegistered verification module · frontier
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    closes red-team Target A residual 1: #primaries=det(Cartan) ⇒ holomorphy (E8 det 1) is necessary AND sufficient — (D8)₁=SO(16)₁ shares c=8 but has 4 primaries; E8 the unique even-unimodular rank-8 lattice (mass=1/|W(E8)|). A drops 3→2 residuals; + Target B reduced to the half-spinor midpoint K=(g−1)/2

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