A registered result in its source context

CAR.LADDER.01

Original ledger classification: Identity/Lattice [I]/[L] (ladder, equivalence, controls, overdetermination) + [P] (QBL)

Original claim text

PASCAL LADDER THEOREM (Target B residual sharpened to zero slack): the closure 2^{g-1} = sum_{k<=K} C(g,k) has for every K exactly one solution g = 2K+1 (K=1..6 scanned over g=1..60; structurally: odd-g midpoint identity by binomial symmetry, even-g strict straddle around 2^{g-1} excludes all even g). EXACT EQUIVALENCE [I]: the carrier selection g=5 <=> the truncation degree K=2 - the Pascal-selection residual (CAR.PASCAL.01/REDTEAM.B.01, typed [A]/[P]) is therefore EXACTLY the one named hypothesis Quadratic Boundary Locality (ARCH.QUAD.01). NEIGHBOUR WORLDS [I]: K=1 -> g=3 (one-family world), K=2 -> g=5 (three families), K=3 -> g=7 (nine families), K=4 -> g=9 inconsistent (N_fam = 255/9 not integer). OVERDETERMINATION [I]: only K=2 also satisfies the independent rank closure g+N_fam = 8 = rank E8 (CAR.UNIQ.01/v14) - two independent selections agree. THE ONE HYPOTHESIS [P] (recorded, not claimed): QBL = the seam Calderon datum is a single two-point kernel and the carrier code is generated by the degrees it certifies (K<=2); if proven from reflection positivity the carrier choice upgrades [A]/[P] -> [L] along QBL => K=2 <=> g=5 => 16 => D5 => E8

Original classification detail

Identity: g=5 <=> K=2 exactly; Target B residual = one hypothesis (QBL)

Dependencies as recorded

CAR.PASCAL.01; REDTEAM.B.01; ARCH.QUAD.01 (QBL named); CAR.UNIQ.01 (v14)