Selfcounting channel
v112_selfcounting_channel.py · registry
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SELF-COUNTING CHANNEL (the Pascal closure is an IDENTITY of the certified channel, not an extra requirement): CANONICAL BIJECTION — for odd g negation w ↦ −w maps S⁺ bijectively into the opposite sheet, so the Cartan-neutral kernels of the certified channel are exactly the pairs (w,−w), ONE PER CODE STATE: #neutral kernels = dim S⁺ = 2^{g−1} exactly (4, 16, 64 for g = 3,5,7) — the channel counts the code; PASCAL PARTITION: the same neutral set graded by pair-degree m has sizes C(g,m) — g=5: (1,5,10); THE CLOSURE IS AN IDENTITY: two countings of one set give 2^{g−1} = Σ_{m≤K} C(g,m) (symbolic, all odd g=3..13) — v108's closure condition is the channel counting itself; HODGE FOLD: code minus-grading C(g,2j) = C(g,min(2j,g−2j)) with min ≤ K — every code sector appears at pair-degree ≤ K; carries NO g-selection (stays with rank-8 g+N_fam=8 + integrality); RESIDUE RE-TYPE [P]: QBL clause (b') is now the channel's definition — the remaining physical input is 'the seam certifies through a single scalar 2-point kernel' (free c=8 seam net: Wick extends it to the whole even tower); QBL = structural consistency frame, no longer a missing selector
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