feat(PCP): the PCP theorem and the material needed to prove it - #32
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August 30, 2026 14:51
Adds `PCP_theorem`: `NP` equals the union of `PCP r q` over constructible `r =O log` and constant `q`, proved via Dinur's gap amplification (the `NP ⊆ PCP` direction) and a guess-and-verify simulation (`PCP ⊆ NP`). Cut down to what the proof actually uses, at declaration level: the `Classes/PCP` tree (Defs, surface, 115 internal modules, with ~150 declarations unreachable from `PCP_theorem` removed), and a small `FP` toolkit relocated to `Classes/P/Cobham/Internal` (pair-decoder bridge, head-of-list ops, polynomial rulers, bounded binary values and counter increments, and a P language as an FP decision function). Adds `PolyBound.exists_mul_pow_bound` and `pairSnd_length_le` to their home files. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Ah, looks like the other one was merged, I'll close this one |
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The PCP theorem, cut down to what its proof actually uses, in case that's easier: