M15-v1 exact original mapping
The original fixes d,k and asks a uniform worst-case polynomial-time classical
sampler for the full output law of every depth-d arbitrary-connectivity circuit
with peak at least n^-k, exact bounded-degree algebraic gates of encoding length
b and polynomial entry evaluation, and n^-k <= epsilon <= 1/4. No heavy string
is supplied. The theorem preserves each clause and runs at error e=n^-k, so it
need not read an arbitrarily long irrelevant epsilon encoding. Local marginals
supply a center; neither a weak-gate decomposition nor geometric locality nor
a polynomial support list is assumed. Positive joint-moment domination, rooted
probability correction and a global L1 budget produce full-law TV sampling.
The explicit integer attempt cap makes runtime worst-case polynomial in n,b.
Fixed depth/peak exponent constants may be enormous; practicality is not claimed.
Inherited source: 2610.02146v1 rooted decomposition and good-zero framework,
with analytic and finite-bit interfaces derived in the proof. Prior source
2309.08405 gives quasipolynomial sampling. Current comparison does not supply
worldwide novelty clearance. Internal support is not external expert review.
No manuscript, publication or exact-sampling result is claimed.
