README.md

# bitserial-modmul-v7 (tier 9, L=1024)

Submission for the SAIR Modular Arithmetic Challenge. One shared, p-conditioned recurrent cell
in a fixed bit-serial Horner loop computes (a * b) mod p; the cell learns the per-step transition
s' = (2*s + d*x) mod p and the loop only sequences bits. entry_class model.BitSerialReducer,
output_base 2, ~471K params, L=1024 (warm-started from the L=512 cell).

## Local evaluation (official open-source scorer, run locally; not the organizers' leaderboard)
- modchallenge evaluate (full 1100, public/default seed, A100-class hardware): tiers 1-9 = 1.00,
  highest tier 9, overall 0.902, wall-clock 139s (inside the 300s budget on this hardware; the
  organizers' sandbox may be slower).
- Randomising the weights collapses every solved tier to 0.00 (capability is in the trained parameters).

## Limitation (honest)
Not exact. The per-step map is exact on random states and exhaustively on primes < 64, but a sparse
set of structured-trajectory inputs (powers-of-two-times-random) still fails at large primes,
reproducing the Neural GPU limitation (Price, Zaremba, Sutskever 2016). The benchmark tiers reflect
average-case accuracy on the official scorer's random-operand distribution, not worst-case exactness.
Not organizer-verified; compliance ruling on the loop scaffold pending.