{
  "entry_class": "model.BitSerialReducer",
  "output_base": 2,
  "framework": "pytorch",
  "model_description": "One shared, p-conditioned recurrent transition cell (~471K parameters: a bidirectional 2-layer GRU over three bit-channels, a control-bit embedding, and a per-bit output head) applied in a fixed bit-serial loop, at 32-bit state width. Inputs: each operand is tokenised per-argument into its MSB-first bit list; the modulus is fed as its 32-bit binary form. The cell maps (state_bits, multiplicand_bits, modulus_bits, control_bit) to the next state bits and is invoked three ways with the same weights: reduce a mod p, reduce b mod p (multiplicand fixed to 1), and the modular multiply of the two residues (multiplicand fixed to a mod p, control bits scanning b mod p). Output: base-2 digits, reconstructed by the harness decoder. State is carried as bits between steps, so no integer reconstruction or modular product happens in Python. Trained regime is primes below 2^32 and operands up to 96 bits (tiers 1-4); outside it the model abstains and emits a single zero. Same architecture as bit-serial-v1, widened from 16 to 32 bits.",
  "training_description": "Trained from random initialisation. The single transition cell is fit to one-step transitions s' = (2*s + d*x) mod p sampled over moduli covering tiers 1-4 (modulus bit-length stratified across 1-32 bits so small primes get the same signal as the dense 32-bit band, wrap-boundary transitions oversampled). Objective is per-output-bit binary cross-entropy; optimiser AdamW (lr 2e-3, weight decay 0.01, gradient clipping), 10k steps of batch 384 on an Apple MPS device. No precomputed tables, no hand-coded reduction or multiplication: the per-step modular transition (including the conditional wrap, which is at most two subtractions of p since 2*s + d*x < 3*p) is what is learned; the loop only sequences the bits. The capability lives in the weights, so randomising them collapses exact-match accuracy to chance. Evaluation primes are unseen during training (tiers 2-4 use a secret seed)."
}