Currently, int(a_enc) % p is deemed ineligible under SAIR. https://github.com/SAIRcompetition/modular-arithmetic-challenge/commit/99cac6ef5c2f82e53105ec0ddcbb9b8d37bf6fca Commits on Aug 11, 2026

This submission routes by the bit-length of p, using output_base: "p" (a single base-p digit per problem):

Both the T2 and T3 branches reduce each operand with int(a_enc) % p / int(b_enc) % p inside predict_digits_batch before the reduced residues enter their respective networks (the same single-operator-per-operand pattern my-t2-model/model.py already uses, and the same pattern used by this repository's digit_transformer reference example). This is a disclosed deviation from a stricter standard the project's T3 research has otherwise been holding itself to; it is necessary here because the T3 Stage B networks were trained purely on already-reduced residues (ra, rb < p) and have no other way to receive in-distribution input from the much larger raw operands Tier 3 actually uses (up to 64 bits vs. a 9-16 bit p). Beyond that reduction, no arithmetic is used to compute or correct the answer: the T3 branch's only other post-processing step masks output classes >= p to -inf in the composer's joint log_softmax(low) + log_softmax(high) grid and takes the argmax over what remains -- the same "mask invalid classes, then argmax" pattern already used by ResidueProductNet and ProductBytePairQuotientNet internally.

Current packaged T3 checkpoint is the RTX 4070 scale-up run results/t3_4070_b2048_bf16_wd0_bit15x2_20260703_1525, best step 44000 of 45000. Local bit-balanced prime-holdout accuracy is 69.1% overall (15-16 bit bucket: 30.2%); count-weighted official-shaped estimate is 41.5%. This remains below the eventual 90% target; see manifest.json for fuller disclosure and experiments/t3/README.md for the underlying Stage B research notes.

Evaluate locally:

For a minimal HuggingFace submission, keep manifest.json, model.py, t2_weights.pt, t3_weights.pt, and this README.