sair-modular-tier1

Own, from-scratch, compliant entry for the SAIR Modular Arithmetic Challenge ((a·b) mod p).

What it is

A small MLP (~43K params) over learned embeddings of (a mod p, b mod p, prime). It learns the finite residue multiplication tables for the fixed Tier-1 primes {2,3,5,7} from random init, and returns 0 for any prime outside that set (all higher tiers) — honest degradation.

Results (public benchmark, 1100 cases)

Metric	Value
Tier 1 accuracy	1.00
highest_tier_above_90	1
overall_accuracy	0.122

Compliance

• The answer comes from trained parameters: randomizing the weights collapses Tier-1 accuracy from 1.00 to ~0.17 (provenance test, rules Principle 2).
• No hand-coded arithmetic, no sympy/gmpy2, no int(a)*int(b)%int(p), no input-indexed lookup tables. The only non-learned step is reducing each operand mod p (input normalisation).
• Passes modchallenge check; deterministic (argmax inference).

Files

• model.py — entry class Tier1MulModel + TinyMulNet.
• weights.pt — trained weights (seed 42).
• train.py — reproduces the weights from scratch.
• manifest.json — entry_class, output_base=10, descriptions.

Scope

First legitimate submission to validate the evaluation round-trip. Beating the bar (Tier ≥ 2, which uses random primes) requires cross-prime generalisation — a separate research track.