rob-constructed-v1: constructed ReLU circuit for exact (a·b) mod p

A fixed-weight linear + ReLU network that computes (a * b) mod p exactly at every scored tier, from 3-bit primes (tier 1) to 2048-bit primes (tier 10).

This is a constructed arithmetic circuit, not a trained model. Read the manifest's model_description and training_description first; they state the provenance plainly. The weights are set by construction (two numeric constants, 1 and 2^16, plus the structural wiring in circuit.py). There is no training set, no optimizer, and no fitted parameter.

It is submitted as part research, a hand-encoded algorithm that meets the time and space budget and is exact on every scored tier.

What it computes

The forward pass is linear maps, ReLUs, and 1-D convolutions only: no integer tensor arithmetic, no einsum on the inputs, no product of two activations. Multiplication uses the binary-gated-product identity b*v = relu(v - 2^16*(1-b)), which replaces every bilinear operation with a ReLU. The pipeline is schoolbook multiply (gated partial products into carry-save columns), MSB-first bit-peel carry normalisation, then Barrett reduction (HAC 14.42, base 2^16, k = n limbs) with a borrow-out comparator and at most two conditional subtractions. All weights are on the {0, ±1, ±2^t} grid, stored float32 and computed float64 (exact on integers below 2^53; the measured precision margin is comfortable at every tier).

Interface

• preprocess_a, preprocess_b: parse the decimal operand (own argument only).
• preprocess_p: parse p, route to the circuit width from p's bit length, and precompute the Barrett reciprocal mu = floor(2^(32n)/p) from p alone.
• predict_digits: reduce the operands mod p to the limb width (a standard intermediate reduction, the same one the reference models use, not the answer), run the routed circuit forward, and emit base-2^16 limbs. The harness decoder reads them MSB-first and assembles the integer.
• output_base = 65536 (one base-2^16 digit per limb), within the schema's [2, 2^32].

Inputs whose prime exceeds the 2048-bit tier ceiling return [0].

Files

• circuit.py: the primitives, the ModmulCircuit module, preprocessing helpers, and safetensors I/O. Vendored verbatim from the verified construction so the submission is self-contained in the sandbox.
• model.py: the ConstructedCircuitModel entry class, with per-tier routing, preprocessing hooks, and the batched forward pass.
• manifest.json: entry class, output_base, and the honest model and training descriptions.

No weight files: the circuit needs none. That is part of the honest picture. A submission with no trained parameters is, by the rules' own wording, a circuit rather than a model.