LAM1: Learned Arithmetic Microcode

Status: mechanics and frozen development composition passed

Date: 2026-08-10

Hypothesis

Shohin's strongest current development compiler converts raw source bytes into an exact stack program, but prior learned ledgers tried to regenerate complete intermediate values and collapsed. LAM1 tests a different architecture: learn only the finite local transition laws of decimal arithmetic, then reuse those learned laws recurrently across arbitrary digit positions and program steps.

The candidate owns three trainable transition tensors:

• ADD(a, b, carry) -> (digit, carry);
• SUB(a, b, borrow) -> (digit, borrow); and
• MUL(a, b, carry) -> (digit, carry).

All legal local states are supervised exactly once per optimization step. The same learned tables execute signed arbitrary-precision integer operations, unreduced rational addition/subtraction/multiplication/division, and a typed postfix stack. Candidate execution manipulates only digit arrays, signs, stack addresses, and argmax table outputs. Python integer/Fraction arithmetic exists only in the independent assessor.

The tensors contain exactly 108,000 trainable logits. There is no answer memorization, pretrained language model, verifier, solver call, source family label, or whole-expression target in microcode training.

Frozen mechanics gate

Train from all-zero logits for exactly 32 full-table SGD updates, learning rate 1.0, seed 2026081041. Evaluate immutable BTT1 programs from the exact 75,935-row train and 3,917-row source-disjoint development splits.

All conditions are conjunctive:

1. all 1,400 legal local transitions are exact;
2. normal terminal rational state is exact on 75,935/75,935 train programs;
3. normal terminal rational state is exact on 3,917/3,917 development programs;
4. normal execution has zero invalid states and zero 256-digit overflow;
5. resetting carry/borrow at every recurrent digit loses at least 20 points on multi-digit development programs; and
6. the fixed opcode permutation loses at least 50 points overall.

Failure closes exact LAM1 without table width, optimizer, duration, seed, digit-base, or overflow variants. A pass opens one composition with the frozen BTT1 checkpoint and unchanged width-64 WGP development projection. It does not reopen WGP1 confirmation and does not authorize a holdout claim.

Frozen composition gate

The only authorized composition uses BTT checkpoint SHA-256 2283c86b1a640c9d5c02ffbc70b4646a0a1ad3538c4e1d4ab4ea3b164363e278, LAM checkpoint SHA-256 baab62ec4a256e89950a257616d9f023b8f5e5c8c98b927052f7e722e815c7c4, the immutable 3,917-row BTT development split SHA-256 de16d5dc8dd3676f4c3f4a69c306ec19a0ea8a42e9750bf93a2aaf16f4be0bf8, and width-64 weighted grammar projection. No checkpoint, projection, source, or learned transition is changed.

All conditions are conjunctive:

1. normal source-to-terminal exactness is 3917/3917;
2. normal compilation and execution have zero invalid states and projection has zero exhaustion;
3. same-family/depth source shuffle and zero-byte input each score at most 25%;
4. resetting carry/borrow loses at least 20 absolute points; and
5. fixed opcode permutation loses at least 50 absolute points.

This is a single development evaluation. Failure closes this exact composition without threshold, beam, seed, source, table, or checkpoint variants. Passing qualifies a complete development architecture, but it does not create held-out evidence or reopen the closed WGP1 confirmation.

Mechanics result

CPU job 749769 passed every frozen mechanics condition. Learned transitions were 1400/1400; normal execution was 75935/75935 on train and 3917/3917 on development with zero invalid states. Carry reset scored 367/3917 = 9.3694%; opcode permutation scored 5/3917 = 0.12765%. Scientific elapsed time was 55.42 seconds. Report SHA-256 is b9a82f97065dce5750a02660a80fa71d4af2a4f14c45a39a5f35c5e0135e63c8.

Composition result

H100 job 749784 completed the only authorized composition in 192.24 scientific seconds. The normal path was exact on 3917/3917 programs with zero compiler invalidity, execution invalidity, or grammar-search exhaustion. The controls scored:

• source shuffled: 7/3917 = 0.1787%;
• zero bytes: 14/3917 = 0.3574%;
• carry reset: 367/3917 = 9.3694%; and
• opcode permutation: 5/3917 = 0.12765%.

Every frozen gate passed. The atomic result is docs/research/SHOHIN_LAM1_COMPOSITION_RESULT.json, SHA-256 60698d0b00bc0fc82d38c54173a956e5e3b74d191960e4f1b1de66c7a549e4cf. This qualifies the complete raw-byte compiler, constrained program projection, and learned arithmetic executor on source-disjoint development data. It is not a held-out confirmation because WGP1 confirmation closed at source admission.

Claim boundary

A mechanics pass establishes that learned finite micro-operations can compose exactly over much longer arithmetic trajectories than those seen by any one transition parameter. It does not establish raw-language generalization, novel arithmetic, broad reasoning, or holdout capability. Only the subsequent frozen compiler composition can establish a complete development system.