R12 Causal Result-Digit Motor — Prereg (sibling to carry motor)

Status: exploratory implementation authorized; confirmation custody deferred until carry-motor reports.

Parameter budget (2026-07-17): the frozen flagship has exactly 125,081,664 unique parameters (verified by instantiating the 300k checkpoint configuration with tied embeddings counted once). The system must remain strictly below 150,000,000 total parameters. Default DigitMotor is 576→4096→4096→10 (19,185,674 trainable; 144,267,338 total), leaving at most 5,732,661 further parameters under the strict ceiling. Tiny rank-8 motors are obsolete for this lane. pass their CPU unit tests, and may be run with --allow-non-canonical for exploratory fits. No result from this lane may be treated as confirmatory, and the canonical git-source-commit seal (and any advertised claim beyond a development-board fit/eval) stays gated until Codex's carry-motor (691928) reports, and until this draft passes the same review bar as R12_CAUSAL_CARRY_MOTOR_PREREG.md.

Custody: do not share outputs, confirmation secrets, or fit boards with the carry-motor lane. Same frozen DRS backbone class, different grammar site.

1. Why this exists

Codex Sol’s critique of SCEB is accepted: host apply_op proves control is learnable, not that Shohin executes. Post-DRS residual probes already show actionable digit directions (~+31 Δlogodds at L17–29). Carry motor asks whether carry is held and only fails to serialize. This sibling asks the same for the result digit at the grammar site after ;r= (position p).

Together they are the honest “two-motor bundle” for the one-bit / one-digit local transition — not a novel primitive.

2. Question

Does the frozen late residual contain enough information for a tiny learned output motor, activated only at the grammar-defined result-digit site, to serialize the correct next digit and improve autonomous multi-step DRS execution without host arithmetic?

3. Architecture (mirror carry motor)

• Frozen DRS checkpoint (same SHA family as carry prereg when reused).
• Residual h after block 29 at the prefix ending at the digit site.
• Motor: m(h) = W_up SiLU(W_mid SiLU(W_down h + b_down) + b_mid) + b_up with digit logits over {0…9} only (10-way, exactly 19,185,674 trainable parameters at the frozen d_model=576).
• Active only when the generated prefix is at the exact ;r= digit position for cursor p (grammar router; no solver in the router).
• All other logits untouched.

4. Arms

Base / treatment / shuffled-label / dead motor / linear diagnostic — same logic as carry prereg. No host ALU. No SCEB host bus.

5. Success

Advance only if treatment beats shuffled and dead on autonomous episode exact and first-failure shifts later, on a secret-bound confirmation board.

6. Relation to SCEB

Neither motor may be advertised as a new computational class.