feat(adr-0250): Tier-2 multi-entity arithmetic — design spike + T2a executor #71

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core-labs merged 1 commit from feat/adr-0250-tier2-multi-entity into main

2026-07-18 21:07:12 +00:00

core-labs commented

2026-07-18 21:02:37 +00:00

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Opens the Tier-2 arc (next arc after ADR-0249). This PR lands the design spike for review and the T2a multi-register executor implementation (landing on this branch).

Design spike (`docs/research/tier2-multi-entity-arithmetic-spike-2026-07-18.md`)

Action-2 finding (probed on real data). All 24 refused GSM8K dev-holdout cases are constant-operand multi-entity (20 contain a transfer). Unknown split: 18 single-entity (pure 2a → 26/50 → 44/50) and 6 total-like (need a certified summation turn = 2b certified-decode staging on real data → up to 50/50). Derived-operand transfers ("half of X") are 0-on-this-holdout — designed + guarded, synthetic-only.

Action-1 model. Multi-entity state = a product of independent conformal lines (one register per entity, no dimensional inflation). Constant-operand transfer = coupled T₋ₖ / T₊ₖ on disjoint registers, exact by P1's per-line exactness. Verified in-tree: Ruth 36→31, Sara 19→24, sum conserved; 200 random transfers exact + conserving to ~6e-11.

Conservation pin (hard-reject). Σ decode(after) ≡ Σ decode(before) is a load-bearing gate — a non-conserving transfer is an algebraic failure, fail-closed.

Transactional atomicity. Registers are an immutable snapshot; a transfer computes both candidate states (prepare), validates (both certified + conservation), then produces a new register set (commit). Failure anywhere → the new set is never built → the original stands → no partial-mutation window, no rollback. Records append only on commit; any abort aborts the whole program (fail-closed, preserves wrong=0).

2b chain of custody (Shay's Q): certificate psi_digest anchor + operand_certificate_id in the TurnRecord + deterministic re-execution / live gate — no trusted-Python assumption.

§7 rulings (Shay, resolved)

"Altogether" = certified summation turn in the substrate (not a Python total). 2. T2b ships designed + guarded. 3. Conservation pin = hard-reject.

Status

Design landed; T2a implementation (multi-register executor) in progress on this branch — do not merge until the executor + tests + real-data measurement land. Off-serving (A-04), no gate activated, TDD + smoke-gated. ADR-0250 (Proposed) to follow.

Opens the Tier-2 arc (next arc after ADR-0249). This PR lands the **design spike** for review and the **T2a multi-register executor** implementation (landing on this branch). ## Design spike (`docs/research/tier2-multi-entity-arithmetic-spike-2026-07-18.md`) **Action-2 finding (probed on real data).** All 24 refused GSM8K dev-holdout cases are constant-operand multi-entity (20 contain a transfer). Unknown split: **18 single-entity** (pure 2a → 26/50 → 44/50) and **6 total-like** (need a certified summation turn = 2b certified-decode staging on *real* data → up to 50/50). Derived-operand transfers ("half of X") are **0-on-this-holdout** — designed + guarded, synthetic-only. **Action-1 model.** Multi-entity state = a product of independent conformal lines (one register per entity, no dimensional inflation). Constant-operand transfer = coupled `T₋ₖ` / `T₊ₖ` on disjoint registers, exact by P1's per-line exactness. Verified in-tree: Ruth 36→31, Sara 19→24, sum conserved; 200 random transfers exact + conserving to ~6e-11. **Conservation pin (hard-reject).** `Σ decode(after) ≡ Σ decode(before)` is a load-bearing gate — a non-conserving transfer is an algebraic failure, fail-closed. **Transactional atomicity.** Registers are an immutable snapshot; a transfer computes both candidate states (prepare), validates (both certified + conservation), then produces a *new* register set (commit). Failure anywhere → the new set is never built → the original stands → no partial-mutation window, no rollback. Records append only on commit; any abort aborts the whole program (fail-closed, preserves wrong=0). **2b chain of custody** (Shay's Q): certificate `psi_digest` anchor + `operand_certificate_id` in the `TurnRecord` + deterministic re-execution / live gate — no trusted-Python assumption. ## §7 rulings (Shay, resolved) 1. "Altogether" = certified summation turn in the substrate (not a Python total). 2. T2b ships designed + guarded. 3. Conservation pin = hard-reject. ## Status Design landed; **T2a implementation (multi-register executor) in progress on this branch** — do not merge until the executor + tests + real-data measurement land. Off-serving (A-04), no gate activated, TDD + smoke-gated. ADR-0250 (Proposed) to follow.

core-labs added 1 commit 2026-07-18 21:02:40 +00:00

docs(research): Tier-2 multi-entity arithmetic design spike bae16cf607

Action 1: multi-register product-of-lines model + coupled-translator transfers
+ transfer-conservation invariant (verified in-tree: Ruth/Sara + 200 random
transfers, conservation & per-register exactness ~6e-11). Transactional
atomicity via immutable register snapshots (prepare-validate-commit; no partial
mutation, no rollback).

Action 2 finding (probe on the 24 refused GSM8K dev cases): ALL 24 are
constant-operand multi-entity (20 contain a transfer). Unknown split: 18
single-entity (pure 2a -> 26/50->44/50), 6 total-like (need certified summation
= 2b certified-decode staging on REAL data -> up to 50/50). Derived-operand
transfers (half-of-X) = 0 on this holdout (synthetic-only, guarded).

Tier-2b certified-decode staging + chain-of-custody (Shay's Q): certificate
psi_digest anchor + operand_certificate_id in the TurnRecord + deterministic
re-execution/live gate — no trusted-Python assumption.

§7 rulings RESOLVED (Shay): certified summation turn; ship 2b designed+guarded;
conservation pin = hard-reject. ADR-0250 (Proposed) to follow.