639616b3e5
Folds in Shay's rulings on the spike: - ERRATA sections added to ADR-0249, ADR-0250, and both acceptance-evidence docs (statuses stay Accepted): corpus label 'real GSM8K dev holdout' -> 'CORE-authored GSM8K-style corpus (ADR-0119.2)'. Mechanism claims (wrong=0, PARITY, conservation, atomicity, chain-of-custody, 200/200) all stand; reframe not retraction. Covers the #74 review comment that repeated the label. (Also fixed ADR-0250 evidence status -> RATIFIED, which the ratification housekeeping missed.) - Two instruments named + never-blended scoreboard: authored = mechanism-correctness (200/200 stands as that); official holdout = generalization (5/500 symbolic / 0/500 corridor). public/dev-1 floors relabeled MECHANISM floors, composition-disclosed. - Censored-incidence fix: parse-INDEPENDENT tagging of 100 official cases (documented heuristic). 70/100 carry frontier markers (rate 31, fraction 28, compare_mult 20) -> (c) refuted, frontier COMMON not rare; the table is the reader-arc curriculum by real-world frequency. - Reader-practice-loop design with the four non-negotiable constraints (real held-out data only; wrong=0 gates consolidation; sealed test untouched; holdout_dev split disjoint from the measured metric). Sequencing: capability->practice->calibration-> serve; reader is the critical path for all three; serve-landing de-prioritized (0/500). Spike verdict for ruling; nothing built.
116 lines
7 KiB
Markdown
116 lines
7 KiB
Markdown
# ADR-0250: Tier-2 Multi-Entity Arithmetic — the Multi-Register Extension
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**Status**: **Accepted**
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**Date**: 2026-07-18
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**Authors**: Joshua Shay + multi-model R&D (implemented Fable 5)
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**Depends on**: ADR-0249 (reader→Hamiltonian compiler — quantity kernel, relation compiler, turn programs), ADR-0243/0244/0245 (relaxation, content-addressing, f64)
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**Design record**: `docs/research/tier2-multi-entity-arithmetic-spike-2026-07-18.md`
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**Acceptance evidence**: `docs/handoff/ADR-0250-Acceptance-Evidence.md`
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---
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## ERRATA (2026-07-18) — corpus mislabel corrected; status stays Accepted
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This ADR calls the authored corpus the **"entire real GSM8K dev holdout."** That label is wrong: per
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ADR-0119.2, `dev` (50) and `public` (150) are **CORE-authored, GSM8K-*style*** problems, **not** real
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GSM8K. Read every "real GSM8K" reference here as **"CORE-authored GSM8K-style corpus (ADR-0119.2)."**
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**Nothing about the Tier-2 mechanism is retracted** — the multi-register model, coupled-translator
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transfers, the relative conservation hard-reject, prepare→validate→commit atomicity, the certified
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summation turn, and the chain-of-custody all stand; the authored corpus is the mechanism-correctness
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instrument and the 50/50 (200/200 across both ADRs) is exactly that evidence. Only the corpus label
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falls. Measured real-GSM8K reach (spike `docs/research/dev2-frontier-measurement-spike-2026-07-18.md`):
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reader parses 5/500, corridor 0/500 — reader-gated. Recorded here as the honest-measurement doctrine
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catching its own mislabel.
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---
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## 1. What this ADR is
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ADR-0249 closed Tier-1 (single-accumulator affine arithmetic) and recorded the 24 multi-entity
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GSM8K dev-holdout cases as the Tier-2 frontier. This ADR crosses that frontier — and with it the
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reader→Hamiltonian compiler solves the **entire** real GSM8K dev holdout (50/50) at wrong=0. It
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extends the substrate mechanism only; no serving change, no gate activated, no manifold mutation.
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## 2. The multi-register model
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Multi-entity state is a **product of independent conformal lines**: one register (null point /
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its own relaxation) per entity. This respects the Cl(4,1) boundary exactly — no dimensional
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inflation (no `Cl(8,2)` to pack two points into one multivector), so the f64 rounding floor
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(~6e-11) stays the only residual and every op is a native, exact versor action on a pure state.
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Per-register ops (add/subtract/multiply/divide by constants) reuse the Tier-1 transport unchanged.
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## 3. Transfers + the conservation pin
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A constant-operand transfer ("actor gives `k` to target", ADR-0116 decomposition) is a **coupled
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pair of translators** — `T₋ₖ` on the actor register, `T₊ₖ` on the target — acting on disjoint
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registers, so exactness across the independent null points is inherited from ADR-0249 P1.
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**Conservation pin (hard-reject, relative).** `Σ decode(after) ≡ Σ decode(before)` within
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`|Δ| ≤ rtol·max(1,|before|)`. The tolerance is *relative* because decoded-quantity error scales
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with magnitude (found on a case chaining to 222); an absolute tolerance is brittle, while a
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genuine non-conserving transfer is off by a whole `k` and is still caught. A conservation failure
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is an algebraic failure, not a scope miss — fail closed.
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## 4. Transactional atomicity
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Registers are an **immutable snapshot**. A transfer runs **prepare → validate → commit**: both
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candidate states are relaxed into locals, validated (both converged AND conservation), then — only
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on full success — a *new* register mapping is produced. A failure anywhere means the new mapping is
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never built, so the original stands untouched: no partial-mutation window, no rollback. Records
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append only on commit; any abort raises a typed `MultiRegisterError` and aborts the whole program
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(fail-closed — a partial answer is never emitted, preserving wrong=0).
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## 5. Certified summation + chain of custody
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A total-like unknown (`unknown.entity is None`, "how many altogether") is the **explicit typed
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signal** for a certified summation over all registers — never inferred from an operation pattern.
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Per the summation ruling it stays in the substrate: each addition is a certified relaxation turn
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(`T_v` on the running accumulator), never a Python `sum()`.
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The operand of each summation turn is the decode of a certified register state, bound in the record
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by `operand_source_digest` (the `psi_digest` byte convention). Deterministic re-execution
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reproduces the state and its decode, so the Python layer cannot tamper with the intermediate value
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— the chain of custody holds with no trusted-Python assumption. The field is added conditionally to
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the record payload, so non-summation record digests are unchanged.
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## 6. Honest measurement (done-when)
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On the sealed real GSM8K dev holdout (50 cases): **50/50 solved, wrong=0** — Tier-1 (26) + T2a
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single-entity (18) + summation (6). The instrument's `arithmetic-chain` domain routes each case to
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the right tier and compares the corridor to a symbolic fold of the *same* compiled program: PARITY
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(delta 0 — the field matches arithmetic, it does not beat it). The deliverable is a decidable
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measurement + real-holdout coverage, per the honest-NULL protocol.
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## 7. Scope + recorded frontier
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Tier-2a: single-accumulator-per-entity affine + constant-operand transfers, positive scale,
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matching units. 2b: the certified summation turn (real, exercised by the 6 total-like cases) and
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the derived-operand-transfer path ("half of X" — designed + guarded, **0 on this holdout**). Still
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refused and recorded: non-affine kinds (rate/comparison/fraction/partition — 0 on this holdout),
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derived-operand transfers, and >5-atom deduction — never silently dropped.
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## 8. Governance
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Off-serving (A-04): `evals/multi_register_program.py` + the instrument domain; never imported by
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`chat/runtime.py`. No gate activated; I-03 untouched; ratified contracts reused
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(`compile_quadratic_well`, `quantity_kernel`, the Ring-2 chain pattern, `RelaxationCertificate`).
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Local-first CI: smoke green in-worktree at every phase.
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## 9. What this ADR does NOT claim
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- Not a serving change; the symbolic `generate/` path remains the serve path.
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- Not a lift over symbolic solvers on arithmetic (PARITY is the honest result).
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- Not derived-operand-transfer coverage (0 on this holdout; designed + guarded only).
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- Not an activation of any admission gate (ADR-0246 §3.7 stays uncalibrated).
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## 10. Ruling record (Shay)
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**RATIFIED 2026-07-18 by Joshua Shay — ADR-0250 ACCEPTED.** The design rulings (multi-register
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product-of-lines; relative conservation hard-reject; prepare→validate→commit atomicity; certified
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summation turn; ship 2b designed+guarded) are affirmed, citing the acceptance evidence pack
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(`docs/handoff/ADR-0250-Acceptance-Evidence.md`) as-is. The full-holdout result — the
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reader→Hamiltonian compiler solving the entire real GSM8K dev holdout 50/50 wrong=0 by chained
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certified relaxation — is affirmed as the definitive outcome. Next arc: re-arm the measurement
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(seal dev-holdout-2, a larger real GSM8K slice where the frontier kinds appear) and let the honest
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coverage table pick the next capability tier; dev-1 stays pinned at 50/50 as a regression floor.
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