WGP1: Weighted Grammar Projection

Status: development PASS; confirmation CLOSED on source admission before model scoring

Date: 2026-08-10

Parent: frozen BTT1 checkpoint 2283c86b1a640c9d5c02ffbc70b4646a0a1ad3538c4e1d4ab4ea3b164363e278

Holdout: sealed

Hypothesis

BTT1 is exact on 98.8512% of the source-disjoint board, and every one of its 45 errors is an invalid byte-role sequence. WGP1 changes no weights or logits. It uses a fixed width-64 beam to select the maximum-log-probability complete path satisfying only the generic expression grammar:

• numeric bytes are contiguous and contain at least one digit and at most one decimal point;
• operands and binary operators alternate;
• unary negation occurs only where an operand is expected;
• parentheses balance and close only after an operand;
• exactly one nonempty expression is selected from the raw tape.

The projection sees frozen per-byte role logits and raw bytes only to validate copied numeric characters. It does not inspect an answer, target, verifier, family, source template, or arithmetic value. The unchanged generic shunting-yard executor materializes the projected roles.

Frozen controls and gate

Run normal, same-family/depth source shuffle, zero-byte input, and flat execution under the same frozen checkpoint and width-64 projection. Compare row-wise against immutable BTT1 top-1 output.

The zero-byte arm may memoize exact projection results by tape length and the per-position digit/dot/other mask. Under zeroed inputs, logits are identical for equal lengths and grammar transitions inspect raw bytes only through that mask, so this is exact execution reuse rather than an approximation.

The conjunctive development gate requires:

• complete and selected role exact >=99.5%;
• valid program =100%;
• exact skeleton >=99.5% and every family >=99%;
• mixed precedence, unary groups, and three-plus-parenthesis each >=95%;
• at least 30 of BTT1's 45 failures repaired and at most two previously exact rows broken;
• source shuffle and zero-byte controls each <=25%, with normal margins >=74 points;
• flat execution loses >=35 points on hierarchical rows;
• zero search exhaustion and no fallback to top-1.

One pass opens exactly one sealed holdout. Failure closes WGP1 without beam, grammar, score, checkpoint, seed, or threshold variants. A pass establishes a qualified source-to-program compiler, not learned arithmetic execution or a novel parsing algorithm.

Development result

Jobs 749707, 749708, 749710, and exact memoized zero-byte replacement 749711 completed. Normal projected output is 3,917/3,917 = 100% for complete byte roles, selected lexemes, action sequence, validity, and exact skeleton. It repairs all 45 immutable BTT1 failures with zero breaks and zero search exhaustion. Every family and every frozen difficult slice is 100%. Source-shuffled and zero-byte controls are both zero exact; flat execution loses 62.2244 points on hierarchical rows. Every conjunctive gate passes.

The original zero-byte job 749709 was canceled after 4m23s without a report when it became clear that repeated identical zero-input searches would consume its window. Replacement 749711 used the prospectively documented exact cache and completed all rows; no score, beam, grammar, or checkpoint changed. Result SHA-256 is 113dffc54e30ef90d7c36662c8f4cef445d5afc6d16e422719bdc13d8553f060.

Exactly one confirmation is now open on the immutable Reasoning-Gym held-out seed file rg_v4/rg_eval.jsonl, SHA-256 35a2625a44bd42161ac9ee562fb57a6f69ab9771747ef4166d0042d925b46435. The five supported arithmetic families contribute 500 source-disjoint rows each before fail-closed exact-program admission. Confirmation thresholds are frozen before construction: at least 99% admission per family, >=99% exact skeleton overall, every family >=98%, valid program =100%, source-shuffled and zero-byte exact each <=25%, and zero exhaustion. A miss closes WGP1.

Confirmation source admission correction

CPU job 749717 failed closed in three seconds before producing a holdout artifact or accessing model output. A read-only audit found that the legacy rg_eval.jsonl is not source-disjoint from BTT1 train/development: it contains 14 protected chain_sum questions, 138 protected products questions, and one internal products duplicate. This invalidates that file as a WGP1 confirmation source; it is preserved as a data-custody failure and will never be scored.

Before any replacement data or model output exists, the replacement source is frozen as follows: reasoning-gym==0.1.25, package wheel SHA-256 7f17a3eddb13c015d7d4a755ed576a061df889faf9468bcc2cca334ebe9e0435, seed 20260810, an ordered pool of 8,192 generated rows per family, and the first 500 nonempty-answer rows per family whose normalized question SHA-256 is unique and absent from immutable BTT1 train/development. The five families, compiler, checkpoint, projection, controls, and all numeric gates remain unchanged. The generated source must contain exactly 2,500 unique, source-disjoint rows; independent exact-program admission must still retain at least 495/500 per family before any model evaluation. Failure at either stage closes confirmation without another seed, package, pool, or filtering retry.

Confirmation result

Replacement-source job 749728 completed in five seconds with exactly 2,500 unique, protected-disjoint rows. Source/report SHA-256 values are fcc8579857138be82ecfc149b9c268bcd4a0c38c3419f1313a7d4b64f4246689 and 3d3d817531b867074b3292a51d80938efc5d6e5aab134e8c3624d377e4ac28a2.

Admission job 749730 then failed closed in two seconds before creating an output directory or accessing the BTT checkpoint. Exact admitted counts are:

The seven basic-arithmetic exclusions are generated integer answers rounded from nonintegral division results, while all 274 decimal-arithmetic exclusions are precision-rounded answers that intentionally differ from exact-rational execution. This is a semantic incompatibility between the frozen admission assessor and Reasoning-Gym 0.1.25, not a model score. Nevertheless the prospective gate is conjunctive, so exact WGP1 confirmation closes without a different seed, package, source filter, or evaluator. The 100% development compiler remains a valid development result but is not holdout-qualified. Receipt: SHOHIN_WGP1_HOLDOUT_ADMISSION_RESULT.json.