DIVERGE-AQC1: Antisymmetric Quotient Commit

Status: complete on 2026-08-08. Both learned commit policies pass the frozen capability floors. The antisymmetric treatment wins the practical comparison by one answer but fails the required five-answer causal margin over its matched independent-score control.

Capability hypothesis

IDR1 and its untrained same-family continuation solve complementary cases on source-disjoint holdout. IDR1 solves 625/1,279; the continuation solves 495; their coherent whole-answer union is 671. A fixed classifier trained only on development metadata reaches 645, proving at least twenty answers of deployable selection headroom without holdout fitting.

Prior CVG1 scored candidates independently and lost to its strongest lineage. Prior PCJ1 compared a joint ordered sequence and was only about 60% invariant to swapping A/B. AQC1 tests a different interface: shared candidate encodings feed an antisymmetric relational margin. For candidate representations a,b,

margin(a,b) = phi(a,b) - phi(b,a).

Swapping candidates therefore negates the margin exactly. The selected object is always one complete trajectory; fields are never averaged.

Frozen data

• Candidate 0: exact trained IDR1 source-disjoint output.
• Candidate 1: exact original-9B-B1 source + internal draft control output.
• Source pool: the 1,289-row IDR1 development split and untouched 1,279-row IDR1 holdout split.
• Seed 2026080820 partitions development identities 80/20 into AQC1 train and development. Original holdout remains entirely holdout.
• Both candidate orders are presented during training. Candidate provenance, correctness, answer labels, and task labels are supervisor-only.
• Runtime input is only the problem and two complete candidate trajectories.

Frozen arms

1. AQC1 treatment: shared 9B B1 plus trainable LoRA, shared candidate encoder, and antisymmetric relational head.
2. Independent-score control: same host, candidate encoder, data, update count, optimizer, seed family, and selection rule, but each candidate gets an independent scalar correctness score and the larger score wins.
3. Always-IDR control: 625/1,279 holdout.
4. Development-trained metadata control: 645/1,279 holdout. This is a diagnostic control, not the model-owned architectural result.
5. Whole-answer oracle ceiling: 671/1,279; not deployable.

Both learned arms use 128 updates, gradient accumulation 8, maximum sequence length 3,072, head width 512, backbone LR 2e-6, head LR 2e-4, AdamW, and fixed seeds 2026080821 treatment / 2026080822 control. Training is balanced across task and candidate-outcome class. Decisive pairs receive pairwise logistic loss; ties receive a zero-margin calibration loss.

Gates

The source-disjoint holdout gate is conjunctive:

• selected overall at least 646/1,279;
• MATH at least 255/621;
• logic at least 349/625;
• code at least 24/33;
• exact 100% A/B order consistency;
• control-only cases selected often enough to produce a net positive delta;
• treatment exceeds the matched independent-score control by at least five answers for the AQC mechanism claim.

If the independent scorer reaches the capability floors but AQC1 does not beat it by five, preserve the scorer as the practical commit policy and reject the relational novelty. If neither learned arm reaches 646, close this same-family branch-arbitration direction without width, duration, seed, loss, threshold, or renderer variants. Product evaluation remains sealed unless an arm passes every capability floor. Prelaunch total estimate: 2--4 H100-hours for both arms including evaluation.

Claim boundary

A pass would establish useful model-owned coherent trajectory commitment on a Qwen3.5-9B host. It would not establish native reasoning in the 125M Shohin backbone, broad frontier competitiveness, or novelty of ensembling by itself.

Result

Two-update integration jobs 745675/745676 exposed one order-dependent selection bug: an exact zero margin selected the first candidate in either ordering even though both heads satisfied margin(a,b) = -margin(b,a) with zero numerical error. Commit 38bc1f3 replaces only that tie behavior with a lexical, candidate-owned canonical tie rule. Five focused tests pass. The scientific settings, data, model states, losses, seeds, thresholds, and evaluator did not change.

Full jobs 745677/745678 then completed all 128 updates and 1,024 pair presentations in 19m59s/19m58s. Both protected B1 adapter hashes remain bit-identical. Training and development have zero truncated prompts; holdout contains one pre-existing truncated candidate prompt in each arm. Maximum swap error is exactly zero and semantic order consistency is 100%.

Both arms clear every capability floor. AQC1 treatment improves over IDR1 by 27 answers and the frozen metadata selector by seven. However, treatment exceeds its matched control by only one answer, not the required five. The correct conclusion is therefore:

promote_the_652_answer_whole_trajectory_commit_as_the_practical_same_family_architecture;_reject_a_distinct_antisymmetric_relational_mechanism_claim;_do_not_run_nearby_aqc1_variants.

Treatment/control/aggregate report SHA-256 values are 9f72644c...5563, fdf9ead0...26b, and c56b0401...e74. The two full jobs consume 0.666 H100-hours; the two integration canaries consume another 0.368 H100-hours.

Protected Product Result

Passing source-disjoint capability opened one exact seven-task application. The same B1 owner generated 568 internal drafts; the trained IDR1 adapter and matched original-B1 control each revised those exact drafts. The frozen AQC1 treatment and independent control then selected whole trajectories without new training, labels, task routing, verifier feedback, or threshold fitting.

AQC1 passes every frozen product condition. Relative to VCR1 it adds 15 main answers, +3.513 macro points, and six code answers. Relative to IDR1, commit adds nine main answers and three AIME answers. It trades one GSM8K and three logic answers for three MATH and ten GPQA answers; this is a measured boundary, not a Pareto claim on every domain.

Treatment has zero swap error, 100% order consistency, and three truncated candidate-assessment prompts. Treatment report and selected-candidate hashes are 3e86751b...7187 and a7faca96...43e1; independent report hash is 605f2197...c3e. Product work consumed 3.518 H100-hours. The final claim is same-family model-owned draft/revision/whole-trajectory commitment, not a distinct benefit from antisymmetry and not a sub-200M Shohin result.