R12 S6 Contextual Affine Law Induction: Development Result

Date: 2026-07-19
Decision: reject_s6_contextual_affine_law_development
Confirmation: forbidden; no confirmation board was generated or read

Question

Can a small card-conditioned transformer infer an operation law absent from training, execute it recurrently, and preserve exact state without receiving the hidden slope or intercept?

For prime modulus m, each law is

d(x) = a*x + b (mod m), a != 0

The treatment receives only (m, 0->y0, 1->y1, x). Two witnesses uniquely identify the law; one witness leaves exactly m-1 laws possible. Training uses atomic destination supervision on training laws only. Development uses disjoint laws in recurrent programs of depth three through eight.

Frozen evidence

• Source/prereg commits: 93418b0, c09024b, 48e6182
• Board seed: 4930377975126057597
• Training seed: 412095620685111169
• Atomic training rows: 961
• Primary development rows: 2,048
• Modulus-13 scale diagnostics: 512
• Train/development law overlap: zero
• Treatment parameters: 4,753,677
• Complete system parameters: 138,448,546
• Favorable law-ID control parameters: 4,780,301
• Primary development SHA-256: 8fd78f761207e8446562c75e1816d1a0821d90ecd64fcb6b837f7a92fe808047
• CPU mechanics SHA-256: a31a232c83a53d0b7aff87b4a495abd6740d98589059325951e2e4688e2bded6

Custody

Submission 693291 failed before Python initialization because the frozen 64-bit training seed was assigned directly to CPython's unsigned 32-bit PYTHONHASHSEED. It created an empty output directory and did not initialize a model, read the board, or produce a statistic. Launcher-only commit 676af2c derives the interpreter seed modulo 2^32 while retaining the full frozen seed for model and data RNGs. The distinct retry1 output is the only scientific run.

Job 693293 completed once on H100 evc25 in 3m42s with exit 0:0. Treatment and favorable control each fit 961/961 atomic training rows. The evaluator read development once and confirmation zero times.

Scores

Held-out atomic destination accuracy is 78/318 = 24.528% despite exact training fit. Recurrent treatment state accuracy decays with depth:

Nonce-name recoding is bit-identical, as expected because names do not enter the law unit.

Gate outcome

Passed:

• atomic-only training contract;
• treatment and favorable-control training fit at least 99%;
• one development access and zero confirmation access;
• parameter caps;
• nonce-name invariance.

Failed:

• held-out atomic destination at least 95%;
• exact state and answer at least 95%;
• every depth at least 92%;
• host parity;
• all required causal-drop margins;
• favorable law-ID control trailing by at least 40 points.

Interpretation

This is not an optimization failure: both arms fit every training cell with final losses below 2e-5. It is an algorithmic-generalization failure. The treatment's +6.88-point state advantage over card derangement and +7.03-point advantage over one-witness input show that both demonstrations carry causal signal. But a generic categorical transformer represents that signal as a weak interpolating lookup surface rather than the identified affine law.

The failure rules out widening, extra epochs, or post-score tuning of this arm as the next scientific move. The surviving hypothesis is architectural: compile contextual demonstrations into a compositional group action whose reuse is enforced by representation structure, then compare that mechanism to this frozen transformer and matched structure-breaking controls on a wholly fresh board.

Artifact hashes

• Checkpoint SHA-256: a440e8677f2006235b76f7fa50dcdfb3541e9667c5f609d6d319062bd85af6d6
• Evaluation SHA-256: 1cfd88a86bd8ad2de2c263af29b989f61e787dfc44db60f929040d6d7a87aa5b
• Assessment SHA-256: e9f0f6a1354fd8a8bf950d814757f737775bce115ebe984af5e70ddcd0ad718c

The checkpoint and reports are mirrored locally under train/s6_contextual_affine_law_4930377975126057597_412095620685111169_retry1/ and at the matching Newton path. The model checkpoint is not a promoted reasoning artifact.