R12 Format-Conjugacy No-Go and Source-Scheduled Continuation Diagnostic

Status: unlabeled format-only training rejected as a reasoning mechanism. Source-Scheduled Continuation (SSC) is admitted only as a counted diagnostic of selector/halting failure, not as a new primitive or promotion candidate.

1. Evidence boundary

Raw 260k continuation confirmation finds 8/20 strict first-segment answers under two solved worked examples, 4/20 under direct QA, and 1/20 under bare expressions. The four discordant worked wins and zero direct wins give two-sided exact McNemar p=0.125. More importantly, worked prompts contain target- relevant solved states and answers, so they are not an unlabeled change of format.

Sequential add/multiply/subtract is the only robust family: 5/5 worked and 4/5 direct. Correct intermediates are present in 12/20 direct and 12/20 worked responses even though finals are less reliable. Base conversion is 0/5 in every mode. This supports a narrow selector/halting diagnosis, not a general reasoning claim.

2. Unlabeled format-orbit no-go

Consider any learner that receives only fixed base weights, unlabeled problems, known format maps, model output distributions, and target-independent randomness. It receives no answer, verifier result, target-dependent reward, or privileged state.

Two semantic target worlds can share the identical unlabeled problems and format orbits while assigning complementary binary answers. The learner sees the same transcript and therefore emits the same model in both worlds; its errors across the two worlds sum to one. Thus format orbits alone cannot guarantee correctness or strict improvement. They can only reorganize information already present in the weights.

Agreement losses reduce to prompt consistency regularization. Transported same-model targets are self-distillation. Model-authored chains are self-training/CoT SFT. Voting is prompt ensembling/self-consistency. Hard format maps are canonicalization/equivariant sharing. None is a new source of target information.

3. SSC diagnostic

Factor a generated procedural case into a public operation schedule and hidden numeric states:

selector: choose the next requested operation or STOP
executor: predict U_operation(current_state).

SSC deterministically copies only the operation schedule from the structured source. It asks the frozen model for one next state per operation, parses one integer, and carries that model-produced integer forward. It supplies no intermediate state value, final answer, verifier feedback, repair, search, or retry.

If forced transition t has error at most epsilon_t, the ordinary union bound gives

P(entire chain correct) >= 1 - sum_t epsilon_t.

SSC can therefore reveal an executor hidden by operation selection or stopping failures. It is constrained decoding with an external schedule and parser. Its controller code, state, calls, generated tokens, context, and sequential depth must be counted.

4. Interpretation

• If SSC fails individual transitions, Shohin lacks the executor for that family; answer-boundary tuning cannot fix it.
• If SSC succeeds while ordinary decoding fails, the missing component is selector/halting behavior under that structured contract.
• If only solved demonstrations succeed, classify the effect as in-context trace imitation.
• Any attempt to amortize SSC into weights must compete with a deterministic compiler, true-trace SFT, prompt consistency, and self-distillation at matched resources.

The pilot may reuse the immutable 20-case confirmation manifest and is post-hoc diagnostic evidence only. A claim-bearing follow-up requires a sealed 1,024-case, four-family board with unseen renderers, corrupted demonstrations, operation swaps, exact ordered intermediates, stopping checks, and a frozen resource ledger.

5. Raw-260k SSC result: 2026-07-15

The frozen diagnostic is negative. Across the same 20 cases and 55 scheduled one-operation calls, raw 260k obtained:

first transition correct:  0 / 20
all transitions correct:   0 / 20
final chains correct:      0 / 20

Every family is 0/5 on the first scheduled transition. However, this is a renderer failure rather than clean executor evidence: 16/20 first outputs and 43/55 outputs overall are exactly input_state + 1. The prompt says both "Return only the next integer" and "Next state", so the frozen model usually selects a literal successor-integer continuation rather than applying the named operation. The immutable artifact is artifacts/eval_history/raw260k_ssc_diagnostic_20260715_mps.json, SHA-256 a152e85294d02173a697e29d8537bf4b53428d747d16c7e3baf692095d9b6a2f.

This rejects the narrow claim that Shohin exposes a source-free atomic executor under the preregistered Current state / Requested operation contract. It does not distinguish missing arithmetic from a renderer that overwhelmingly selects the wrong lexical transition. The 20-case confirmation already shows strong renderer dependence, so a fixed no-demonstration format matrix is allowed as a post-hoc access diagnostic; it must score every arm, cannot select a winning prompt after seeing answers, and cannot establish a reasoning mechanism by itself.

6. Frozen-format access matrix

The allowed matrix evaluated all three formats on every one of the 55 atomic transitions and all 20 model-carried chains, with no demonstrations, retries, repair, search, or verifier feedback:

renderer          atomic transitions   full model-carried chains
Question/Answer       40 / 55                    7 / 20
bare equation          8 / 55                    1 / 20
Problem/Work          44 / 55                   10 / 20

Problem/Work is strongest in every aggregate. Its family results are base conversion 16/20 atomic and 1/5 chains, modular update 7/10 and 2/5, multiply-subtract 6/10 and 2/5, and sequential state 15/15 and 5/5. By operation it reaches add 19/20, multiply 15/20, subtract 8/10, and remainder 2/5. The immutable artifact is artifacts/eval_history/raw260k_atomic_operation_formats_20260715_mps.json, SHA-256 b33c26b3963296c0d97b2a6d3332c0be18af40f460137c25652b881824a1ca4b.

This is the first source-free multi-call capability foothold in R12: a fixed deterministic schedule plus model-produced visible states improves strict final chains from 4/20 direct to 10/20. The controller still imports the operation schedule, parser, repeated model calls, and sequential state carry, so this is a capability-system result rather than autonomous Shohin reasoning.

7. Causal renderer interchange

A crossed-prefix diagnostic held the requested operation fixed while making the visible state disagree with the state implied by the source context. In all six add/multiply/subtract cells, the displayed-state candidate received higher summed log probability than the source-implied candidate; the minimum absolute margin was 0.79386. There were 18 candidate sequence evaluations and no generated or training tokens. The artifact is artifacts/eval_history/raw260k_renderer_interchange_20260715_mps.json, SHA-256 963177139b6abb333710f0db19a521c341a039fce3f65743ebdd698be6f12170.

This establishes a narrow causal fact: under a familiar equation-like chart, the model reads and transforms the displayed state rather than merely replaying the source-implied answer. It does not localize a parser or prove a reusable latent program. Prompt canonicalization, visible scratchpad recurrence, and ordinary process supervision remain resource-preserving explanations.

8. Fresh confirmation

R12_SOURCE_SCHEDULED_REASONING_CONFIRMATION.md freezes a new 256-case board before model evaluation: 64 cases each for multiply-subtract, base conversion, sequential state, and modular update. Board SHA-256 is 19a84165f15b19911fc8ef229022e47753833d703d77d1e8cc25db9dfc993474; its canonical 256-row payload hash is 4afc6c4b0c271ea2f723078ab183e8d1ac1851fd1728898384ef52275887b0e4. Newton job 689535 evaluates direct, whole-work, oracle-state atomic, and model-carried scheduled arms against immutable raw 260k. Passing can authorize only an internalization experiment; it cannot itself establish standalone or latent reasoning.