CYCLE 5 - A01 Process-Level Spec v0.1

Date: 2026-05-01
Theorem: A01
Claim type: comparative
Evidence class target: L1 empirical external (process-trace based)

Claim under test

"Compositional pipelines with high ordinative coherence show lower semantic degeneration than classically valid-only pipelines."

Core correction from Cycle 3

Cycle 3 relied on output-level proxy blending, which does not test process-level ordinativity.
Cycle 5 enforces process-level comparison with trajectory evidence.

Required process instrumentation

For each task run and each step i:

1. step_id
2. morphism_id
3. Syn_i
4. Coh_i
5. Phi_i
6. gate_decision_i (admit/refine/reject/abort)
7. trajectory_event_hash
8. timestamp

Both pipelines must be run:

1. P_cls (classical baseline)
2. P_ord (ordinative gate enabled)

Primary metrics (pre-registered)

1. Delta_cum: cumulative process degradation over trajectory.
2. Err_sem_final: final semantic error against gold/anchor.
3. Reject_rate: fraction of steps rejected or refined.
4. Trajectory_length: number of effective transitions.
5. mean_Coh_trajectory: mean process-level Coh over effective trajectory.

Confirmation criterion (pre-registered)

A01 is pass_candidate only if all are true:

1. E[Delta_cum(P_ord)] < E[Delta_cum(P_cls)] in at least 2/3 contexts.
2. E[Err_sem_final(P_ord)] < E[Err_sem_final(P_cls)] in at least 2/3 contexts.
3. E[mean_Coh_trajectory(P_ord)] > E[mean_Coh_trajectory(P_cls)] in at least 2/3 contexts.
4. At least one subset shows equal/similar final output but different trajectory quality favoring P_ord.

Reject conditions (pre-registered)

A01 is reject_candidate if one or more hold:

1. Process logs are missing/incomplete for either pipeline.
2. Claimed effect is supported only by output-level metric without process advantage.
3. P_ord does not beat P_cls on either primary metric in all contexts.
4. Gate decisions are not auditable (no append-only trace).

Review conditions (pre-registered)

A01 is revise_needed if:

1. one primary metric passes and one fails, or
2. process advantage exists but semantic advantage is unstable, or
3. contextual variance exceeds pre-registered warning threshold.

Anti-pattern lock

1. No level-shift: output-only proxy cannot be decisive.
2. No hidden metric substitution after first run.
3. No threshold adjustment on same dataset after fail.