CYCLE 5 - D02 Evidence-Class Spec v0.1

Date: 2026-05-01
Theorem: D02
Claim type: existential
Evidence class target: split-lane reporting (L2 formal and L1 empirical) with no auto-accumulation

Claim under test

"There exist classical commutative diagrams with Phi = 0."

Core correction from prior cycles

D02 previously mixed heterogeneous evidence classes as if additive.
Cycle 5 separates lanes and blocks false accumulation.

Evidence lanes (mandatory separation)

1. Lane L2 formal pilot
   • typed consistency
   • witness construction/proof obligations
2. Lane L1 empirical external
   • explicit commutativity check per sample
   • explicit Phi mapping with falsifiability reachability

Decision must report lane-wise status before any global status.

Mandatory empirical prerequisites

1. is_commutative cannot be hardcoded by fiat; it must be verified or constructed with proof trace.
2. Phi mapping must include rationale and not reduce to guaranteed-pass geometry.
3. At least one reachable context where all candidates would fail under absent-phenomenon assumption must be documented.

Confirmation criterion (pre-registered)

L1 empirical pass_candidate only if:

1. non-empty commutative set with Phi = 0 appears in at least 2/3 contexts,
2. commutativity is explicitly verified for those samples,
3. falsification route is reachable and tested negative.

L2 formal pass_candidate only if:

1. witness/proof obligations are independently checked,
2. assumptions and limits are explicitly declared.

Reject conditions (pre-registered)

D02 empirical lane is reject_candidate if one or more hold:

1. is_commutative is assigned universally without verification.
2. Phi threshold makes pass structurally guaranteed by dataset sparsity.
3. no reachable fail configuration exists (vacuum-pass).

D02 formal lane is reject_candidate if:

1. witness cannot be independently reconstructed, or
2. formal assumptions are internally inconsistent.

Review conditions (pre-registered)

D02 is revise_needed if:

1. one lane passes and one lane fails, or
2. empirical lane passes but with narrow context robustness.

Anti-pattern lock

1. No false accumulation across lanes.
2. Final theorem status must cite lane-specific status matrix.
3. Any global promotion ignoring lane split is invalid.