Results D02 - Cycle 1 (Pilot)

Theorem: D02 - Non-productive commutativityCycle date: 2026-04-16Cycle type: formal pilot (not yet full external benchmark)

Cycle objective

Verify that theorem D02 is:1. formally well placed in the OCT typed picture;2. equipped with an explicit constructive witness;3. ready for empirical testing on commutative diagram datasets.

Execution Cycle 1

1. Typed consistency check with OCT_TYPED_FORMAL_SPEC_v0_1.md.2. Check integration in the manuscript OCT_FOUNDATIONAL_OPERA_DRAFT_v0_7.md.3. Theoretical witness construction:- classical commutative square;- compositional redundancy regime;- Phi_Omega(D)=0_E even with preserved commutativity.

Outcome

• Cycle status 1: PASS (formal pilot)- Theorem status: in_proof (not yet validated)

What is validated in this cycle

• logical correctness of the statement;- compatibility with the typed layer (Diag_fin, Phi_Omega, 0_E);- existence of a theoretical non-empty witness class.

What's missing for validated

1. independent benchmark #1 with real commutative diagrams;2. independent benchmark #2;3. replicate on at least 2 contexts Omega;4. Reproducible logs and final statistical decision.

Decision

D02 remains in_proof and advances to Cycle 2 (empirical validation).