OCT Validation Protocol v0.1

Date: 2026-04-16Purpose: Single protocol to bring OCT theorems from in_proof to validated. Formal Baseline:- OCT_TYPED_FORMAL_SPEC_v0_1.md- OCT_FOUNDATIONAL_OPERA_DRAFT_v0_7.md

1) Validation objective

Go from structural demonstration to repeatable evidence on benchmarks. At this stage:- D02, D03, D04 (differentials)- A01, A02, A03 (applications)

2) Canonical metrics

For each experiment (context Omega):- Coh_Omega(D) in [0,1]- Phi_Omega(D) to E_Omega- Delta_Omega(D) = 1 - Coh_Omega(D) Auxiliary metrics:- Err_sem (task-specific semantic error)- Err_struct (structural reconstruction error)- Var_Omega (cross-context variance)

3) Minimal experimental design

Each test must have:1. declared domain;2. dataset/fixed version;3. classic baseline pipeline (P_cls / F_cls);4. ordering pipeline (P_ord / F_OCT);5. pre-registered confirmation/falsification criteria.

4) Test suite for theorem

D02 - Non-productive commutativity

Input:- set of classical commutative diagrams. Test:1. verify classical commutativity;2. measure Phi_Omega(D);3. classify commutative-productive vs commutative-non-productive. He confirms:- non-empty class exists with Phi_Omega(D)=0_E. Forgery:- all tested commutatives have non-zero emergence.

D03 - Ontological loss of forgetting functors

Input:- pairs of pre/post diagrams U. Test:1. estimate Loss_U on order invariants;2. separate condom and degenerative cases. He confirms:- both regimes coexist in a robust way. Forgery:- always neutral or always degenerative loss without distinction.

D04 - Conditional symmetry

Input:- domains with real functional asymmetry. Test:1. apply sigma where defined;2. measure variation of Phi_Omega and Delta_Omega. He confirms:- there is a subclass where the exchange is strictly inadmissible. Forgery:- symmetry always neutral on all cases.

A01 - AI pipeline order established

Input:- multi-step tasks with gold reference. Test:1. run P_ord and P_cls;2. plot Coh, Phi, Delta by step;3. measure final Err_sem. He confirms:- E[Delta_cum(P_ord)] < E[Delta_cum(P_cls)]- E[Err_sem(P_ord)] < E[Err_sem(P_cls)] Forgery:- inequalities not robust across multiple benchmarks.

A02 - Reconstruction from linguistic projections

Input:- dataset (source structure, linguistic projection). Test:1. reconstruction with F_OCT and F_cls;2. measures Err_struct and Var_Omega. He confirms:- robust lead of F_OCT on both metrics. Forgery:- absence of advantage or high contextual instability.

A03 - Degeneration in narrative social systems

Input:- longitudinal discursive networks. Test:1. extract D_t on time windows;2. measure Coh_Omega(D_t), Phi_Omega(D_t), Delta_Omega(D_t);3. correlate with external indicators of degradation. He confirms:- "high rhetorical coherence + low emergency" regime anticipates systemic degradation. Forgery:- no robust association between Phi collapse and observable degradation.

5) Global validation criteria

A theorem passes to validated when:1. at least 2 independent benchmarks confirm the criterion;2. results replicated in at least 2 contexts Omega;3. esito statistico supera soglia dichiarata; 4. esistono log completi e riproducibili.

6) Output richiesti per ogni teorema validato

1. results file (results_<theorem>.md or equivalent table)2. execution protocol3. analysis of errors/limitations4. final decision: validated / rejected / revised

7) Recommended sequence (next days)

1. D022. A013. D034. A025. D046. A03 Reason:- first minimum structural difference (D02),- then immediate operating value (A01),- therefore differential/applicative completion.