22 — Theory Claims, Assumptions, and Theorem Sketches
Claim 1 — Productive conflict is not generic contradiction
Statement. Productive synthesis pairs require both chiral opposition and evidential entanglement.
Assumptions.
- Evidence identifiers are stable.
- Evidence quality weights are available or default to uniform.
- SNOs contain aligned claim/relation structures.
Prediction. A pair selector using chirality × entanglement outperforms selectors using contradiction count or embedding distance alone.
Claim 2 — Zero-temperature proof closure blocks strict hallucination
Statement. If a strict claim is promoted only when a proof trace exists under monotone zero-temperature rules grounded in evidence atoms, unsupported strict claims are blocked.
Assumptions.
- Rule set is monotone and finite.
- Evidence atoms resolve.
- Proof traces are required for strict promotion.
- Parser cannot bypass proof status.
Test. ZTHR must equal zero on constrained toy and fact-verification subsets.
Claim 3 — Persistent residual contradiction implies missing structure or true unresolved conflict
Statement. If support and refute mass persist after proof closure, either the predicate vocabulary lacks a relevant context or the evidence cannot support a synthesis.
Assumptions.
- Grounding critics are reliable enough to avoid extraction-error residuals dominating.
- Residual tensor is built over aligned predicates.
Test. On synthetic tasks with planted hidden contexts, predicate invention recovers the hidden context; on no-solution tasks, CNS reports unresolved rather than inventing spurious predicates.
Claim 4 — Orthesis is a stability condition
Statement. A synthesized SNO that survives render/re-ground cycles with low proof-critical distortion is more stable than an ordinary narrative summary.
Assumptions.
- Grounding function $G$ is deterministic or variance-bounded under fixed configuration.
- Logic state comparison weights proof-critical atoms.
Test. CNS output has lower $\chi_{LL}$ than baseline summaries.
Claim 5 — Possible-world ranking improves uncertainty reporting but does not create synthesis
Statement. Possible worlds help report remaining uncertainty after synthesis, but possible-world posterior mass alone does not produce an SNO with proof traces and synthesis lineage.
Test. Possible-world-only baseline should perform worse on narrative synthesis quality and orthesis stability, even when calibrated.
Claim 6 — Predicate invention increases information only when grounded
Statement. Latent predicates improve CNS only when they reduce residual contradiction and have independent evidence support.
Assumptions.
- Predicate complexity is penalized.
- Grounding is evaluated on held-out evidence when possible.
Test. Measure PIU and false predicate rate.
Claim 7 — Topology is diagnostic, not a replacement for proof
Statement. Beta-1 and related topology metrics can predict synthesis difficulty and detect circular support, but cannot alone prove or refute claims.
Test. Compare beta-1-only against chirality+entanglement+proof metrics.