OR1 Self-Coherence

OR1 is the first of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the self-coherence requirement: any τ-categorical reality candidate must be internally consistent — no τ-morphism can compose with its own inverse to a non-identity, no register can read a contradiction.

Categorical invariant. Self-coherence narrowing: ∀ candidate ontic structure τ', if τ' satisfies the τ-framework's morphism composition laws, then τ' has no internal contradictions.

Primary registry anchor: VII.L31

Supporting items: VII.D37, VII.P08

1. I.K0 — Universe Postulate
2. VII.D37 — Six Ontic Requirements (OR1-OR6) define the foundational metaphysical narrowing rules
3. VII.L31 — OR1+OR2 Narrowing — combined self-coherence + completeness lemma
4. VII.P08 — Each Requirement Independently Necessary

OR1 is instantiated whenever a metaphysical / scientific claim is rejected on grounds of internal contradiction. Examples: rejecting 'square circle' as non-existent; rejecting time-travel paradox-loops as physically realized; rejecting logical inconsistencies in formal systems.

Examples:

• Logic: rejecting any system that proves both P and ¬P (Gödel-Rosser inconsistency)
• Physics: rejecting 'closed timelike curve with paradox' as a real spacetime (Novikov self-consistency)
• Mathematics: ZFC consistency — the foundational narrowing of set theory

Register codomain: Proof (diagrammatic — OR1 lives in Reg_D's codomain because self-coherence is a proof-theoretic constraint)

Manuscript reference: manuscript-sources/book-07/part02/ch10-ontic-requirements.tex

Status: Planned

Related glossary entries

• MG-R01-empirical-register Empirical Register (Reg_E)

Referenced by

• MG-A01-ci-operator-graph CI Operator Graph
• MG-A03-tau-modal-operators τ-Modal Operators (□, ◇)
• MG-O01-being Being (categorical existence)
• MG-O03-modality Modality (necessity, possibility, contingency)
• MG-P02-or2-finite-signature OR2 Finite Signature
• MG-P03-or3-diagonal-free-self-reference OR3 Diagonal-Free Self-Reference
• MG-P07-six-ontic-requirements Six Ontic Requirements (OR1-OR6)
• MG-P10-independent-necessity Independent Necessity of Each Ontic Requirement