OR4 NF-Addressability

OR4 is the fourth of six original-rule narrowing principles (the Six Ontic Requirements, VII.D37). It states the address-centric access requirement: every admissible construction in a τ-categorical reality candidate must have a unique normal-form (NF) address — a canonical name that picks out the entity uniquely and renders it findable.

Categorical invariant. Address-centric narrowing: ∀ candidate ontic structure τ', for every admissible construction c ∈ τ' there exists a unique NF-address α(c) in a well-defined address space A, and the address determines the construction.

Primary registry anchor: VII.D37

Supporting items: VII.L32, VII.P08, VII.T14

1. I.K0 — Universe Postulate
2. VII.D37 — Six Ontic Requirements (OR1-OR6) — OR4 is NF-addressability
3. VII.L32 — OR3+OR4 Narrowing — diagonal-free self-description plus NF-addressability
4. VII.P08 — Each Requirement Independently Necessary — dropping OR4 admits non-constructive entities (axiom-of-choice objects without canonical addresses)

OR4 is instantiated whenever an entity's existence is rejected — or downgraded — because it lacks a canonical address. The intuition: every real thing must be findable. Examples: rejecting non-measurable sets as 'real' physical structures; preferring constructive proofs over non-constructive ones; demanding that every quantum state have a computable description.

Examples:

• τ-framework: every admissible construction has a unique NF-address; the address space A is the substrate of computation in τ
• Set theory: rejecting Banach-Tarski 'pieces' as physically realizable — they have no NF-address (require AC)
• Constructive mathematics: the demand that every existence proof yield a witness — i.e., a canonical address
• Physics: every quantum state must be specifiable by a finite procedure (state preparation = address-construction)
• Computing: every datum has a memory address; addressability is a precondition for retrieval

Register codomain: Proof (diagrammatic — NF-addressability is a structural / decidability constraint on the address space, lives in Reg_D's codomain)

Manuscript reference: manuscript-sources/book-07/part02/ch29.tex

Status: Planned

Related glossary entries

• 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

Referenced by

• 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