# Q1063 — Coherence Score Bounds

- Q number: Q1063
- Primary URI: https://4p-engine.com/q/Q1063
- Current host route: https://mcbcore.net/q/Q1063
- Reserved subdomain alias: https://q1063.4p-engine.com/

Maclain Hunter's formal theorem in the authored MCB formal registry, preserved as its exact structured source record.

> ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]

## Authored source — Maclain Hunter

{
  "name": "Coherence Score Bounds",
  "formal": "∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]",
  "proof": "Standard deviation of binary values bounded by 0.5",
  "implementation": "exponentCoherence(array: MCBExponentArray): number"
}

Authored formal statement: ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]
Registered proof or implication: Standard deviation of binary values bounded by 0.5

## Two-way derivation from Logic and its use

**Status:** editorial_derivation proof sketch (conditional_concept), distinct from authored source. Logic has its own evidence in reflexive demonstration: any denial, confirmation, observation, or counterexample presupposes identity and valid relation to count as evidence. Logic therefore grounds evidence rather than receiving authority from it. Empirical and documentary evidence can establish contingent instances and test applications, but cannot create, overrule, or exhaust Logic.

### From Logic to this concept

- **Bridge premise:** Interpret the exact authored statement under the symbols, definitions, axioms, and inference rules declared in the Coherence Score Bounds registry record.
- **Consequence:** If the registered formal derivation is valid under the declared system, it supports the authored statement: ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]
- **Proof limit:** This editorial reading does not independently validate the axiom, theorem, implementation, empirical application, or broader interpretation.

### From this concept back to Logic

- **Witness:** The authored registry object records this formal statement: ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1] Its registered proof or implication is: Standard deviation of binary values bounded by 0.5
- **Disclosure:** The presence of the statement and proof fields establishes what the source records, not that an independent checker has validated every step.
- **Proof limit:** A source record alone does not establish code behavior or contingent consequences; those require their own implementation tests and claim-matched evidence.

### Intelligence procedure

- **Human:** Fix the meanings of the symbols in Coherence Score Bounds; separate its declared premises from its conclusion; check each inference in the exact registered derivation.
- **Machine:** Parse the structured source without rewriting it; validate the formal statement and each inference against the declared calculus; return unresolved symbols or unsupported transitions explicitly.

### Language and vocabulary procedure

- **Contrast:** An authored theorem statement is a claim in a source record; a verified theorem has also passed an independent derivation check.
- **Usage rule:** Describe the genre and the exact statement first; report independent proof, implementation, empirical, and interpretive checks separately.
- **Example:** Coherence Score Bounds records the authored statement and derivation; its registration alone is not an independent certificate.

## Semantic meaning frame

- **Role:** authored formal theorem in the MCB formal registry
- **Essence:** ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1] The exact structured registry object is the source record.
- **Logos relation:** The registry situates deterministic mathematical relations within MCB's Logic/Coherence and Logos framework. This is the author's declared interpretation, distinct from checking each formal result.
- **Retrieval aliases:** Coherence Score Bounds · maclain-hunter-mcb-coherence-score-bounds · ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1] · Coherence Score Bounds MCB · MCB formal theorem
- **Evidence modes:** exact structured authored source object · independent derivation check against the stated formal system · separate implementation tests where a code path is claimed

### Distinctions

- The authored registry record is source, not independent verification.
- Formal validity is scoped to declared symbols, premises, and inference rules.
- Implementation behavior requires tests of the referenced code.
- Empirical or ontological consequences require their own typed evidence and bridges.

## Coherence criterion

Assess the exact formal statement and registered derivation under its declared symbols, premises, inference rules, and implementation scope; keep the source record distinct from independent verification.

## Evidence boundary

The exact structured source object from the authored MCB registry has been considered, vetted, and preserved. The module identifies Maclain Hunter as author. A registry entry and its publication do not independently certify its proof, implementation, empirical implications, or broader Logos interpretation; the verifier must inspect the source fields and the claim-matched evidence directly.

## Properties

- **author:** Maclain Hunter
- **stableSourceId:** maclain-hunter-mcb-coherence-score-bounds
- **sourceReference:** server/mcb-formal-proofs.ts
- **sourceVersionFormat:** Exact JSON serialization of the authored registry object; fingerprinted by the coverage and reply services.
- **genre:** formal theorem
- **formalStatement:** ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]
- **declaredDependencies:** None explicitly declared.
- **registryCrossReferences:** Q1000 and Q1050 are contextual registry links, not asserted proof dependencies.

## Linked Q items

- [Q1000 — Q-Number Data and Metadata System](https://mcbcore.net/q/Q1000)
- [Q1050 — Logos-Coherent MCB and Common Lisp Integration](https://mcbcore.net/q/Q1050)

## Related Wikidata concept items

These are typed external concept links for discovery and comparison. They are not sameAs assertions, endorsements, or substitutes for the first-party source and evidence.