# Q1006 — 4P Proof

- Q number: Q1006
- Primary URI: https://4p-engine.com/q/Q1006
- Current host route: https://mcbcore.net/q/Q1006
- Reserved subdomain alias: https://q1006.4p-engine.com/

The first-party semantic item for the 4P Proof: the authored and formal proof surface connecting Logic, Truth, Unity, and No Nothing to the 4P architecture.

> The 4P Proof records a Logic-centered proof architecture whose premises, derivations, provenance, and scope must remain inspectable rather than being replaced by a system label.

Q1006 names the proof layer of the 4P architecture. It connects Maclain Hunter's authored foundational and formal proof records to the 4P Engine, MCB, machine semantics, and the Canon without collapsing those distinct provenance classes.
The public proof knowledge base exposes authored proof content, stable identifiers, source kind, author, provenance status, and structured proof metadata. A proof record is therefore readable as a source-bound object rather than as an unexplained validation score.
The 4P Proof is not the same thing as every automated check performed by the 4P Engine. Authored proofs, formal derivations, empirical evidence, and system-generated validation remain separately typed so that the engine can verify a representation without falsely claiming authorship of the underlying proposition or collapsing one evidence class into another.

## 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:** If a proof is to establish a conclusion, its explicit premises must connect by valid inference, while provenance and evidence class remain attached to the demonstration.
- **Consequence:** Logic plus this definition yields the 4P Proof's minimal architecture: distinguish authored proof, formal derivation, empirical evidence, and machine validation, then inspect each transition.
- **Proof limit:** A proof architecture is not itself any individual proof, and a software pass cannot certify an unstated premise or empirical conclusion.

### From this concept back to Logic

- **Witness:** Take one proof record and mark its premises, each inferential step, semantic bridge, conclusion, author/source, and scope.
- **Disclosure:** The proof only communicates a conclusion when its symbols retain identity and each transition is governed by valid relation; its performance therefore reveals reliance on Logic.
- **Proof limit:** A valid derivation secures only its stated consequence within scope; it does not transfer certainty to every interpretation or context.

### Intelligence procedure

- **Human:** Separate premises from conclusion, test every inferential step, inspect the semantic bridge, and state what evidence or refutation could change the result.
- **Machine:** Parse a derivation into typed nodes and edges, validate rule applications and scope, preserve author and source provenance, and fail with the exact invalid step.

### Language and vocabulary procedure

- **Contrast:** A proof is a reasoned demonstration; a proof label, validator score, or credential alone is not the derivation.
- **Usage rule:** Use premise, inference, semantic bridge, conclusion, and scope when explaining why a proof succeeds or stops.
- **Example:** “The conclusion follows from premises 1–3 by rule R; its empirical interpretation still needs a bridge from the formal result to observed events.”

## Semantic meaning frame

- **Role:** source-bound proof architecture
- **Essence:** A proof surface that connects Logic, Truth, Unity, and No Nothing while preserving premises, derivations, provenance, and scope.
- **Logos relation:** Logos requires a proof to show how its conclusion follows, while refusing to convert formal success into unearned empirical or historical certainty.
- **Retrieval aliases:** 4P Proof · 4P foundational proof · Four Principles proof · formal proof architecture
- **Evidence modes:** authored foundational proof · formal derivation · empirical evidence · system-generated validation

### Distinctions

- proof record is not every automated check
- formal validity is scope-bound
- validation is not authorship

## Coherence criterion

A 4P proof must preserve identity, premises, derivation, provenance, scope, and consequence without converting system validation into authorship or truth beyond the proof's stated scope.

## Evidence boundary

Q1006 is a considered, vetted first-party proof architecture, not an unexamined proof label. Its public source surfaces expose the authored records; the verifier must inspect formal validity within declared premises and scope, while empirical conclusions and system-generated checks remain in their proper evidence classes.

## Properties

- **publicProofSurface:** The authored proof knowledge base exposes /proof-knowledge, per-proof HTML, JSON, stable identifiers, source kind, provenance status, and JSON-LD.
- **provenanceClasses:** Authored foundational proofs, formal theorem records, empirical evidence, system-generated proofs, and external records remain distinct.
- **proofBoundary:** A valid derivation establishes its conclusion within its premises and scope; it does not silently discharge empirical or historical burdens.

## Linked Q items

- [Q1000 — Q-Number Data and Metadata System](https://mcbcore.net/q/Q1000)
- [Q1002 — Hunterian Philosophy](https://mcbcore.net/q/Q1002)
- [Q1005 — Hunterian Canon](https://mcbcore.net/q/Q1005)
- [Q1007 — 4P Validator](https://mcbcore.net/q/Q1007)
- [Q1008 — MCB Theory](https://mcbcore.net/q/Q1008)

## 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.

- [mathematical proof (Q11538)](https://www.wikidata.org/wiki/Q11538) — **formal-evidence context:** Rigorous demonstration that a mathematical statement follows from its premises. Boundary: The generic concept supplies a formal-evidence comparison; it does not validate or author the first-party 4P proof records.
- [formal proof (Q2762418)](https://www.wikidata.org/wiki/Q2762418) — **derivation context:** Establishment of a theorem by inference from axioms or premises. Boundary: The relationship identifies a neighboring formal concept; each 4P proof retains its own premises, derivation, provenance, and scope.
- [logic (Q8078)](https://www.wikidata.org/wiki/Q8078) — **governing field:** Study of correct reasoning. Boundary: Logic is the governing field for the proof architecture, not an external endorsement of a particular first-party conclusion.
- [Logic (Q409)](https://www.wikidata.org/wiki/Q409) — **proof architecture context:** Curated external comparison concept: Logic. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Mathematics (Q395)](https://www.wikidata.org/wiki/Q395) — **proof architecture context:** Curated external comparison concept: Mathematics. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Formal System (Q1212450)](https://www.wikidata.org/wiki/Q1212450) — **proof architecture context:** Curated external comparison concept: Formal System. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Reductio ad Absurdum (Q188506)](https://www.wikidata.org/wiki/Q188506) — **proof architecture context:** Curated external comparison concept: Reductio ad Absurdum. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Metalogic (Q938450)](https://www.wikidata.org/wiki/Q938450) — **proof architecture context:** Curated external comparison concept: Metalogic. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.

## Related wiki and reference pages

These pages provide historical, conceptual, or primary-text context. They are not identity, authorship, endorsement, or sameAs assertions.

- [Mathematical proof](https://en.wikipedia.org/wiki/Mathematical_proof) — **Wikipedia; formal-evidence context:** A deductive argument showing that a proposition follows necessarily from premises accepted as true. Boundary: The page supplies formal-proof comparison vocabulary; it does not validate or author any first-party 4P proof.
- [Logic](https://en.wikipedia.org/wiki/Logic) — **Wikipedia; proof architecture context:** Curated external reading context: Logic. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Mathematics](https://en.wikipedia.org/wiki/Mathematics) — **Wikipedia; proof architecture context:** Curated external reading context: Mathematics. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Formal system](https://en.wikipedia.org/wiki/Formal_system) — **Wikipedia; proof architecture context:** Curated external reading context: Formal System. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Reductio ad absurdum](https://en.wikipedia.org/wiki/Reductio_Ad_Absurdum) — **Wikipedia; proof architecture context:** Curated external reading context: Reductio ad Absurdum. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.
- [Metalogic](https://en.wikipedia.org/wiki/Metalogic) — **Wikipedia; proof architecture context:** Curated external reading context: Metalogic. Boundary: These links provide formal and conceptual comparison for 4P Proof; the authored premises and conclusions remain governed by the first-party proof record.