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Claim Boundary Doctrine

A mathematical statement must never be stronger than its support. Status is part of the mathematics because it determines what kind of reliance is permitted.

The central rule

Discovery may suggest. Evidence may support. Proof may establish. Certification may warrant public reliance. None of these verbs is interchangeable.

Scope of this doctrine

This page governs claim and support status. It does not define artifact lifecycle or campaign disposition.

  • A claim can remain conjectural while its source-audit artifact is completed.
  • A restricted target can be selected while remaining unproved.
  • A note can be published while making no novelty claim.
  • A Referee disposition can qualify readiness without changing theorem truth.

Use the Programme Status Taxonomy for the complete mapping.

The support route

01IdeaA candidate structure or direction
→
02EvidenceExamples, computation, literature, experiment
→
03ClaimAn exact statement with assumptions
→
04Support routeProof, replay, interval, SAT/SMT
→
05PromotionA status earned at a declared boundary

If any arrow is missing, the claim remains below the corresponding promotion boundary.

Promotion ladder

0Lead

A possible direction worth reconstructing.

Reader may explore it.
1Heuristic

A useful intuition or organizing picture.

Reader may reason with caution.
2Exact evidence

A checked finite or computational fact under stated assumptions.

Reader may rely on the bounded fact.
3Proved locally

A theorem established inside the Work Package dependency boundary.

Reader may rely within that boundary.
4Certification-ready

A precise target with explicit dependencies and replay route.

Reader may audit the handoff.
5Certified

A checked proof or independently replayed certificate.

Reader may rely on the declared checked statement.

Certification is local. A checked finite evaluator, a formalized lemma, or a replayed certificate supports exactly the statement and imported relations named by its contract.

The five dangerous substitutions

01

Citation for proof

A source may establish history, context, or an imported theorem. It does not certify a new derived claim unless the dependency is explicit.

02

Computation for theorem

A finite computation proves a finite statement. An infinite conclusion requires a proved bridge from the finite domain.

03

Exposition for derivation

A compelling explanation can reveal the idea. It cannot discharge a missing logical obligation.

04

Formal syntax for meaning

A theorem prover may verify a statement other than the one humans intended. Semantic correspondence is itself an obligation.

05

Governance status for theorem status

Completion, publication, archival readiness, and Referee promotion describe artifacts or process. They cannot substitute for mathematical support.

Downgrade protocol

A trustworthy programme must be able to move claims downward as deliberately as it moves them upward. Downgrade when:

  • an assumption was omitted or misstated;
  • a finite computation was generalized without a bridge;
  • the formal statement does not match the human claim;
  • a dependency changes status;
  • independent replay fails;
  • a counterexample enters the declared domain;
  • the support artifact cannot be reconstructed;
  • an artifact disposition was mistaken for proof status.
Downgrading is not embarrassment.

It is the mechanism by which the programme protects accumulated trust.

Review questions

  1. What is the exact claim?
  2. Which assumptions and model class are active?
  3. What is the support route?
  4. Which artifact can an independent reviewer inspect?
  5. What domain does the support actually cover?
  6. Is the status word describing a claim, artifact lifecycle, or disposition?
  7. What would refute or downgrade the claim?
  8. What exact action would promote it one level?

Motto

Trust is not a tone. Trust is a boundary.