Commit-Interface Seal Preservation

Abstract

A commit interface seals every digest coordinate and confines committed artifacts to the input bundle, decision candidates, and dependency closure.

Theorem 1.1 (Commit outputs preserve their seal and artifact boundaries).

$$\forall RoundState\in \mathrm{Type}\left(\right),Digest\in \mathrm{Type}\left(\right),EventId\in \mathrm{Type}\left(\right),Evidence\in \mathrm{Type}\left(\right),Round\in \mathrm{Type}\left(\right),Artifact\in \mathrm{Type}\left(\right),Time\in \mathrm{Type}\left(\right),TargetChain\in \mathrm{Type}\left(\right),Domain\in \mathrm{Type}\left(\right),Epsilon\in \mathrm{Type}\left(\right),Condition\in \mathrm{Type}\left(\right),Comparator\in \mathrm{Type}\left(\right),TestPlan\in \mathrm{Type}\left(\right),Baseline\in \mathrm{Type}\left(\right),WeightSpec\in \mathrm{Type}\left(\right),n\in Round,I\in \mathrm{CommitInterface}\left(RoundState,Digest,EventId,Evidence,Round,Artifact,Time,TargetChain,Domain,Epsilon,Condition,Comparator,TestPlan,Baseline,WeightSpec,n\right),B\in \mathrm{CandidateBundle}\left(Artifact\right),\mathrm{digest}\left(\mathrm{snd}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)=\mathrm{digestOf}\left(I,\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right),\mathrm{freezeEvent}\left(\mathrm{adjudication}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right),\mathrm{dependencyClosure}\left(\mathrm{adjudication}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)\right)\wedge \left(\mathrm{sealedCommitment}\left(\mathrm{snd}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)=\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\wedge \left(\mathrm{sealedFreezeEvent}\left(\mathrm{snd}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)=\mathrm{freezeEvent}\left(\mathrm{adjudication}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)\wedge \left(\mathrm{sealedDependencyClosure}\left(\mathrm{snd}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)=\mathrm{dependencyClosure}\left(\mathrm{adjudication}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)\wedge \left(\mathrm{candidates}\left(\mathrm{decision}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)=\mathrm{artifacts}\left(B\right)\wedge \left(\forall a\in Artifact,a\in \mathrm{committedArtifacts}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\Rightarrow \left(a\in \mathrm{artifacts}\left(B\right)\wedge \left(a\in \mathrm{candidates}\left(\mathrm{decision}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)\wedge a\in \mathrm{dependencyClosure}\left(\mathrm{adjudication}\left(\mathrm{fst}\left(\mathrm{commitStep}\left(I,B\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/Governance/CommitInterfaceSealPreservation.commit_interface_seal_and_artifact_preservation (✓ std3). ∎

Source. Repository-derived.

Commentary.

The displayed statement unfolds the Lean let-bound commitment and output seal as the first and dependent second projections of commitStep(I,B).

The first four clauses expose the seal fields: the digest consumes the whole commitment together with its freeze event and dependency closure, and the stored commitment, event, and closure equal those same inputs.

The candidate equality is supplied by CommitInterface. For every committed artifact, input-bundle membership follows from the interface, while candidate and dependency-closure membership come from the imported ProspectiveCommitment carrier.

The module also constructs a finite Unit-valued interface and nonempty bundle, so the quantified interface and artifact domains are machine-checked as inhabited.

References

• Truth anchor: D5/S3/ConceptDynamics/Governance/CommitInterfaceSealPreservation.commit_interface_seal_and_artifact_preservation
• Dependency: D5/S3/ConceptDynamics/Governance/TargetLaunderingCriterion