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Irreversibility-Inference Convergence Theorem

Canonical Source Repository​

Admissible-Existence/IICT

Definition​

The Irreversibility-Inference Convergence Theorem, or IICT, is a theorem candidate under Commit-Time Admissibility.

IICT proposes that governance systems subjected to repeated admissibility optimization converge toward structures that minimize the distance between irreversible commitment and the final admissible inference while preserving reconstructability.

Relationship to Commit-Time Admissibility​

IICT is for Commit-Time Admissibility. It does not replace Commit-Time Admissibility.

Commit-Time Admissibility asks whether a transition still has standing at the moment of commitment.

IICT asks whether repeated admissibility optimization causes governance systems to converge toward structures that make commit-time standing necessary or optimal.

Relationship to Inference-Window Governance​

Inference-Window and Irreversibility-Bounded Governance is the operational formalism for evaluating one proposed transition. It defines evidence freshness, commit-time standing, consequence-adjusted assurance, hard failures, recovery posture, and the ALLOW, DENY, DEFER, and ESCALATE dispositions.

IICT is different. It is a theorem candidate about what may happen to governance architecture after such commit-time controls are applied repeatedly.

Inference-window governance
  -> evaluates a proposed transition now

IICT
  -> studies whether repeated governed evaluation causes
     architecture to converge toward a smaller distance
     between final valid inference and irreversible commitment

The operational formalism can be useful and testable without IICT being proven. A passing inference-window validator does not prove IICT. It is not proof of architectural convergence.

Pre-Commit and Post-Commit Responsibilities​

IICT concerns the placement of valid inference relative to irreversible commitment. It should not collapse pre-commit revalidation and post-commit recovery into one responsibility.

proposal
  -> commit-time revalidation
  -> bounded execution
  -> consequence observation
  -> recovery, correction, or accountability
  -> reconstruction

Commit-time revalidation asks whether evidence, policy, authority, delegation, consent, scope, and context still retain standing before execution.

Recovery governance asks what obligations remain when an admitted action still produces error, harm, or an unforeseen consequence.

Reconstruction preserves enough material to determine what occurred and whether the pre-commit and post-commit responsibilities were satisfied.

Core Theorem Candidate​

A governance system subjected to repeated admissibility optimization will converge toward structures that minimize the distance between irreversible commitment and the final admissible inference while preserving reconstructability.

Core Terms​

TermDefinition
Inference WindowThe interval in which authority, policy, evidence, context, delegation, and memory are still valid enough to support a standing determination.
Point of IrreversibilityThe point after which an action cannot be fully recalled, reversed, re-bound, or restored to its prior admissible state.
Governance DistanceThe distance between the final valid inference and the point of irreversibility.
Final Valid InferenceThe most recent inference that still retains standing under current authority, policy, evidence, context, delegation, and memory conditions.
Irreversible CommitmentThe crossing point where a proposed transition becomes practically, procedurally, or materially non-recoverable without a new recovery or remediation process.
ReconstructabilityThe ability to recover the evidence, receipts, policy references, state, context, and decision path needed to explain or replay why a transition did or did not have standing.
Admissibility GeometryThe structural relationship among authority, policy, evidence, context, delegation, memory, inference timing, and irreversible action.

Transition Element Construction​

Inference Window Declaration
  -> Irreversibility Point Declaration
  -> Governance Distance Measurement
  -> Convergence Observation
  -> Theorem Evaluation

Expected Structural Classes​

  • clean admissible path
  • stale but reconstructable path
  • authority gap
  • delegation leak
  • memory contamination
  • context collapse
  • fail-closed recovery path

Validation Candidates​

Current baseline validation is maintained in the source repository:

tests/run_iict_tests.py
tests/fixtures/iict_cases.json

Expected current result:

IICT baseline tests passed: 5 cases

Mirror Handoff​

Current root handoff:

IICT_MIRROR_HANDOFF.md

The handoff identifies source files, downstream mirror targets, validation command, expected result, install order, and boundary statements.

Publisher Artifacts​

Publisher currently carries sv-iict-2026 as a draft paper record. The draft record does not imply peer review completion or theorem proof.

Non-Claims​

The wiki does not prove IICT by listing it.
IICT baseline tests do not prove the theorem.
Inference-window governance validation does not prove IICT.
IICT does not replace Commit-Time Admissibility.
IICT does not replace recovery governance.
A theorem-supporting case is not final theorem validation.
A public page is not proof of admissibility by itself.