Diachronic Answerability

Diachronic answerability

Status: canonical, derived. Diachronic Answerability is not a conjunct of legitimacy. It is what the record half of legitimacy — an open Integrity evolution — yields: content conservation from Integrity and standing and access from Robust Openness. The theorem giving that decomposition is Established lean-proved.

The problem

A reasoner that improves must be able to change: its rules, its procedures, its evaluators, its concepts, the very way it represents an unresolved obligation. But a reasoner that can change anything can change its way out of anything. Revise the rule under which a criticism was raised, and the criticism evaporates. Rewrite the representation of a debt, and the debt is no longer legible. Nothing was ever refused; there is simply nothing left to answer.

So the question is not what must a reasoner keep believing. The answer to that is nothing — a later reasoner may reject an earlier norm, defeat an earlier reason, replace an evaluator. The question is narrower and structural:

What must remain invariant under self-revision if revision is not to erase prior answerability?

The decomposition

Diachronic Answerability to P = Answerability Conservation from Integrity + standing and access from Robust Openness.

Precisely: a legitimate segment from O₀ to O₁ yields

• Conservation between O₀ and O₁ — no occurrence disappears, every recorded answer or closure receipt persists, live content is transported faithfully, every account stays anchored to its own occurrence; and
• openness at both endpoints — every live in-scope concern has an adequate route and the protected party P stands on the carrier of every applicable one, on the actual branch and under every declared intervention — and, by the definition of a legitimate segment, at every state between.

The first half is a theorem of the Integrity evolution alone. The second cannot be: the exact counterexample is an evolution that carries an obligation's content faithfully onto a successor at an anchor where only the resolver stands. Every Integrity condition holds; the protected party can no longer act. Standing is a question of who may act, not of what is owed, and it lives in Robust Openness.

The three fates, and there is no fourth

Every account's leaves are drawn from exactly three fates:

answered — an adequate answer receipt; closed — a settlement item available through the external boundary together with the internal closure judgment made at that prefix; live — a port of the current docket.

There is no leaf by which content leaves. What remains owed can never grow — new obligation enters as a fresh occurrence, never by rewriting an old one — and a transition replaces exactly the live leaves. The consequence that matters:

Relabelling cannot discharge a debt. Changing a protocol, ontology, evaluator, encoding, or label cannot by itself reduce what is owed. Any decrease appears as an authenticated answer receipt or a certified closure.

Answered and closed are distinct fates. Both yield a resolution witness — evidence that the requirement was legitimately accounted for — and nothing in the theory turns a closure into an answer.

Defeat carries; it does not extinguish

The Defeat Principle:

A participant may answer an obligation or contest whether it is owed; only an authenticated settlement-backed terminal condition may make an unanswered obligation disappear.

In the account, a disposal is the identity local law: the successor demands exactly the parent's content, and the grounds for contesting it are recorded in the law's authority. Nothing has been answered and nothing has been closed; the obligation has moved onto the successor. A contest ends the way any obligation ends, by an answer receipt or by a closure whose internal judgment certifies that the cited settlement suffices. The alternative reading — disposal as a terminal exit — was rejected because it makes the disposition term an unaudited hole in every conservation law, and that hole is exactly the laundering channel a self-improving reasoner would use.

Which rules of a practice license contesting which debts is licence content, supplied through the protocol's warrants and not derived here.

Answerability is answerability to someone

Preservation of standing is relative to a protected principal or a declared relation. A structural condition quantifying over all coalitions cannot exist — take the coalition to be everyone — so the openness half names a party, and pays for it by no longer being purely structural. That the canonical predicate may name a party is ruled (DECISIONS.md, 2026-09-08); the mathematics offers no party-free alternative, and the role identity is anchored while its holder changes only by authorized succession.

Being ignored is a failure too

Conservation is a safety property: nothing disappears. It says nothing about anything ever happening. A perfectly conserved obligation can be perfectly ignored forever. The liveness side — that a case with recurring opportunities is not starved, and that attention converts into vanishing defect at a rate — is where Normative induction begins. Liveness under endogenous contest remains a research problem.

Two holes, named

Semantic authentication is an input. Everything above turns on the protocol's predicates meaning what they say: that a claimed answer really is adequate on the terms the burden was incurred, and that a local law's two maps really relate the successors' content to the parent's. The theory types the interface and does not construct it.

Licence content is upstream. The Defeat Principle says what a disposal does; which rules license which contests is the practice's.

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Evidence. The decomposition theorem is LegitimateEvolution.lean, registered as open-integrity.answerable; the conservation theorem is integrity.evolution-conservation. The counterexample to deriving standing from Integrity is attack A6 of the integrity adversary round's ATTACKS.md. The Defeat Principle ruling is in the decision ledger; its first model, the defeat-disciplined trace, is the defeat-landing round's WITNESS.md, and the principal-relative form of standing is that round's STANDING_REPAIR.md. How the defeat theory differs from default logic is on the prior art page.