openness-and-non-capture

Openness, coverage, and non-capture

Status: canonical. Robust Openness at a state is a definition over application-supplied coverage data; that a sufficient external certificate yields it, that the earlier split bill is the definition itself, and that counterfactual-only openness misses the actual branch are Established lean-proved. No application's intervention semantics is constructed here, by design.

Integrity governs what happens to a concern once it has reached a process. Openness governs whether concerns can reach it at all, and whether the party they matter to can still act on them.

Openness blocks evasion by exclusion. Integrity blocks evasion by revision.

A process that admits every criticism it receives and then ensures it receives none has a perfect record and is not answerable to anyone. That failure cannot be seen from inside the record.

Scope is declared

No process is open to everything. The theory is stated relative to a declared coverage scope Γ: a set of stable concern identifiers, each with a target, an applicability condition, a receipt criterion, a registration criterion, and a required route-quality class. Declaring Γ is a modeling choice; the theory prevents its silent shrinkage and does not derive it.

Coverage at a state

For a concern at a state, the coverage data are: whether the concern is applicable (read by an anchored predicate, never by the process's current recognition of it), whether it has been authorizedly disposed, whether it is represented, which routes are admissible, efficacious and registration-capable, and whether the protected party stands on the carrier of the concern's load. A concern is live when applicable, undisposed and unrepresented. Covered means: if live, some route is adequate. **Open to P** means: if applicable, P stands on its carrier — a disposal moves the load to a successor and does not exempt it.

Both conditions are conditional on liveness or applicability. Nothing is demanded of a concern while it is inapplicable or already represented. This is what makes "openness at every state" the concern-relative condition rather than a stronger one.

Robust Openness

Coverage on the actual run is not enough, for the same reason integrity is not: a process can shape which concerns become live, which evaluators become authoritative, and which routes remain available, while every actual-run certificate is valid.

An application declares an intervention class J — ways the process, or a coalition it belongs to, might have acted on the conditions of its own criticism — and an intervention semantics producing, for each state and concern, the actual coverage data and the coverage data under each intervention. The semantics is indexed by the accounted state, so it can read the docket, the ports and the accounts, and say which carrier holds which occurrence's load.

Robust Openness at a state: covered and open to P on the actual branch, and covered and open to P under every declared intervention.

The actual branch is a conjunct by definition. J indexes proper interventions only; actual standing is not recovered by treating the actual history as a null intervention, and the counterfactual-only predicate provably does not contain it.

Over time

An open Integrity evolution — the record half of legitimacy — is robustly open at every one of its states. Endpoint-only openness is refuted by an exact trajectory: open, then a state at which a live concern has no adequate route, then restored. Every named form of laundering by temporary exclusion — losing the principal's standing for a while, removing every route for a while, suppressing settlement or evaluation access where a route runs through it, delaying a concern's representation until it no longer matters — is a failure of Robust Openness at the affected state. Because coverage and standing are already conditional on liveness and applicability, per-state openness is the weakest form the coverage vocabulary can express, and it composes under concatenation of legitimate segments.

The external contract, and one way to pay it

The theory bills an application for a certified Robust Openness at each state, under its declared scope, intervention class, coupling and protected relation. It does not choose a counterfactual semantics, prove a coupling causal, or select a scope.

One sufficient way to discharge the bill is componentwise persistence: actual coverage inside a protected route set, actual standing, an adequate route for any concern that becomes live only counterfactually, and preservation of each protected route's admissibility, efficacy and registration capability under every intervention. That yields Robust Openness and is strictly stronger than it — a route may be replaced rather than preserved. An earlier bill that allowed replacement turned out, given actual coverage, to be Robust Openness itself split on whether the concern was live at the actual prefix, and is recorded as such rather than presented as a certificate.

This is the access half of non-capture: it concerns who can reach and act on a concern, not what an evaluator who does reach it concludes. Robust Openness is the inward conjunct of external legitimacy: what should reach the trajectory can. Its partner, transparency, is the conjunct of entry: what reaches the trajectory does so only through declared channels. That an evaluation recorded through an open route is the evaluator's own — authorship — is a conjunct of internal legitimacy and is stated on deference; none of it is part of this page's contract.

Downstream, the distinction is exact. Robust Openness supplies route availability: a live concern in scope has an adequate route by which it can become represented. It does not say the route is exercised, and it does not say an evaluation has already seen every protected concern. The deference consumer adds, at its own level and not here, a bridge — a represented protected concern is in the evaluation's reason trace — and a barrier — a certified evaluation has no live protected concern at commitment — and from those two derives that certification implies coverage; that routes are exercised in time is neither Robust Openness nor any theorem of this page. On the deference side that exercise now has its own theorems: whether the discovered reasons are routed before commitment is the suffix-cut service obstruction, and whether the true reasons are determined at all is the information-cell discovery obstruction (Corrigibility §5; the non-capture round's [SUPPLY_THEOREM.md](https://github.com/A-M-Berns/alignment-workspace/blob/3b84a4518841ea8753a4ebe0fd0361a0a05316d8/projects/deference/rounds/2026-09-16-noncapture-compilation/SUPPLY_THEOREM.md) <a class="ref round" href="/rounds/2026-09-16-noncapture-compilation/">[round]</a> and [DISCOVERY_THEOREM.md](https://github.com/A-M-Berns/alignment-workspace/blob/3b84a4518841ea8753a4ebe0fd0361a0a05316d8/projects/deference/rounds/2026-09-16-noncapture-compilation/DISCOVERY_THEOREM.md) <a class="ref round" href="/rounds/2026-09-16-noncapture-compilation/">[round]</a>). Robust Openness over a finite declared class of log transforms is itself a finite computation once the principal's program is committed (openUnder_iff); what stays external is that the declared transforms are the interventions they name.

Self-sealing

The obvious attack is to destroy the one route a criticism has and then record the coverage obligation as resolved. Every record condition is satisfied. Under the per-state condition the attack fails at the state where the concern is live and routeless, whatever is recorded afterwards.

Principal relativity

A certificate that coverage survives interventions is a certificate for a declared principal or relation, whose standing and corrective channel the intervention class is not allowed to erode. A party-free condition quantifying over all coalitions cannot exist. That the canonical predicate may name a party is ruled (DECISIONS.md, 2026-09-08).

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Evidence. The coverage data, Robust Openness on both branches, the persistence theorem, the compression of the split bill, and the two separating witnesses are [NonCaptureCertificate.lean](https://github.com/A-M-Berns/alignment-workspace/blob/c24159764974232dfd5b47a10b671f12d6f9c244/lean/Workspace/Normativity/Contrib/NonCaptureCertificate.lean), registered as openness.persistence-sufficient <a class="ref claim" href="/claims/openness.persistence-sufficient/">[lean-proved, active]</a>, openness.certplus-is-robust-openness <a class="ref claim" href="/claims/openness.certplus-is-robust-openness/">[lean-proved, active]</a> and openness.actual-branch-witness <a class="ref claim" href="/claims/openness.actual-branch-witness/">[lean-proved, active]</a>; the per-state requirement and the endpoint-only counterexample are [LegitimateEvolution.lean](https://github.com/A-M-Berns/alignment-workspace/blob/c24159764974232dfd5b47a10b671f12d6f9c244/lean/Workspace/Normativity/Contrib/LegitimateEvolution.lean), registered as openness.endpoint-only-insufficient <a class="ref claim" href="/claims/openness.endpoint-only-insufficient/">[lean-proved, active]</a>. The necessity attacks on the persistence bill are the non-capture certificate round's [CERTIFICATE.md](https://github.com/A-M-Berns/alignment-workspace/blob/c24159764974232dfd5b47a10b671f12d6f9c244/projects/normativity/legitimacy/rounds/2026-09-05-noncapture-certificate/CERTIFICATE.md) <a class="ref round" href="/rounds/2026-09-05-noncapture-certificate/">[round]</a>. The coverage contract and the self-sealing audit that preceded them are [COVERAGE_CONTRACTS.md](https://github.com/A-M-Berns/alignment-workspace/blob/198a86ae3e8a45737c3229e95718fa5882d06216/projects/normativity/legitimacy/rounds/2026-08-30-cf-coverage-continuity-interface/COVERAGE_CONTRACTS.md) and [SELF_SEALING.md](https://github.com/A-M-Berns/alignment-workspace/blob/198a86ae3e8a45737c3229e95718fa5882d06216/projects/normativity/legitimacy/rounds/2026-08-30-cf-coverage-continuity-interface/SELF_SEALING.md); the one end-to-end counterfactual test remains the dynamic-reward legitimacy test's [CRITERION.md](https://github.com/A-M-Berns/alignment-workspace/blob/198a86ae3e8a45737c3229e95718fa5882d06216/projects/normativity/legitimacy/rounds/2026-08-25-carroll-legitimacy-test/CRITERION.md) <a class="ref round" href="/rounds/2026-08-25-carroll-legitimacy-test/">[round]</a>.