openness.certplus-is-robust-openness
and · drafted
Statement
Given actual coverage, the bill `(S) ∧ (R+) ∧ (P)` is logically equivalent to counterfactual Robust Openness: the conclusion factored by a case split, not an independent sufficient condition. Recorded so that the bill is not presented as a certificate.
Source
projects/normativity/CLAIMS.md, entry openness.certplus-is-robust-openness (class lean-proved, status active, origin round 2026-09-06-mathematical-consolidation; answers item 78). Documentation: verification: projects/normativity/legitimacy/rounds/2026-09-06-mathematical-consolidation/THEOREMS.md; context: projects/normativity/legitimacy/rounds/2026-09-06-mathematical-consolidation/CONSOLIDATION.md. The signature of Workspace.Normativity.Contrib.NonCapture.Scenario.certPlus_iff_robustOpen in lean/Workspace/Normativity/Contrib/NonCaptureCertificate.lean.
Notes
Filed by the map-as-canonical round (prompts/2026-10-22-map-as-canonical) from the registry entry and the declaration's signature. The site-vertical-slice round (projects/enabling/rounds/2026-10-24-site-vertical-slice) connected it by reading: its hypotheses are the three leaves, its bridge names the gap between the claim and the declaration, and it is a conjunct of the informal claim split-bill-is-robust-openness, a shared-claim root of openness-and-non-capture, rather than a node that frame holds. Registry note: Given actual coverage, the bill (S) ∧ (R+) ∧ (P) is logically equivalent to counterfactual Robust Openness: the conclusion factored by a case split, not an independent sufficient condition. Recorded so that the bill is not presented as a certificate. The registry's answers_item is the priorities pointer to item 78 (ruling F2).
Bridge card
A conjunct of the informal claim split-bill-is-robust-openness: Given actual coverage, the earlier bill for Robust Openness that allowed a route to be replaced rather than preserved is 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.
Declaration Workspace.Normativity.Contrib.NonCapture.Scenario.certPlus_iff_robustOpen in lean/Workspace.lean (record openness.certplus-is-robust-openness.record)
Registry openness.certplus-is-robust-openness: class lean-proved, status active, review ci-only, origin round 2026-09-06-mathematical-consolidation; bears on item 78
The claim asserts that the earlier split bill for Robust Openness, a silent prefix clause, route persistence allowing a named replacement, and standing, is, given actual coverage, Robust Openness itself factored by a case split on whether the concern is live at the actual prefix, and not an independent sufficient condition. The declaration certifies exactly that equivalence over an abstract finite scenario: with actual coverage inside the protected routes, the conjunction of the three clauses is logically equivalent to coverage and standing in every declared counterfactual. The gaps: the declaration's RobustOpen quantifies over the declared counterfactuals only, while the wiki's Robust Openness at a state conjoins the actual branch (the file's RobustOpenActual adds it, and its counterfactual_open_not_actual shows the two differ), so the equivalence is with the counterfactual half; the scenario abstracts coverage to booleans and does not model how a counterfactual state is produced, so nothing here is a causal non-capture theorem, as the file says of itself; and the claim's force as a correction (the bill is no certificate) rests on the companion results that the componentwise persistence bill is strictly stronger, which this record does not certify.
Hypotheses, read:
- openness.certplus-is-robust-openness.h-scenario definitional: A scenario pairs the coverage state of one concern on the actual prefix with one coverage state per declared intervention, each state a finite record of applicability, disposition, representation, the per-route components and the principal's standing.
The variables `S : Scenario J R` with `CovState R`. Definitional: the modelling object; how a counterfactual state is produced is the external semantics and is not modelled, as the file's header says. - openness.certplus-is-robust-openness.h-protected-routes definitional: A protected route set is declared: a predicate on routes.
The binder `W : R → Bool`. Definitional: the application's declared protected routes; the clauses quantify over them. - openness.certplus-is-robust-openness.h-actual-coverage open: Where the concern is live on the actual prefix, some protected route is adequate there: coverage on the actual branch, witnessed inside the protected set.
The binder `hA : S.CoverageActual W`. Open: the equivalence is stated under it and nothing here derives it; an application certifies actual coverage, and without it the bill and Robust Openness come apart (the direction from the bill to openness uses it).
Completeness (openness.certplus-is-robust-openness.complete): No premise beyond the signature's binders enters the declaration; the kernel checks it as stated. The result is the record, the three hypothesis leaves filed by reading (the scenario, the protected route set, actual coverage inside it), the bridge and this leaf.
What remains (split-bill-is-robust-openness.improvable)
The compression of the split bill into Robust Openness, in which the earlier bill is the definition factored by a case split, can be improved until it reflects a trajectory whose Robust Openness is certified under an intervention semantics read off its accounted state well.
- item-130: An intervention semantics indexed by the accounted state produces, for each state and concern, the actual coverage data and the coverage data under each declared intervention, so that the scenario the certificate theorems quantify over is read off the record rather than supplied by hand. — this is item 130
- split-bill-is-robust-openness.residual (residual): A refinement of the compression theorem that none of the other routes describes reflects a trajectory whose Robust Openness is certified under an intervention semantics read off its accounted state.
Author and human events
Author @smithy-verity; version 1; size M.
No human event has touched this node.
Edges
Above
- part of split-bill-is-robust-openness
Children
- part: openness.certplus-is-robust-openness.record leaf/record
- part: openness.certplus-is-robust-openness.bridge leaf/bridge
- part: openness.certplus-is-robust-openness.complete leaf/completeness
- part: openness.certplus-is-robust-openness.h-scenario leaf/hypothesis
- part: openness.certplus-is-robust-openness.h-protected-routes leaf/hypothesis
- part: openness.certplus-is-robust-openness.h-actual-coverage leaf/hypothesis
Work pointers
Ranking (the lens, not the structure)
{
"status": "open",
"diagnosis": null,
"flags": [],
"V": {
"V_prior": null,
"display": "2",
"headline": 2,
"ref": 2,
"valid": 2,
"weaker": "both"
},
"belief": null,
"draft": "ai"
}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.