Item 78: Canonicalize the legitimacy spine from the consolidation
Deference line — second wave · difficulty entry · project normativity · closed · node item-78
— answered 2026-09-08
The mathematical-consolidation round states, in projects/normativity/legitimacy/rounds/2026-09-06-mathematical-consolidation/CONSOLIDATION.md, what the canonical pages should now say: Integrity as a boundary-indexed segment of per-port accounts, Robust Openness as the definition with the persistence bill as its external certificate, Legitimacy as their product with Diachronic Answerability derived, the occurrence-indexed export, Progress at the edge endpoint, and the two conditional Normative Inductor theorems. Its §11 is a page-by-page migration map.
Rewrite the wiki's Legitimacy, Integrity, Diachronic Answerability, Openness, Settlement interface, Normative induction and Normative Inductor pages from that document, and demote the fixed-era pages as the map says. Register the theorems the map names as canonical, against this item.
Deliverable shape: wiki edits under a dispatch that grants wiki scope, plus projects/normativity/CLAIMS.md entries of class lean-proved for OccurrenceIntegrity.Segment.complete_accounting, Program.terminals_subst, NonCapture.Scenario.certPlus_iff_robustOpen, NormativeInductorComposition.edge_progress_bound_quadratic, and NormativeInductionInterface.Evaluation.deductive_normative_inductor. Acceptance check: python3 -m checkers.run, python3 -m checkers.wiki_links and python3 -m checkers.wiki_state_bindings pass; python3 tests/run.py green.
Context: the consolidation round's CONSOLIDATION.md and THEOREMS.md, as amended by the final pressure pass's projects/normativity/legitimacy/rounds/2026-09-07-final-pressure-pass/READINESS.md (accounted state, evolution relation, per-state openness, RobustOpenActual, Resolution, unary local laws); the two DECISIONS.md queue entries the consolidation names (protected principal; settlement independence). A solution ships: the rewritten pages and the registry entries; register also LegitimateEvolution.Evolution.conservation, LegitimateSegment.answerable, and NonCapture.Scenario.robustOpenActual_of_persistence.
Answered, 2026-09-08, by prompts/2026-09-08-canonicalization/. Shipped: the seven core wiki pages, the Roadmap's legitimacy section, the Glossary and vocabulary rewritten around the pressure pass's theory; sixteen claims registered as The legitimacy spine in projects/normativity/CLAIMS.md, including the three named above. Not registered, deliberately: the two conditional Normative Inductor theorems, until a witness inhabits their joint hypothesis packages — a realization item, not a theory item.
Deliverable shape: wiki edits under a dispatch that grants wiki scope, plus projects/normativity/CLAIMS.md entries of class lean-proved for OccurrenceIntegrity.Segment.complete_accounting, Program.terminals_subst, NonCapture.Scenario.certPlus_iff_robustOpen, NormativeInductorComposition.edge_progress_bound_quadratic, and NormativeInductionInterface.Evaluation.deductive_normative_inductor.
Acceptance check: python3 -m checkers.run, python3 -m checkers.wiki_links and python3 -m checkers.wiki_state_bindings pass; python3 tests/run.py green.
Context: DECISIONS.md; projects/normativity/legitimacy/rounds/2026-09-07-final-pressure-pass/READINESS.md
Registered results bearing on this item
- integrity.evolution-conservation: Answerability Conservation: along an Integrity evolution between accounted states, exposure only grows, every recorded answer or closure receipt persists, and the resolution witness each occurrence's
- integrity.faithful-carry: The resolution witness a substituted account denotes is the original account's witness with each live port read through its replacement. Faithful transformation of live content is a consequence of the
- integrity.multiplicity-witness: Two occurrences with the same anchor, one answered and one carried by a single transition, have accounts with fates `{answered}` and `{live}`. Occurrence identity lives outside the content type and th
- integrity.propagate-to-segment: An evolution's target account equals the propagation of its source account along the underlying segment: the account is determined by the certificate, so witnesses cannot disagree about either endpoin
- integrity.receipts-immutable: Substitution at live ports keeps every terminal receipt and adds only the terminals of the substituted accounts. With `livePorts_subst` this is the three-fate accounting at the leaf level: terminal fa
- ni.progress-bound: The quadratic bound typed on `Evaluation (O : ObligationState)`: the practical/uptake certificate at the realized market gives the three-term bound. Inhabited by `Witness.uptake` and `Witness.bound` a
- open-integrity.answerable: A legitimate segment yields Answerability Conservation from Integrity and Robust Openness (coverage of every live concern and the protected party's standing on every applicable one, actual branch and
- open-integrity.endpoint-trans: `Legitimate` is `Nonempty LegitimateSegment`; it hides the witness for consumers and is transitive. The certificate remains available for audit.
- open-integrity.segment-trans: Composition of legitimate-evolution certificates: the underlying evolutions concatenate at the literally shared state and per-state openness composes (`AllStates.trans`). Inhabited by `Witness.compose
- openness.actual-branch-witness: Exact witness: counterfactual-only Robust Openness holds while the actual prefix has a live concern with no route and no principal standing. The public predicate is therefore `RobustOpenActual`, actua
- openness.certplus-is-robust-openness: 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
- openness.endpoint-only-insufficient: Exact counterexample: a two-transition evolution open at both endpoints whose middle state has a live concern with no adequate route; it is not a legitimate segment. This is why openness is required a
- openness.persistence-sufficient: Actual coverage inside the protected route set, actual standing, silent-prefix coverage, componentwise persistence of protected routes, and principal standing give `RobustOpenActual`. A sufficient ext
- progress.edge-bound: Transport-weighted edge response loss plus residual is bounded by the amplification-weighted service-mean defect, the transport-weighted error, and the residual charge, from nonnegative transport and
- progress.edge-bound-quadratic: With intensity-normalized service weights and the uptake certificate `λ_s d_s² ≤ ρ_s`, the first term is `Γ √(Σρ/Σλ)`. Inhabited by `edge_progress_witness` with all three terms positive.
- progress.headline-separation: Two equally weighted services with edge losses 0 and 1 average to one half, below a headline loss of one. The exposure-headline theorems remain as an optional corollary needing a dominance premise thi
Where it hangs
- held by normativity