From e6fda7ef630a39abcea5a672a144e4c2af649f9b Mon Sep 17 00:00:00 2001 From: Claude Date: Mon, 26 Oct 2026 16:56:15 +0000 Subject: [PATCH 1/2] docs: point the ordinal lane at hyperpolymath/ordinal-notation echo-types#349 removed the ordinal lane, but the docs still described it as present. Update them to match the tree. - Living status documents now say the lane moved: CLAUDE.md, EXPLAINME, PROOF-STATUS, TOPOLOGY, roadmap Lane 3, MAP, proof-debt, bridge-status, proof-obligations, the kernel note, what-echo-is and the wiki. - proof-debt: (d) is empty here. The two Fidelity postulates left with the lane, so one quarantined postulate block remains, under (c). - EXPLAINME: correct "no Echo*.agda imports from Ordinal/". EchoOrdinal imports the two bridge leaves that stayed. - The seven documents that moved with the lane keep a frozen copy here with a "moved" banner. - Dated records (AFFIRMATION, proof logs, dated status files) are left as written. The paper's ordinal appendix gets a one-line note. Docs only. kernel-guard and check-guardrails pass. Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_01MF5GeeBBDF6sUzr6pZTjWV --- CHANGELOG.adoc | 19 ++++++ CLAUDE.md | 41 +++++++++-- EXPLAINME.adoc | 14 +++- Fidelity-OPEN-postulates.adoc | 10 +++ PROOF-STATUS.adoc | 48 +++++++------ TOPOLOGY.adoc | 4 +- docs/CLAIMS_AUDIT.adoc | 11 +++ docs/bridge-status.adoc | 14 ++-- docs/bridges/buchholz-extended-wf.adoc | 10 +++ docs/bridges/buchholz-plan.adoc | 10 +++ docs/bridges/buchholz-rank-obstruction.adoc | 10 +++ docs/echo-types/MAP.adoc | 68 ++++--------------- .../echo-types/buchholz-rank-obstruction.adoc | 10 +++ .../ordinal-bh-order-type-fidelity-open.adoc | 10 +++ .../ordinal-fidelity-ladder-parked.adoc | 10 +++ docs/echo-types/echo-kernel-note.adoc | 8 ++- docs/echo-types/paper.adoc | 5 ++ docs/echo-types/what-echo-is.adoc | 4 +- docs/proof-debt.adoc | 59 +++++----------- docs/proof-obligations.adoc | 4 +- roadmap.adoc | 16 ++++- wiki/Architecture.adoc | 6 +- wiki/Home.adoc | 8 +-- wiki/Roadmap.adoc | 5 +- 24 files changed, 252 insertions(+), 152 deletions(-) diff --git a/CHANGELOG.adoc b/CHANGELOG.adoc index 375471d..9feccc1 100644 --- a/CHANGELOG.adoc +++ b/CHANGELOG.adoc @@ -7,6 +7,25 @@ Changelog]. === [Unreleased] +==== Removed (2026-10-20) + +* _The ordinal lane._ echo-types#349 removed `+proofs/agda/Ordinal/**+` +except `+Ordinal/OmegaMarkers.agda+` and `+Ordinal/Buchholz/Syntax.agda+`, +which the `+EchoOrdinal+` bridge imports. The lane now lives in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], +carrying out decision `+D-2026-06-21+`. echo-types' quarantined postulates +go from three to one: the two `+Fidelity.agda+` postulates left with the +lane. + +==== Changed (2026-10-26) + +* _Docs point at ordinal-notation._ The living status documents (CLAUDE.md, +EXPLAINME, PROOF-STATUS, TOPOLOGY, roadmap, MAP, proof-debt, bridge +status, proof obligations, kernel note and the wiki) now say the ordinal +lane has moved. The design documents that moved with it are kept here as +frozen copies with a "moved" banner. Dated records (AFFIRMATION, proof +logs, dated status files) are unchanged. + ==== Removed (2026-09-30) * _The 27 `+.a2ml+` machine-readable records._ Removed by owner ruling: diff --git a/CLAUDE.md b/CLAUDE.md index 000b659..d684a0f 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -7,8 +7,8 @@ Adjacent projects, in one line each, for session bootstrapping: - echo-types — constructive Agda formalization of fiber-based structured loss ("echo types"); `Echo f y := Σ (x : A) , (f x ≡ y)`. Gated - identity-claim development; `--safe --without-K` throughout. Current - workstream: E (ordinal-notation / Buchholz collapsing layer). + identity-claim development; `--safe --without-K` throughout. The + ordinal-notation / Buchholz lane moved out on 2026-10-20 (see below). https://github.com/hyperpolymath/echo-types - PanLL — three-pane cognitive-relief HTI; Ambient/Symbolic/Neural/World panes. https://github.com/hyperpolymath/panll @@ -40,6 +40,11 @@ Adjacent projects, in one line each, for session bootstrapping: repo 2026-05-30 — see echo-types#159) + `arghda-panll` (Gossamer/AffineScript presentation, planned). See docs/buchholz-plan.adoc appendix for the motivating proof pipeline. +- ordinal-notation — the Brouwer / Veblen / Buchholz ordinal lane extracted + from echo-types on 2026-10-20 (#349; decision D-2026-06-21). Frozen + hand-off record; order-type fidelity to ψ₀(Ω_ω) OPEN, with its two + quarantined `Fidelity.agda` postulates. + https://github.com/hyperpolymath/ordinal-notation - EchoTypes.jl — executable Julia companion to echo-types, mirroring the finite-domain shadow of the Tier-1 + Tier-2 spine + the unconditional F5 OFS fragment. v0.2.0 (2026-05-27) extends v0.1.0's `Echo` / @@ -72,7 +77,11 @@ Two active workstreams: the equivalence-record packaging `Echo-comp-pent-Σ-assoc : ... ↔ ...` (stdlib `Function.Bundles._↔_`) is in place. -2. **Ordinal track — RETIRED FROM ECHO-TYPES (D-2026-06-21).** This research +2. **Ordinal track — MOVED to hyperpolymath/ordinal-notation (2026-10-20, + #349).** Only `EchoOrdinal` + `Ordinal.OmegaMarkers` + + `Ordinal.Buchholz.Syntax` remain here; every other path named below is + gone from this repo. Ordinal TODOs belong in that repo. RETIRED FROM + ECHO-TYPES (D-2026-06-21). This research ladder *outgrew echo-types* and is no longer echo-types work: do NOT open new rungs here; the disposition is extraction to its own ordinal-notation repo (see `docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc` + the @@ -215,7 +224,31 @@ work to `main` and refresh all documentation: name, the commits folded in, the remaining open pieces of the milestone, and the proposed smallest useful next advance. -## Current rung state (2026-06-21) +## Current rung state (2026-10-26) + +### Session arc 2026-10-20→26 — ordinal lane physically extracted (read this FIRST) + +The `D-2026-06-21` disposition is carried out. echo-types#349 (`b1dcc29`) +removed `proofs/agda/Ordinal/**` except the two bridge leaves +(`Ordinal/OmegaMarkers.agda`, `Ordinal/Buchholz/Syntax.agda`), unwired them +from `All.agda` / `Smoke.agda`, and dropped `Fidelity` from the guardrail's +`EXPLORATORY_EXEMPT`. The lane now lives in +https://github.com/hyperpolymath/ordinal-notation (imported from `703dd77`, +history kept in a filter-repo bundle; Agda under +`verification/proofs/agda/`, gated by that repo's proof MANIFEST). + +* *Trust boundary here: 3 → 1 quarantined postulate block* — + only `EchoImageFactorizationPropPostulated` (c) remains. The two Fidelity + postulates left with the lane. +* *Docs:* the living status docs point at the new repo. The moved design + documents (`docs/bridges/buchholz-*.adoc`, + `docs/echo-types/buchholz-rank-obstruction.adoc`, the two ordinal + decision records, `Fidelity-OPEN-postulates.adoc`) are kept here as + frozen copies with a "moved" banner. Dated records (AFFIRMATION, + CHANGELOG history, proof logs, dated STATUS files) are left as written. +* *Ordinal sections in this file below are history.* Do not act on any + ordinal "next rung" / "open piece" here. + ### Session arc 2026-06-21 (close-out) — gap-closing proofs #249–#258 + cross-repo docs audit + ⚠ ordinal-ledger contradiction flag (read this FIRST) diff --git a/EXPLAINME.adoc b/EXPLAINME.adoc index cdb1619..dc1e73d 100644 --- a/EXPLAINME.adoc +++ b/EXPLAINME.adoc @@ -147,10 +147,18 @@ Echo Core does NOT depend on the Ordinal / Buchholz track. ____ How this is implemented:: -All ordinal modules live under `link:proofs/agda/Ordinal/[]`. No `Echo*.agda` file imports from `Ordinal/`. Dependency separation is structural (directory-level). +The ordinal lane no longer lives here. It moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +on 2026-10-20 (echo-types#349, decision `D-2026-06-21`). What stays in echo-types +is the echo-to-ordinal bridge `link:proofs/agda/EchoOrdinal.agda[]` and the two +small modules it imports, `Ordinal.OmegaMarkers` and `Ordinal.Buchholz.Syntax`. +No other `Echo*.agda` file imports from `Ordinal/`. Caveat:: -The Ordinal track has open problems (unbudgeted `wf-<ᵇʳᶠ` closure, shared-binder internalization). These do not affect Echo Core. See `link:docs/buchholz-plan.adoc[]`. +The ordinal lane's open problems (order-type fidelity to ψ₀(Ω_ω), the unbudgeted +`wf-<ᵇʳᶠ` closure over the native order) are tracked in ordinal-notation. They do +not affect Echo Core. The two bridge modules exist in both repositories and can +drift; ordinal-notation's copies are the maintained ones. == Dogfooded Across The Account @@ -200,7 +208,7 @@ The Ordinal track has open problems (unbudgeted `wf-<ᵇʳᶠ` closure, shared-b [CAUTION] ==== -**Buchholz shared-binder internalization is open.** The Ordinal track has well-foundedness for the current constructor core, but historical same-binder shapes are not internalized as constructors of the real order. Does not affect Echo Core. See `link:docs/buchholz-plan.adoc[]`. +**The ordinal lane has moved.** The Buchholz / Veblen development, including its open problems, now lives in https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation]. Only the `EchoOrdinal` bridge stays here. Does not affect Echo Core. ==== == Evidence Index diff --git a/Fidelity-OPEN-postulates.adoc b/Fidelity-OPEN-postulates.adoc index a5d77d9..c7800ae 100644 --- a/Fidelity-OPEN-postulates.adoc +++ b/Fidelity-OPEN-postulates.adoc @@ -1,5 +1,15 @@ == Fidelity — open postulates (trust boundaries) +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + Companion to `+proofs/agda/Ordinal/Buchholz/Fidelity.agda+`. Open problem *`+D-2026-06-14+`* (`+docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc+`). diff --git a/PROOF-STATUS.adoc b/PROOF-STATUS.adoc index 45c6bfa..0c17470 100644 --- a/PROOF-STATUS.adoc +++ b/PROOF-STATUS.adoc @@ -8,8 +8,11 @@ Honest status of the echo-types Agda formalisation: what is *proved*, what is *open*, and the build/guardrail invariant. echo-types is a constructive Agda development (`--safe --without-K`); the main verified suite (`proofs/agda/All.agda`) -is *postulate-free*. The single isolated exception (the order-type *Fidelity* -scaffold) is enumerated explicitly below. +is *postulate-free*. The one quarantined postulate block outside that suite +(the `--safe --without-K` shadow of propositional truncation) is enumerated +below. The ordinal lane, including its order-type *Fidelity* scaffold, moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +on 2026-10-20. == Build invariant (verified) @@ -47,41 +50,36 @@ scaffold) is enumerated explicitly below. `EchoDeniability`, and `EchoAggregation` (micro→macro aggregation as an Echo map; `aggregate-non-injective` + `no-canonical-disaggregation`). -=== Ordinal / Buchholz track (sound carrier) -* Doubled-ladder relation `_<ᵇ²_` over the 12 core constructors + the umbrella - `rank2-mono-<ᵇ²` + `wf-<ᵇ²` (Gate 1 closed *for the sound carrier*). -* `RecursiveSurfaceSound._<ᵇʳᶠ²_` + its *unbudgeted* `wf-<ᵇʳᶠ²`. -* `Ordinal/Brouwer/OrdinalExp.agda` — `ω^^_` + the first ε-number `ε₀` - (Bachmann–Howard climb rung 1). -* `Ordinal/Buchholz/BHTarget.agda` — a real `BHNotation` order + its - well-foundedness (no postulate). +=== Ordinal / Buchholz track — moved +The ordinal lane left echo-types on 2026-10-20 (echo-types#349, decision +`D-2026-06-21`) and now lives in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], +with its results and open problems. What stays here is the echo-to-ordinal +bridge `EchoOrdinal` (`ordinal-collapse-non-injective`) and the two modules it +imports, `Ordinal.OmegaMarkers` and `Ordinal.Buchholz.Syntax`. == Open (honest — NOT proved) -* *Bachmann–Howard milestone* `ψ₀(Ω_ω)` order-type fidelity — *OPEN* - (`D-2026-06-14`). ε₀ is astronomically below the target - (ε₀ ≪ Γ₀ ≪ … ≪ ψ₀(Ω_ω)); the collapsing-function climb is the multi-session - frontier. The headline ordinal milestone is *not* reached. -* *`Ordinal/Buchholz/Fidelity.agda` — 2 isolated postulates* (`denotation`, - `ordinal-upper-bound`). These are the ONLY postulates in the development, - quarantined under `Ordinal/Buchholz/` and tracked in `docs/.../proof-debt.md` - + `Fidelity-OPEN-postulates.md`. Dischargeable once the target collapse - heights exist. +* *Bachmann–Howard order-type fidelity* — *OPEN*, now tracked in + ordinal-notation together with its two quarantined postulates (`denotation`, + `ordinal-upper-bound`). +* *`EchoImageFactorizationPropPostulated.agda` — 1 isolated postulate block* + (four truncation primitives). Not imported by `All.agda`; tracked as (c) in + `docs/proof-debt.adoc`. * *(epi, mono) image truncation* — `∥_∥` is *constructed* only in the `--cubical` island `EchoImageFactorizationPropCubical.agda`; under `--safe --without-K` it remains a shadow (it cannot be built within `--safe --without-K` without HITs). -* *Unbudgeted global `wf-<ᵇʳᶠ` over native `_<ᵇ_`* — walled: native `_<ᵇ_` is - ordinally unsound (documented counterexample), so no rank embedding maps it. - The achievable form landed on the sound carrier (`wf-<ᵇʳᶠ²`). * *Pillar E paper* (`docs/echo-types/paper.adoc`) — LIVING DRAFT with `[EXPAND]` tags (background, related work, evaluation, ordinal consumer-evidence - appendix gated on the BH milestone). Not submitted. + appendix gated on the BH milestone, now an ordinal-notation milestone). Not + submitted. == Discipline -* No `postulate` in load-bearing tracks (the 2 Fidelity postulates are the - sole, isolated, documented exception). +* No `postulate` in load-bearing tracks (the one truncation-shadow block in + `EchoImageFactorizationPropPostulated.agda` is the sole, isolated, documented + exception). * Every headline theorem is pinned in `Smoke.agda`; every module is wired into `All.agda` (orphan modules that compile but are not in `All.agda` are treated as dead code). diff --git a/TOPOLOGY.adoc b/TOPOLOGY.adoc index 94bcd32..2567720 100644 --- a/TOPOLOGY.adoc +++ b/TOPOLOGY.adoc @@ -13,7 +13,7 @@ echo-types/ │ ├── EchoCharacteristic.agda │ ├── EchoExamples.agda │ ├── Echo*Bridge.agda # cross-system bridges (linear/graded/tropical/etc.) -│ ├── Ordinal/ # Buchholz / Veblen track +│ ├── Ordinal/ # bridge leaves only (OmegaMarkers, Buchholz/Syntax); the ordinal lane moved to hyperpolymath/ordinal-notation │ ├── examples/ # concrete usage demos │ └── characteristic/ # characteristic-style results (RoleGraded, etc.) ├── docs/ # supplementary documentation @@ -55,7 +55,7 @@ This is a foundation library; consumers are downstream Agda formalisations and d | Core echo theorems | constructive Agda, no postulates | `echo-intro`, `map-over`, `map-over-id`, `map-over-comp`, `map-square` | Characteristic family | constructive | `collapse-non-injective`, `no-section-*`, `echo-true≢echo-false`, `visible-constraint` | Bridge modules | constructive (per bridge) | linear / graded / tropical / choreo / epistemic / CNO / Janus / Dyadic / Ordinal -| Ordinal Buchholz track | mostly admitted, some closed | `WellFounded`, extended-order tower; closure pending +| Ordinal Buchholz track | moved (2026-10-20) | Now in https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation]; only the `EchoOrdinal` bridge and its two imports stay here | EI-2 (integration recipe) | TERMINATED NEGATIVELY (PATH B) | Per-axis halves proved; full 2D iff theorem parked as not formalisable in safe Agda without postulates |=== diff --git a/docs/CLAIMS_AUDIT.adoc b/docs/CLAIMS_AUDIT.adoc index d92790b..4d04440 100644 --- a/docs/CLAIMS_AUDIT.adoc +++ b/docs/CLAIMS_AUDIT.adoc @@ -15,6 +15,17 @@ unjustified; the rows pair each surface sentence with a proposed `(module, theorem)` mapping or the literal token `NONE-PROPOSED` when no in-repo artefact corresponds. +[NOTE] +==== +*Since 2026-10-20 the ordinal lane is no longer in this repository.* It +moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +(echo-types#349). Rows below that map to `Ordinal.*`, `Ordinal/Buchholz/*` +or `Ordinal/Buchholz/Smoke.agda` (S-002, S-015, S-063 and others) describe +the tree as audited, not the current one. Only `EchoOrdinal`, +`Ordinal.OmegaMarkers` and `Ordinal.Buchholz.Syntax` remain here. +==== + toc::[] == Scope and absent surfaces diff --git a/docs/bridge-status.adoc b/docs/bridge-status.adoc index 6d4bf2f..3aac636 100644 --- a/docs/bridge-status.adoc +++ b/docs/bridge-status.adoc @@ -32,16 +32,12 @@ but broader ecosystem mapping remains incomplete. === 4. Buchholz / Veblen Ordinals -* *Status:* PARTIAL (11/13 constructors closed under WfCNF; 1 in flight) +* *Status:* MOVED (2026-10-20) to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +(echo-types#349). Status, blockers and open problems are tracked there. * *Dependencies:* Standard Agda -* *Blockers:* `+<ᵇ-+1+` joint-bplus is the single remaining open -constructor. The head-Ω domination route (option A) has its abstraction -+ per-marker dominances at both branches + the option-(b) head-Ω -inversion lemmas all landed across 2026-05-27 (PRs #124 / #130 / #131); -only the WfCNF-carrier structural recursion (Slice 2-bplus) remains. The -earlier shared-binder-self-lift blocker is resolved (`+RankAdm+` + -`+RankLex+` slices, 2026-05-26/27). Live tracker: -`+docs/echo-types/buchholz-rank-obstruction.adoc+`. +* *Still here:* the `+EchoOrdinal+` bridge and its two imports +(`+Ordinal.OmegaMarkers+`, `+Ordinal.Buchholz.Syntax+`). * *Core Affect:* NO === 5. JanusKey / Categorical diff --git a/docs/bridges/buchholz-extended-wf.adoc b/docs/bridges/buchholz-extended-wf.adoc index 76c377f..16219db 100644 --- a/docs/bridges/buchholz-extended-wf.adoc +++ b/docs/bridges/buchholz-extended-wf.adoc @@ -1,5 +1,15 @@ == Buchholz `+_<ᵇ⁺_+`: well-foundedness gap +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + `+Ordinal.Buchholz.OrderExtended._<ᵇ⁺_+` adds two shared-binder lex constructors on top of `+Ordinal.Buchholz.Order._<ᵇ_+`: diff --git a/docs/bridges/buchholz-plan.adoc b/docs/bridges/buchholz-plan.adoc index dd267b4..496423a 100644 --- a/docs/bridges/buchholz-plan.adoc +++ b/docs/bridges/buchholz-plan.adoc @@ -6,6 +6,16 @@ :sectnums: :sectnumlevels: 2 +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + [CAUTION] ==== *Historical spec.* This document is the original phased plan for the diff --git a/docs/bridges/buchholz-rank-obstruction.adoc b/docs/bridges/buchholz-rank-obstruction.adoc index 4b7adb4..1086ee1 100644 --- a/docs/bridges/buchholz-rank-obstruction.adoc +++ b/docs/bridges/buchholz-rank-obstruction.adoc @@ -3,6 +3,16 @@ :date: 2026-05-20 :toc: +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + This note records why the natural rank-embedding route to unbudgeted `WellFounded _<ᵇʳᶠ_` (and to `WellFounded _<ᵇ⁺_`) is *structurally impossible* for the `Ordinal.Buchholz.Order._<ᵇ_` relation as diff --git a/docs/echo-types/MAP.adoc b/docs/echo-types/MAP.adoc index f4fe625..6d3493f 100644 --- a/docs/echo-types/MAP.adoc +++ b/docs/echo-types/MAP.adoc @@ -381,59 +381,21 @@ the standing B- freeze lifted because O-THERMO-∞ is now discharged `docs/adjacency/hott-fibers.adoc`. * Build: `just test-thermo`. -=== Buchholz / Veblen ordinals — higher-order number systems `[REAL]` -Staged Buchholz-style collapsing in `--safe --without-K`. - -* Proofs: `proofs/agda/Ordinal/` (`Buchholz/`, `Brouwer`, `CNF`, - `Closure`, `Psi…`, `ExtendedOrder`, `RankPow`, `RankAdm`, - `RankLex`, `HeadOmega`, `HeadOmegaInversion`, `RankPowDomination`, - `RankPowSlice3` (2026-05-28 — `NonBzero` + strict-jump bridge + - head-Ω lower bound), `RankPowSlice3Headline` (2026-05-28 — Slice 3 - headline `rank-mono-<ᵇ-+1-via-head-Ω` closed under a strict-head - premise; umbrella case-split bumps `bpsi=bpsi at equal markers` - to rank-adm / rank-lex)), `RankLexJointBplus` (2026-05-28 PR #147 - — parallel rank with `leftmost-α` discriminator for the bpsi-source- - at-equality joint-bplus sub-case; second-component strict-mono at - equal first components scaffolded; (a)+(b)+(c) assembly - completed 2026-05-30 via PRs #165 (b lex-first primitive) + #166 - (c `BplusFirstTri` trichotomy + `first-eq-from-bpsi-source-at- - equal-head` consumer-side derivation)), `RankMonoUmbrellaSlice4` - (2026-05-28 PR #149 — narrowed `_<ᵇ⁻ⁿ_` umbrella record bundling - WfCNF endpoints + `_<ᵇ¹_` derivation; covers all 10 inherited - `_<ᵇ⁰_` cases + the strict-head joint-bplus; two shortfalls - (`<ᵇ-ψΩ≤` boundary; `<ᵇ-+1` at equal-head) pinned as `⊤`-aliases - with explicit lex-rank / rank-lex-jb pointers), - `RankMonoSameLeft` (2026-05-30 PR #167 — Path-3 prototype - source-rule enrichment via `<ᵇ⁺²-same-left`; one-line closure via - `rank-pow-bplus-right-mono`), `RankMonoUnion` (2026-05-30 PR #168 - — architectural realisation: union umbrella - `_<ᵇᵘ_ = _<ᵇ¹_ ⊎ _<ᵇ⁺²_` via Sum + `[_,_]` mediator; per-extension - proof work + structural composition; extension recipe in preamble), - `RankMonoUnionWfCNF` (2026-05-30 PR #169 — WfCNF wrap `_<ᵇᵘⁿ_` - bundling canonical-form invariant alongside the union; mirrors - Slice 4's pattern, propagates automatically through new - extensions), `RankMonoUnionWF` (2026-05-30 PR #170 — Gate 2 - closure: `WellFounded _<ᵇᵘ_` via `Subrelation.wellFounded` + - `On.wellFounded` rank-embedding transport from `wf-<′`). -* Fidelity climb (2026-06-15 → 18): `Ordinal.Buchholz.BHTarget` (the - BH order-type target structure + its well-foundedness CONSTRUCTED - for real from the Brouwer order `Ord`/`_<′_`/`wf-<′`; zero - postulates; reduces the `Fidelity.agda` trust boundary from three - postulates to two), and `Ordinal.Brouwer.OrdinalExp` (ordinal - exponentiation `ω^^_ : Ord → Ord` + the first ε-number `ε₀`; rung 1 - of the target-side climb). Order-type fidelity (ψ₀(Ω_ω)) itself - remains OPEN (`D-2026-06-14`) — these shrink the trust boundary and - start the climb; ε₀ ≪ ψ₀(Ω_ω). -* Docs: `docs/buchholz-plan.adoc`, - `docs/echo-types/buchholz-extended-wf.md`, - `docs/echo-types/buchholz-rank-obstruction.adoc` (per-constructor - verdict table — see ledger for live count). -* Direct-constructor `_<ᵇ_` same-binder cases (Buchholz item B): - status tracked solely in the earn-back ledger - (`docs/echo-types/earn-back-plan.adoc`, row B) and - `docs/retractions.adoc` (F-2026-05-18b) — off the paper critical - path. (Reference-only by design: no status is snapshotted here, so - this line never drifts as the ledger moves.) +=== Buchholz / Veblen ordinals — moved to ordinal-notation +The ordinal lane left echo-types on 2026-10-20 (echo-types#349, decision +`D-2026-06-21`). Its proofs, design documents and open problems, including +order-type fidelity to ψ₀(Ω_ω) and the two `Fidelity.agda` postulates, now +live in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation]. + +* Still here: `proofs/agda/EchoOrdinal.agda` (the echo-to-ordinal bridge, + `ordinal-collapse-non-injective`) and the two modules it imports, + `proofs/agda/Ordinal/OmegaMarkers.agda` and + `proofs/agda/Ordinal/Buchholz/Syntax.agda`. +* The design documents (`docs/bridges/buchholz-*.adoc`, + `docs/echo-types/buchholz-rank-obstruction.adoc` and the two ordinal + decision records) are kept here as frozen copies, each marked as moved. + The maintained copies are in ordinal-notation. === Characteristic / EI — epistemic, choreographic, roles `[REAL]` The echo-invariant line: epistemic structure, choreographies, roles. diff --git a/docs/echo-types/buchholz-rank-obstruction.adoc b/docs/echo-types/buchholz-rank-obstruction.adoc index d1f399d..089b104 100644 --- a/docs/echo-types/buchholz-rank-obstruction.adoc +++ b/docs/echo-types/buchholz-rank-obstruction.adoc @@ -3,6 +3,16 @@ :date: 2026-05-20 :toc: +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + This note records why the natural rank-embedding route to unbudgeted `WellFounded _<ᵇʳᶠ_` (and to `WellFounded _<ᵇ⁺_`) is *structurally impossible* for the `Ordinal.Buchholz.Order._<ᵇ_` relation as diff --git a/docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc b/docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc index 27a3909..f0a6ba2 100644 --- a/docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc +++ b/docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc @@ -7,6 +7,16 @@ :sectnumlevels: 2 :icons: font +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + [.lead] Records the remaining ordinal-track frontier in the same dated idiom as the retraction log's `R-2026-05-18`, so it is findable in the diff --git a/docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc b/docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc index bbd1009..d6da988 100644 --- a/docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc +++ b/docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc @@ -7,6 +7,16 @@ :sectnumlevels: 2 :icons: font +[IMPORTANT] +==== +*Moved.* This document moved to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] +with the ordinal lane on 2026-10-20 (echo-types#349). The copy maintained there +is the live one. This copy is frozen as of echo-types `703dd77`, and the +`proofs/agda/Ordinal/…` paths it names, other than `OmegaMarkers` and +`Buchholz/Syntax`, no longer exist in this repository. +==== + [.lead] Records, in the same dated idiom as `D-2026-06-14` (its parent) and the retraction log's `R-2026-05-18`, the decision to *park* the transfinite diff --git a/docs/echo-types/echo-kernel-note.adoc b/docs/echo-types/echo-kernel-note.adoc index bb37e71..57011c9 100644 --- a/docs/echo-types/echo-kernel-note.adoc +++ b/docs/echo-types/echo-kernel-note.adoc @@ -231,9 +231,11 @@ kernel** — the boundary is real and lives outside this core. discoverability. Not kernel (the kernel remains exactly `Echo`). |=== -`EchoOrdinal` is Tier-1 off `Echo` but additionally pulls the -`Ordinal/` subtree; it belongs to the Buchholz/Veblen Direction in -the MAP, not the foundation kernel. +`EchoOrdinal` is Tier-1 off `Echo` but additionally pulls two +`Ordinal/` leaves (`Ordinal.OmegaMarkers`, `Ordinal.Buchholz.Syntax`); +it is the echo-to-ordinal bridge, not the foundation kernel. The rest +of the ordinal lane moved to `hyperpolymath/ordinal-notation` on +2026-10-20. == Maintenance diff --git a/docs/echo-types/paper.adoc b/docs/echo-types/paper.adoc index a93884d..0a03fa5 100644 --- a/docs/echo-types/paper.adoc +++ b/docs/echo-types/paper.adoc @@ -1395,6 +1395,11 @@ instance. External validation is the remaining step. [#ordinal-appendix] == Ordinal / Buchholz consumer-evidence +NOTE: Since 2026-10-20 the modules this appendix cites live in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], not in echo-types (echo-types#349). Only the `EchoOrdinal` bridge stays +here. The appendix text is unchanged; module names are the same in both +repositories. + *Status: written at the well-foundedness milestone; order-type fidelity OPEN (decision-log `D-2026-06-14`, `docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc`).* diff --git a/docs/echo-types/what-echo-is.adoc b/docs/echo-types/what-echo-is.adoc index 49eb51c..19815dd 100644 --- a/docs/echo-types/what-echo-is.adoc +++ b/docs/echo-types/what-echo-is.adoc @@ -168,7 +168,9 @@ negatively, EI-2.) `echo-additive/` modules are absent from `All.agda`). Treat the variance result as a real-but-unwired artefact, exactly as `AFFIRMATION.adoc` records it. * *Bachmann–Howard order-type fidelity is POSTULATED*, in - `Ordinal/Buchholz/Fidelity.agda`, *outside* the `--safe` kernel cone. The + `Ordinal/Buchholz/Fidelity.agda`, *outside* the `--safe` kernel cone. (Since + 2026-10-20 that file and the whole ordinal tower live in + https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], not here.) The ordinal-notation tower's sound-carrier well-foundedness is proved and in the closure; the bridge from that notation to the Bachmann–Howard ordinal is an explicit, auditable trust boundary, not a closed theorem. "Mechanized diff --git a/docs/proof-debt.adoc b/docs/proof-debt.adoc index 1b01971..f136d1d 100644 --- a/docs/proof-debt.adoc +++ b/docs/proof-debt.adoc @@ -19,7 +19,11 @@ closing by the cubical endpoint rule), then re-proves `+prop-factor-left-mere-surjective+` (epi). This realises the axiom the `+--without-K+` demo under (c) only assumes — see (c). * *Bachmann–Howard target structure (`+BHNotation+` + its -well-foundedness)* — discharged 2026-06-15 in the `+--safe --without-K+` +well-foundedness)* — *moved out of this repository* (2026-10-20, +echo-types#349) to +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], +where it is still discharged. The record below is historical; the paths +it names no longer exist here. Originally discharged 2026-06-15 in the `+--safe --without-K+` kernel by `+proofs/agda/Ordinal/Buchholz/BHTarget.agda+` (zero postulates; wired into `+All.agda+`, pinned in `+Ordinal/Buchholz/Smoke.agda+`). The abstract `+BHNotation+` interface @@ -65,46 +69,17 @@ because `+∥_∥+` cannot be built WITHIN `+--safe --without-K+` itself. === (d) DEBT — actively to be closed -* `+proofs/agda/Ordinal/Buchholz/Fidelity.agda+` — *two* top-level -`+postulate+`s (reduced from three on 2026-06-15; see (a)) forming the -trust boundary of the *order-type fidelity scaffold* (open problem -`+D-2026-06-14+`, -`+docs/echo-types/decisions/ordinal-bh-order-type-fidelity-open.adoc+`): -** `+denotation+` — assumed faithful, height-preserving order-embedding -`+⟦·⟧ : BT → 𝒪+` into the (now-real) Brouwer target (the missing object; -*not* `+rank2+`, which deliberately collapses heights and is a -termination measure only). -** `+ordinal-upper-bound+` — the `+⟦·⟧+`-level upper half of the -sandwich (downstream of `+denotation+`). -** *Discharged (2026-06-15)*: the former `+bh-notation+` postulate (an -opaque whole BH structure) is gone — the `+BHNotation+` interface and a -real `+bh-notation-from+` instance now live in the `+--safe+` kernel -module `+Ordinal.Buchholz.BHTarget+`, so the target order and its -well-foundedness (Brouwer `+_<′_+` / `+wf-<′+`) are proved, not assumed. -The candidate BH height is an explicit parameter to -`+Fidelity.AtHeight+`, not a postulate. See (a). -** *Classification*: DEBT, to be discharged when order-type fidelity is -proved — these are _not_ permanently-accepted axioms. Each is annotated -inline with an `+AXIOM:+` leading comment. -** *Justification / scope*: the module is quarantined — `+--without-K+` -only, NOT imported by `+All.agda+` / `+Smoke.agda+` — so the `+--safe+` -kernel cone depends on neither postulate. Nothing in the module asserts -that order type ψ₀(Ω_ω) is _proven_; the status surfaces (appendix, -decision log, roadmap) read "`written at WF milestone; order-type -fidelity OPEN`". -** *Citation*: `+D-2026-06-14+`; full per-postulate spec (statement / -what closes it / owner) in `+Fidelity-OPEN-postulates.md+`. -** *PARKED (2026-06-20, `+D-2026-06-20+`)*: the transfinite ladder these -postulates sit atop is now _consumer-less_ — the Groove cleave (the only -consumer of ψ₀(Ω_ω) order-type fidelity) is resolved as a finite -exact-round-trip zipper needing well-foundedness only, and RC-11 forbids -ε₀+ in cleave ranks. The debt is therefore _parked, resumable_, not -actively being closed. No postulate closed; `+D-2026-06-14+` stands. See -`+docs/echo-types/decisions/ordinal-fidelity-ladder-parked.adoc+`. -** *Guardrail status*: allow-listed in `+tools/check-guardrails.sh+` -(`+EXPLORATORY_EXEMPT+`) and the inline `+hypatia: allow+` pragma at the -module head. (`+BHTarget+` is NOT exempt — it is real kernel content and -passes the guardrail.) +* (none in this repository) + +*Moved (2026-10-20, echo-types#349).* The order-type fidelity scaffold +`+Ordinal/Buchholz/Fidelity.agda+` and its two postulates +(`+denotation+`, `+ordinal-upper-bound+`) left echo-types with the rest of +the ordinal lane (`+D-2026-06-21+`). They now live in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation], +quarantined in its proof MANIFEST and tracked in its +`+Fidelity-OPEN-postulates.adoc+`. Order-type fidelity to ψ₀(Ω_ω) +remains OPEN there (`+D-2026-06-14+` stands). echo-types now carries +exactly *one* quarantined postulate block, under (c). === Notes @@ -131,6 +106,8 @@ often-cited "`676 files / 52k lines`" headline is inflated by `+.claude/worktrees/+` duplicate snapshots; real source ≈ 190 `+.agda+` files / ~36k lines. * *The quarantined postulates are correctly _outside_ the wired cone.* +(Audit-time state. Since 2026-10-20 the `+Fidelity.agda+` file is no +longer in this repository; see (d).) The audit independently confirms the two postulate-bearing files this ledger already lists — `+EchoImageFactorizationPropPostulated.agda+` (c) and `+Ordinal/Buchholz/Fidelity.agda+` (d) — are guardrail-exempt, diff --git a/docs/proof-obligations.adoc b/docs/proof-obligations.adoc index fb33f81..b0fba5f 100644 --- a/docs/proof-obligations.adoc +++ b/docs/proof-obligations.adoc @@ -26,5 +26,5 @@ natively constructible. See `+docs/retracted/retractions.adoc+`) * *CNO Bridge (Absolute Zero):* PARTIAL * *JanusKey Integration:* PARTIAL * *Tropical Semantics (Argmin residues):* PARTIAL -* *Buchholz/Veblen Ordinal Representation:* BLOCKED (Well-foundedness of -shared-binder cases blocked on self-lift) +* *Buchholz/Veblen Ordinal Representation:* MOVED (2026-10-20) to +`hyperpolymath/ordinal-notation`; its obligations are tracked there diff --git a/roadmap.adoc b/roadmap.adoc index 4a3f14f..6d08339 100644 --- a/roadmap.adoc +++ b/roadmap.adoc @@ -158,8 +158,9 @@ DOI mint, library packaging, outreach — which is author-driven notation primer) cleared 2026-05-20 via PR #73; tag 3 (evaluation — proof-size / cost table, common-upper-bound idiom) cleared in PR #84 (§"Evaluation and discussion"). Tag 4 (ordinal - consumer-evidence appendix) is gated on the Lane 3 Buchholz - milestone and is not load-bearing for Lane 1 — see paper status + consumer-evidence appendix) is gated on the Buchholz milestone, + which now belongs to hyperpolymath/ordinal-notation, and is not + load-bearing for Lane 1 — see paper status banner. . *LANDED 2026-05-26.* `proofs/agda/EchoAbstractionBarrier.agda` ships the consumer-side free theorem at the affine instance @@ -305,7 +306,16 @@ narrowed — no unique-mediator claim. Demand 4 ("parametricity") must be *consumer-side at the affine instance*, not full Reynolds. See respective §s in the synthesis doc. -=== Lane 3 [RETIRED FROM ECHO-TYPES 2026-06-21 — outgrew the project] — Ordinal / Buchholz +=== Lane 3 [MOVED 2026-10-20 to hyperpolymath/ordinal-notation] — Ordinal / Buchholz + +*MOVED (2026-10-20, echo-types#349).* The extraction decided in +`D-2026-06-21` is done. The ordinal lane, its design documents and its two +open `Fidelity.agda` postulates now live in +https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation]. +echo-types keeps only the `EchoOrdinal` bridge and its two imports +(`Ordinal.OmegaMarkers`, `Ordinal.Buchholz.Syntax`). The rest of this +section is the record as of the retirement; module paths it names are no +longer in this repository. *RETIRED FROM ECHO-TYPES (`D-2026-06-21`, escalating the `D-2026-06-20` PARK).* The transfinite ordinal-fidelity ladder has *outgrown the diff --git a/wiki/Architecture.adoc b/wiki/Architecture.adoc index 00df191..2eac303 100644 --- a/wiki/Architecture.adoc +++ b/wiki/Architecture.adoc @@ -55,7 +55,11 @@ The Σ-algebra of echoes under function composition. Docs: `docs/echo-types/{composition,fibration-package,universal-property}.adoc`. -== Track 2 — Ordinal (RETIRED from echo-types, owner decision D-2026-06-21) +== Track 2 — Ordinal (MOVED to ordinal-notation, 2026-10-20) + +*Moved.* Since 2026-10-20 (echo-types#349) the lane lives in https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation]. What +follows is the record at the retirement; only the `EchoOrdinal` bridge and its +two imports remain under `proofs/agda/`. A Buchholz collapsing layer; the consumer-evidence that echo's non-injectivity bridges to ordinal-collapsing non-injectivity. diff --git a/wiki/Home.adoc b/wiki/Home.adoc index fc7a8a0..5099baa 100644 --- a/wiki/Home.adoc +++ b/wiki/Home.adoc @@ -131,10 +131,10 @@ This wiki is a *distillation*. The authoritative records are: (`aggregation-as-fold`; #175), with `no-canonical-disaggregation` (the Sonnenschein–Mantel–Debreu / representative-agent critique, stated type-theoretically). -* *Ordinal track* — *RETIRED from echo-types* (owner decision `D-2026-06-21`): - the transfinite Buchholz/Veblen ladder outgrew the project. The landed - artifact is correct and stays; the disposition is *extraction to its own - ordinal-notation repo* (the physical cut is the owner's; tracking: #263). +* *Ordinal track* — *MOVED* to https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] on 2026-10-20 (echo-types#349), + carrying out owner decision `D-2026-06-21`: the transfinite Buchholz/Veblen + ladder outgrew the project. Only the `EchoOrdinal` bridge and its two + imports stay here. See <>. * *Deniability track* — `EchoDeniability.agda` landed: perfect/partial duality, `IsConstantOpener` boundary, no-section / section duality as a checked theorem pair. diff --git a/wiki/Roadmap.adoc b/wiki/Roadmap.adoc index 7df31cc..4644183 100644 --- a/wiki/Roadmap.adoc +++ b/wiki/Roadmap.adoc @@ -56,7 +56,10 @@ landed and packaged as `_↔_`. No open headline items; further work is consolidation / doc-threading. [#ordinal] -=== Ordinal track — RETIRED from echo-types (owner decision D-2026-06-21) +=== Ordinal track — MOVED to ordinal-notation (2026-10-20) + +*Moved.* The extraction decided in `D-2026-06-21` is done: the lane now lives +in https://github.com/hyperpolymath/ordinal-notation[hyperpolymath/ordinal-notation] (echo-types#349). What follows is the record at the retirement. The transfinite Buchholz/Veblen ascent *outgrew echo-types* and is *no longer echo-types work*. The landed artifact is correct (`--safe --without-K`, zero From 2d6afddc6e9e458f73a22ad95298ec3774674d3d Mon Sep 17 00:00:00 2001 From: Claude Date: Mon, 26 Oct 2026 18:05:54 +0000 Subject: [PATCH 2/2] docs: date the wiki status block; mark the frozen plan's pointers as at-extraction Two inconsistencies introduced by the previous commit, found in review: - wiki/Home.adoc: the status block was still dated 2026-06-21 but now records the 2026-10-20 move. Re-date it, and point the establishment bullet's open fidelity problem at ordinal-notation. - docs/bridges/buchholz-plan.adoc is a frozen copy, so its "Live" pointers are now wrong. Relabel them as the state at extraction. Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_01MF5GeeBBDF6sUzr6pZTjWV --- docs/bridges/buchholz-plan.adoc | 4 ++-- wiki/Home.adoc | 8 ++++---- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/bridges/buchholz-plan.adoc b/docs/bridges/buchholz-plan.adoc index 496423a..28914d1 100644 --- a/docs/bridges/buchholz-plan.adoc +++ b/docs/bridges/buchholz-plan.adoc @@ -24,8 +24,8 @@ were ahead of us. The "PLANNED" tags below are dated; many phases have since landed under different module names (E1–E7 closed; the WfCNF restriction + `RankPow` / `RankAdm` / `RankLex` slices replace the generic `Phase 2.2 rank-mono`; the WF-0/WF-1 well-foundedness is in -`Ordinal.Buchholz.WellFounded`). *Live per-constructor verdict*: -`docs/echo-types/buchholz-rank-obstruction.adoc`. *Live lane status*: +`Ordinal.Buchholz.WellFounded`). *Per-constructor verdict at extraction*: +`docs/echo-types/buchholz-rank-obstruction.adoc`. *Lane status at extraction*: `roadmap.adoc` § Lane 3. *Per-session ledger*: `CLAUDE.md` § "Current rung state". This file is retained for provenance and design context; treat its concrete "PLANNED" items as superseded. diff --git a/wiki/Home.adoc b/wiki/Home.adoc index 5099baa..6fecb50 100644 --- a/wiki/Home.adoc +++ b/wiki/Home.adoc @@ -115,14 +115,14 @@ This wiki is a *distillation*. The authoritative records are: * `.machine_readable/6a2/STATE.a2ml` — EI-2 record (permanent) + current-state block. * `docs/bridges/cross-repo-bridge-status.md` — cross-repo bridge ledger. -== One-line status (as of 2026-06-21) +== One-line status (as of 2026-10-26) * *Composition track* — landed (Echo-comp-iso, cancel-iso, pentagon). No open headline items. * *Establishment track* — Pillars A–D and F (F1–F4) closed; the in-repo half of - Pillar E is complete at the bounded-claim level. One named *OPEN external* - problem remains: *order-type fidelity* to ψ₀(Ω_ω) (decision-log - `D-2026-06-14`). + Pillar E is complete at the bounded-claim level. The one named *OPEN + external* problem, *order-type fidelity* to ψ₀(Ω_ω) (decision-log + `D-2026-06-14`), moved with the ordinal lane to ordinal-notation (below). * *Variance* — resolved (`EchoVariance.agda`, #243): an echo is a graded *monad of accumulation* with a section/retraction adjunction exact on the grade-0 fibre — *not* a graded comonad (that reading is the lossless