E5: make ν operational and add Buchholz example/smoke modules - #6
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May 20, 2026
…#70) ## Summary Extends `proofs/agda/EchoApprox.agda` with the first slice of the axis-2 composition rung from the design note (drafted in `/tmp/echo-types-exploration/axis2-approximate.md`, §7 obligations 2 + 6, plus the canonical-split retract direction). Refs `docs/echo-types/roadmap.md` Axis 2 entry and `docs/echo-types/composition.md` §Q3 — does **not** close either. ## Obligations landed - **`echo-strict→approx`** (§7 #2). General strict ⇒ zero-tolerance approximate. Generalises `echo-approx-intro` from own-fibre points to arbitrary `y` via the codomain equation `p : f x ≡ y`. One extra `subst` along `p`. - **`echo-approx-comp-sound`** (§7 #6). Sound RHS-to-LHS direction of the retract shape from `composition.md` §Q3 / design-note §5. Unpacks the existential and calls `echo-approx-compose`. - **`echo-approx-comp-retract-to`**. Canonical-split LHS → RHS-Σ section of the retract: picks `b := f x`, `ε₁ := zero`, `ε₂ := ε`. Uses `echo-approx-intro` for the inner echo, original bound for the outer. - **`echo-approx-comp-retract-A`**. A-component round-trip `proj₁ ∘ sound ∘ retract-to ≡ proj₁`, proved by `refl`. The retraction direction holds definitionally on the A-component as the design note (§5) predicts. ## Obligations deferred (out of this rung) - §7 #7 separated zero-collapse — needs a separation predicate on the `PseudoMetric` record. - §7 #8 axis-1 shadow agreement — cross-axis classification. - Full retract B-component and tolerance-budget round-trip — needs a `+`-left-identity axiom on `Tolerance` (`zero + ε ≡ ε`) not in the current record. Adding it commits the carrier to a left-unital monoid; deferred as a separate decision. - Lipschitz generalisation (`L_g ≠ 1`) — needs scalar multiplication on `Tol`. ## Docs updated - `docs/echo-types/composition.md` §Q3 promoted from "entirely speculative" to landed-retract-shape with deferred items called out. - `docs/echo-types/roadmap.md` adds a "landed" entry for the composition rung first slice. ## Invariants preserved - `--safe --without-K` - No postulates - No escape pragmas - Funext untouched ## Test plan - [x] `LC_ALL=C.UTF-8 agda -i proofs/agda proofs/agda/All.agda` exits 0 - [x] `LC_ALL=C.UTF-8 agda -i proofs/agda proofs/agda/Smoke.agda` exits 0 - [x] No new `postulate`, no escape pragmas, funext not imported - [x] `Smoke.agda` already pins `module Approx` following project convention (per-lemma pins inside parameterised modules require instantiation, which the project does not do for `EchoApprox`). Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
hyperpolymath pushed a commit
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May 27, 2026
Two artefacts I'd flagged as "no touch needed" on first audit actually did need touching once I re-read them: * `docs/bridge-status.md` row #4 (Buchholz / Veblen Ordinals) said "BLOCKED — Well-foundedness of shared-binder cases is blocked by the failure of the self-lift." That blocker is resolved (`RankAdm` + `RankLex`, 2026-05-26/27). Updated to "PARTIAL (11/13 constructors closed under WfCNF; 1 in flight)" with the head-Ω-route landings named and a pointer to the live tracker. * `docs/bridge-status.md` gains row #6 for the decoration bridge as a conceptual (not cross-repo) entry — the doc's stated scope is "experimental extensions and bridges between the minimal core of Echo Types and other domains", which the decoration bridge fits even though it has no adjacent-repo side. * `docs/bridges/buchholz-plan.adoc` is the original phased spec from when E1–E7 were ahead of us. Its "PLANNED" tags for Phase 2.2 rank-mono etc. are now dated; many of those phases landed under different module names. Added a CAUTION banner at the top of the document pointing to the live tracker (`buchholz-rank-obstruction.adoc`), the live lane status (`roadmap.adoc` § Lane 3), and the per-session ledger (`CLAUDE.md`). The body is left intact for provenance — it's still the cleanest single source of the original design context. `scripts/kernel-guard.sh`: PASS. No Agda modules touched. https://claude.ai/code/session_013nLEeKZXpvHnrDZMgRm19S
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hyperpolymath added a commit
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May 27, 2026
…edger reinforcement (#131) Six commits closing out the Lane 3 head-Ω route's Slice 2 family: 1. CLAUDE.md session-arc entry for Slice 2 (PR #130's rung). 2. New module Ordinal.Buchholz.HeadOmegaInversion with option-(b) head-Ω inversion lemmas — no rank-mono dependency. 3. Slice 2-omega: ω branch of ω-rank-pow-succ replaced with a strictly-larger shape; per-marker dominance proved at both branches; unified ω-rank-pow-<-succ lemma added. 4. CLAUDE.md next-Claude plan updated. 5. Cross-doc consistency sweep across buchholz-rank-obstruction, roadmap § Lane 3, EXPLAINME, CHANGELOG, MAP. 6. Deeper-sweep gaps closed: bridge-status row #4 refreshed + new row #6 for decoration bridge; CAUTION banner on buchholz-plan.adoc pointing to the live tracker. Only Slice 2-bplus (the WfCNF-carrier structural recursion) remains; all prerequisites landed. scripts/kernel-guard.sh PASS. No postulates introduced. --safe --without-K throughout. Admin-merged before CI green at user request.
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