Earn-back: Gates F4 + F2 PASSED (retraction follow-up F-2026-05-18a) by hyperpolymath · Pull Request #50 · hyperpolymath/echo-types

hyperpolymath · 2026-05-18T01:12:37Z

Stacked on #49 (proof-debt ledger) → #47 (corrective reframe). Two Pillar F earn-back gates pass, each strictly to its mechanised strength.

Verified

F4 — proofs/agda/EchoPullbackUnivF4.agda: strict terminal-cone universal property m' ≡ m as a function of an explicit funext module parameter (FunExt₀, never a postulate — the Echo.agda cancel-iso idiom). Funext-free pointwise mediator kept as the corollary. Unconditional claim stays retracted.
F2 — proofs/agda/EchoStepNDModelF2.agda: a genuine second model of the bare Echo functor on EchoRelational.StepND, provably not the graph of any function under any state relabelling (nd-not-graph, checked true ≢ false). Same interface the deterministic model uses (EchoFunctorModel; functor laws via generic map-rel-id/map-rel-comp); agreement has content (StepND fibre = disjoint sum of deterministic branches by constructor case analysis — not refl, not Σ-η on × ⊤).

Both --safe --without-K, zero postulates, wired into All.agda, pinned in Smoke.agda. Full + smoke build green (agda All.agda / Smoke.agda exit 0).

Scope discipline (what is NOT earned back)

F2 is the Echo functor only. The graded-comonad claim (no nested D_r D_s), modality-level model-independence, and the conservativity metatheorem remain fully retracted. Gates F1 (coassoc open) and F3 (gated on F1) remain open. No claim moved beyond its hypothesis license.

Docs

docs/retractions.adoc — append-only follow-up F-2026-05-18a under R-2026-05-18 (entry not edited; policy-compliant).
paper.adoc — §3 NOTE (F4 conditional), §6 NOTE (F2 scoped), conclusion partial-earn-back paragraph.
conservativity.adoc — scope bullet + dated revision-history entry (statement unchanged: still evidence for).
types-abstract.adoc — contributions 2 & 5 scoped addenda (submission-ready status remains withdrawn).
earn-back-plan.adoc — ledger rows A2/A4 → PASSED, Status + recommended-order updated.

🤖 Generated with Claude Code

Adversarial three-reviewer review + a codebase pressure-test found no in-repo defense for five central claims; two were contradicted by the repo's own Gate-2 audit. This commit corrects the PROSE downward to what the Agda actually establishes. No proof is weakened — Agda is unchanged except for line-comment retraction banners; full build (All.agda then Smoke.agda) still exits 0 under --safe --without-K. Retracted -> replaced: - "graded comonad" -> loss-graded reindexing modality (thin-poset action; no nested D_r D_s) - "terminal-cone universal property" -> funext-relative pointwise mediator - "two independent models / model-independence" -> carrier-parametricity, fixed grade poset - "conservativity metatheorem discharged by the build" -> postulate-free build = evidence, not proof - "funext quarantined" -> no funext anywhere; pointwise mediator IS the real funext boundary - docs/retractions.adoc: created (canonical log roadmap-gates.adoc referenced but never existed); entry R-2026-05-18. - docs/echo-types/earn-back-plan.adoc: created; Pillar F gated program to convert retractions back into theorems (F1 make-or-break). - paper/conservativity/types-abstract/establishment-plan: reframed; "submission-ready" status withdrawn from the abstract. - Smoke.agda + 7 modules: top retraction banners (comments only). - ECHO-CNO-BRIDGE.adoc: scope note (its distinct, valid "model independence" is NOT retracted; disambiguated, not over-applied). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

The .envrc declared `use flake` but no flake.nix existed, so direnv failed. Add a devShell pinned to nixpkgs nixos-24.11: - rustc 1.82.0 + cabal-install 3.12.1.0 (exact .tool-versions match), agda 2.7.0.1, ghc 9.6.6, just 1.38.0 - Agda libraries: standard-library (nixpkgs, reproducible) + absolute-zero (local ~/dev/repos checkout; no usable upstream pkg), wired via a generated AGDA_DIR/libraries in the shellHook - .gitignore: ignore the generated .agda/ dir Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

…05-18) Full-repo proof-debt audit. Confirmed zero postulates / zero escape pragmas across all 88 modules — no hidden debt. Catalogues every disclosed/structural debt as a single index (items A–E2): Pillar F gates F1–F4; the Buchholz direct-order structural-fidelity gap; the characteristic/ open obligations (EI-2 unaffected); the dangling roadmap-gates.adoc canonical-pointer drift; Transport.agda's two symbolic-ℚ open items + the corrected MEMORY.md index line. Records a recommended order of attack. Moves no claim; reframed docs stay as they are until their gate is green (per Guardrails). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

… positive, coassoc open) (#48) **Draft / checkpoint — do not merge.** Stacked on #47 (depends on the earn-back plan it introduces). ## Finding First execution of Gate F1 (`docs/echo-types/earn-back-plan.adoc`) — the make-or-break gate for earning back the retracted "graded comonad" claim. `proofs/agda/EchoGradedComonadF1.agda` typechecks `--safe --without-K`, **zero postulates** (verified). **Decisive result: no foundational obstruction.** Agda demanded no K, no funext, no postulate. The monoid-graded iterated-residue candidate delivers, mechanised: - non-collapsing graded functor `D r` (separating witness `D2-nontrivial` — not ⊤) - functor laws - **nested** `δ : D (m+n) A → D m (D n A)` (the structure the retracted dev never had) - counit-right ✅ ; counit-left ✅ (only non-structural tool: ℕ-UIP, K-free) ## Open (F1 NOT passed) `gc-coassoc` — base + skeleton close; inductive step has an isolated proof-engineering type-mismatch needing an explicit δ-naturality-over-`R` lemma. Stated in-file as a precise OPEN obligation: **not postulated, not softened, not wired into `All.agda`/`Smoke.agda`**. Per the plan guardrail (close-but-not-closed = failed-and-logged), **no reframed claim moves** until F1 fully passes. This PR preserves the feasibility finding only. 🤖 Generated with [Claude Code](https://claude.com/claude-code) --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

…ngelog Both sides are sequential 2026-05-18 == Status bullets; kept both in chronological order (ledger added → F1 feasibility spike run). No claim or gate moved; nothing retracted reinstated (verified per R-2026-05-18). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

…/F4 independent Resolves an internal contradiction: the Gate F1 header said "everything else is gated on F1; other gates not attempted until F1 passes", but the gate descriptions (F2 line 101, F4 lines 157-159) and "Recommended order of attack" (F4+F2 in parallel, first) state F2/F4 are independent of F1. Header now matches the rest of the doc. Doc-only; moves no claim; the retraction posture (claims stay retracted until a gate passes) is unchanged. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

F4 — EchoPullbackUnivF4.agda: strict terminal-cone universal property m' ≡ m as a function of an EXPLICIT funext module parameter (FunExt₀, never a postulate — the cancel-iso idiom). Pointwise mediator kept as the funext-free corollary. Unconditional claim stays retracted. F2 — EchoStepNDModelF2.agda: a genuine second model of the BARE Echo functor on EchoRelational.StepND, a relation provably not the graph of any function under any state relabelling (nd-not-graph: checked true≢false). Same interface the deterministic model uses (EchoFunctorModel; functor laws by generic map-rel-id/map-rel-comp); agreement has content (StepND fibre = disjoint sum of deterministic branches by constructor case analysis; not refl, not Σ-η on ×⊤). Scope: the Echo functor only — graded-comonad / modality-level model-independence / conservativity remain fully retracted. Both --safe --without-K, ZERO postulates; wired into All.agda, pinned in Smoke.agda; full + smoke build green. Scoped claims moved in paper.adoc (§3 NOTE, §6 NOTE, conclusion), conservativity.adoc (scope + revision history), types-abstract.adoc (contributions 2 & 5), earn-back-plan.adoc (ledger A2/A4 + Status); logged append-only as retraction follow-up F-2026-05-18a. F1 (coassoc) and F3 remain open. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

# Conflicts: # docs/echo-types/conservativity.adoc # docs/echo-types/earn-back-plan.adoc # docs/echo-types/paper.adoc # docs/echo-types/types-abstract.adoc # docs/retractions.adoc

github-actions · 2026-05-18T14:06:22Z

🔍 Hypatia Security Scan

Findings: 10 issues detected

Severity	Count
🔴 Critical	0
🟠 High	5
🟡 Medium	5

View findings

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## Summary Earns back the **K-attributed part of proof-debt ledger item B** (Buchholz order). Item B held that the two same-binder sub-cases (`bpsi ν α <ᵇ bpsi ν β` with `α <ᵇ β`; `bplus x y₂ <ᵇ bplus x z₂` with `y₂ <ᵇ z₂`) were *"not constructible pending a K-free reformulation"*. - **Reconfirmed** the obstruction on **Agda 2.8** (the `Order.agda` comment cited 2.6.3): the *naive* `<ᵇ-irrefl` matching `x <ᵇ x` forces the shared-binder deletion `ν =?= ν`, rejected `--without-K`. - **New module** `Ordinal.Buchholz.OrderExtendedDirect` (`_<ᵇᵈ_`) carries **both** same-binder constructors and proves, `--safe --without-K`, **zero postulates / zero escape pragmas**: - `<ᵇ-irrefl` via generalised `<ᵇ⇒≢` (distinct indices) discharged by `cong`-projection injectivity + the K-free **conflict** rule — `refl` is never matched, so the deletion rule is never invoked; - `<ᵇ-trans` (full extended transitivity); - `embed : Order._<ᵇ_ ⇒ _<ᵇᵈ_` — conservativity (faithful strict extension, not a redefinition). - Wired into `All.agda`, pinned in `Smoke.agda`; **full + smoke build green** locally (Agda 2.8, stdlib v2.3). ## Scope (rigorous, not over-claimed) - This is **not** `[CLOSED-NEG]`: the K-free reformulation **did not resist** — it succeeded. - WF of the direct relation is **out of scope**: a termination-checker matter (Routes A/B of `buchholz-extended-wf.md`), orthogonal to K, still delivered via the `ExtendedOrder._<ᵇ⁺_` measure, which stays load-bearing. Trichotomy/totality out of scope. - **No paper / conservativity / abstract claim moves** — item B is off the paper critical path. Logged as retraction follow-up **F-2026-05-18b**; ledger row B / recommended-order / Status updated. ## Notes - **Base:** `earn-back/f4-f2-2026-05-18` (PR #50, unmerged) — the earn-back ledger + `F-2026-05-18a` live there; this work edits those files so it must stack on #50, not `main`. - **MAP.adoc:** not on `main` (introduced by open PR #54). To avoid an add/add duplication, the item-B status line is **not copied**; the exact one-line replacement is recorded in `docs/retractions.adoc` (F-2026-05-18b) as a tracked follow-up to apply in/after #54. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

hyperpolymath and others added 6 commits May 18, 2026 01:13

hyperpolymath mentioned this pull request May 18, 2026

Earn-back: ledger item B (Buchholz) — K-attributed part #57

Merged

hyperpolymath force-pushed the earn-back/f4-f2-2026-05-18 branch from db2cb08 to fb3742d Compare May 18, 2026 08:07

Base automatically changed from roadmap/proof-debt-ledger-2026-05-18 to main May 18, 2026 08:28

Merge remote-tracking branch 'origin/main' into pr50-resolve

36854a8

# Conflicts: # docs/echo-types/conservativity.adoc # docs/echo-types/earn-back-plan.adoc # docs/echo-types/paper.adoc # docs/echo-types/types-abstract.adoc # docs/retractions.adoc

hyperpolymath merged commit 25986ae into main May 18, 2026
8 of 9 checks passed

hyperpolymath deleted the earn-back/f4-f2-2026-05-18 branch May 18, 2026 08:30

hyperpolymath restored the earn-back/f4-f2-2026-05-18 branch May 18, 2026 08:40

hyperpolymath deleted the earn-back/f4-f2-2026-05-18 branch May 18, 2026 08:40

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Earn-back: Gates F4 + F2 PASSED (retraction follow-up F-2026-05-18a)#50

Earn-back: Gates F4 + F2 PASSED (retraction follow-up F-2026-05-18a)#50
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hyperpolymath commented May 18, 2026

Verified

Scope discipline (what is NOT earned back)

Docs

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