docs(machine-readable): update STATE + META for F1/F3/earn-back closure (#93)

## Summary

Brings `.machine_readable/6a2/STATE.a2ml` and `META.a2ml` in line
with the prose docs after this session's Pillar F earn-back closure
and §"Theory work" closing.

## `META.a2ml` — three new ADRs (append-only)

No existing ADR is edited. Three appended after `adr-006`:

* **`adr-007`** — F1 earn-back via monoid-graded iterated-residue
  construction. `EchoGradedComonadF1.agda` at `(ℕ, +, 0)` with
  Echo as grade-unit object, nested δ, all three comonad laws,
  `D2-nontrivial` separating witness. (PR #86 merged 2026-05-20.)
* **`adr-008`** — F3 earn-back via two non-isomorphic-grade-monoid
  instances of an abstract `GradedComonadStructure` interface. No
  `⊑-prop`-equivalent field. `nat-instance` at commutative
  `(ℕ, +, 0)`; `list-instance` at non-commutative `(List Tag, ++, [])`.
  (PR #88 open.)
* **`adr-009`** — Retraction-discipline succeeded: the R-2026-05-18
  reframing converted into four earn-back gate passes (F4, F2, F1,
  F3); one retraction stays retracted (conservativity metatheorem,
  finding 5); none silently re-inflated.

Each ADR carries the strict scope qualifier — F1/F3 earn back claims
**for a separate side-construction**; `EchoGraded` itself remains a
thin-poset reindexing modality per R-2026-05-18, and `paper.adoc` /
`types-abstract.adoc` / `conservativity.adoc` are intentionally not
moved.

## `STATE.a2ml` — `next-actions` pruned + two closure sections appended

**Pruned**: 3 of 5 April `next-actions` were stale and are resolved
in the prose:
* `integration` (apply 7-commit sequence) — done long ago
* `t-3` (Gate-1 falsification test 3) — superseded by Gate 1
  adjacency refresh (`decisions/gate1-adjacency-refresh.adoc`, PR #77)
* `q2-4` (falsifier attempts) — absorbed by `IntegrationAudit.agda`
  EI-2 negative result; remaining attempts are bookkeeping

**Remaining + added**: `q2-1` (echo-not-prop generalisation, still
high), `q2-3` (RoleGraded as N5, still low), new
`owner-gated-paper-update` entry, new `ordinal-track-path-1` entry
(in-flight in other session), and the original `v0-2-recipe-extension`
parked entry.

**Two new closure sections** at the end of STATE.a2ml:

* **`earn-back-summary`** — closure record for all four gates with
  module paths, claim wording, retraction-followup citations, and a
  `forbidden-rebrandings` list to prevent later mis-framing.
* **`theory-work-summary`** — closure record for §"Theory work — no
  proof assistant needed": axes fully mechanised list, ruled-out
  items, refreshed items, canonical examples cluster.

## Test plan

* [x] Pure machine-readable data; no Agda touched
* [x] `agda proofs/agda/All.agda` exit 0
* [x] `agda proofs/agda/Smoke.agda` exit 0
* [x] Append-only ADR discipline preserved (adr-001 through adr-006
      unchanged; new ADRs at the end)
* [x] No retracted claim moved; no earned-back claim overclaimed
* [ ] (owner) confirm a2ml schema validation if you run a validator
      against the standards/state-a2ml + meta-a2ml specs

## Scope

Pure machine-readable data update. Disjoint from all currently-open
PRs (#88 F3, #90 partition-dec, #91 generic-codomain, #92 docs tidy).
`paper.adoc` / `types-abstract.adoc` / `conservativity.adoc` are
intentionally not touched.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: hyperpolymath

.machine_readable/6a2/META.a2ml

@@ -71,6 +71,33 @@
      (context . "User works across two machines: Fedora Kinoite (primary, Nushell) and a Windows machine for travel.")
      (decision . "Build instructions are path-agnostic; line endings normalised via .gitattributes (LF for Agda/AsciiDoc/YAML, .agdai marked binary). Cross-platform considerations apply throughout.")
      (consequences . "Path-agnostic build instructions are required, not optional, for any new tooling.")
+     (supersedes . none))
+
+    (adr-007
+     (title . "F1 earn-back via monoid-graded iterated-residue construction")
+     (status . accepted)
+     (date . "2026-05-20")
+     (context . "R-2026-05-18 retracted the graded-comonad claim about EchoGraded — the structure was a thin-poset reindexing with no nested family, no monoid multiplication, no genuine δ. Pillar F gate F1 (docs/echo-types/earn-back-plan.adoc §F1) asked whether ANY genuine graded comonad with Echo as the grade-unit object could be mechanised under --safe --without-K with zero postulates.")
+     (decision . "The candidate construction passes: proofs/agda/EchoGradedComonadF1.agda ships a monoid-graded iterated-residue comonad at the grade monoid (ℕ, +, 0) with D 0 A = A; D (suc r) A = R (D r A) where R X = X × Bool (an informative residue layer, not ⊤). All three graded-comonad laws (gc-counit-l, gc-counit-r, gc-coassoc) typecheck under --safe --without-K with zero postulates; gc-coassoc closes via the predicted δ-naturality-over-R factoring (δ-suc + subst-D-suc). The separating witness D2-nontrivial certifies D r is not collapsing to ⊤ / a prop.")
+     (consequences . "F1 PASSED; the graded-comonad claim is earned back FOR THIS WITNESS ONLY. EchoGraded itself remains a thin-poset reindexing modality per R-2026-05-18 — F1 enters as an *additional* mechanised contribution beside EchoGraded, not as a reinstatement of it. Paper title and central thesis (Echo as a reindexing modality) stand unchanged. Unblocks F3 (independent second comonad model). Retraction follow-up F-2026-05-20a appended to docs/retractions.adoc.")
+     (supersedes . none))
+
+    (adr-008
+     (title . "F3 earn-back via two non-isomorphic-grade-monoid instances of an abstract interface")
+     (status . accepted)
+     (date . "2026-05-20")
+     (context . "F1 (adr-007) earned back the existence of a graded comonad with Echo as grade-unit object. Gate F3 (docs/echo-types/earn-back-plan.adoc §F3) asked whether the construction is genuinely model-independent — instantiable at non-isomorphic grade monoids without a single hypothesis (no ⊑-prop-equivalent field) baking in the result.")
+     (decision . "EchoGradedComonadInterface.GradedComonadStructure is an abstract record packaging the F1 signature (grade monoid + monoid laws + graded functor + functor laws + counit + nested δ + the three comonad laws stated against subst along the monoid's propositional identities). The record carries NO ⊑-prop-equivalent field — only structure, monoid laws, and comonad laws. Two non-isomorphic-grade-monoid instances inhabit it: EchoGradedComonadInstance1.nat-instance at the commutative monoid (ℕ, +, 0); EchoGradedComonadInstance2.list-instance at the non-commutative free monoid (List Tag, ++, []) over a two-element Tag with per-element residue layers R smol A = A × Bool and R big A = A × ℕ. Non-isomorphism is constructively witnessed by tag-list-non-commutative.")
+     (consequences . "F3 PASSED; the two-models claim is earned back FOR THE F1-STYLE GRADED-COMONAD WITNESS. It does NOT reinstate the older EchoRelModel/GCLaws two-models claim retracted at R-2026-05-18 finding 3 — that situation (same grade poset, ⊑-prop baked in as a field, rel-model = set-model × ⊤, agreement by refl) is unchanged. The two earn-backs are about different abstract interfaces and are not interconvertible. Retraction follow-up F-2026-05-20b appended to docs/retractions.adoc. Pillar F earn-back programme now CLOSED: F4 + F2 (2026-05-18), F1 + F3 (2026-05-20).")
+     (supersedes . none))
+
+    (adr-009
+     (title . "Retraction-discipline succeeded: R-2026-05-18 reframing converted into four earn-back gate passes")
+     (status . accepted)
+     (date . "2026-05-20")
+     (context . "R-2026-05-18 retracted five claims and reframed the project around what the Agda actually shows (thin-poset reindexing modality, not graded comonad; pointwise mediator, not terminal cone; carrier-parametricity, not model-independence; postulate-free build as evidence, not conservativity metatheorem; no funext anywhere, not 'quarantined'). The earn-back plan in docs/echo-types/earn-back-plan.adoc was the falsifiable program for converting the retracted claims back into theorems — or confirming, on the project's own gate discipline, that they cannot be earned at their original strength.")
+     (decision . "All four gates have now passed at the strictly-bounded strength the earn-back plan asked for: F4 (terminal-cone UP as a function of an explicit funext parameter, never a postulate); F2 (genuine second model of the bare Echo functor on a non-graph StepND relation); F1 (genuine graded comonad on iterated-residue carrier with Echo as grade-unit object); F3 (the F1 construction is instantiable at non-isomorphic grade monoids). Each is exactly as strong as the gate specified; nothing is overclaimed. The conservativity metatheorem retraction (R-2026-05-18 finding 5) stays retracted with no gate attempting to earn it back — that one was a meta-statement over all propositions, not discharged by typechecking. The 'not two models for EchoGraded/GCLaws' finding 3 also stays retracted; the F3 earn-back is about the different F1 interface.")
+     (consequences . "The retraction discipline is validated AS A METHODOLOGY: a retraction is not a failure but the mechanism by which claims become falsifiable. Four of five retracted claims were earned back at honest strength, one stays retracted, none was silently re-inflated. paper.adoc / types-abstract.adoc / conservativity.adoc are NOT moved by this ADR — those documents are about EchoGraded's thin-poset structure, which the F1+F3 side-construction does not change. Whether to add a bounded 'new contribution' paragraph is owner-gated.")
      (supersedes . none))))
 
 ;;; ============================================================

.machine_readable/6a2/STATE.a2ml

@@ -234,19 +234,20 @@
 ;;; ============================================================
 
 (define next-actions
-  '(((id . t-3)
-     (title . "Gate-1 falsification test 3 (informativeness collapse)")
-     (status . unstubbed)
-     (relevance . "Now better-targeted post-EI-2: with RoleGraded in place, ask whether the role-or-grade axis is derivable from the other plus a forgetful functor.")
-     (priority . medium))
-
-    ((id . q2-4)
-     (title . "Falsifier attempts for surviving gate-2 nominees")
-     (status . open)
-     (relevance . "Each surviving nominee has an unattempted falsifier. Worth attempting at least one to harden the gate-2 case beyond 'no successful reduction has been attempted'.")
-     (priority . medium))
-
-    ((id . q2-1)
+  ;; Updated 2026-05-20: the April 2026 next-actions list is largely
+  ;; superseded by intervening session activity. Resolutions:
+  ;;   * `integration` (apply 7-commit integration sequence) — DONE,
+  ;;     long since merged.
+  ;;   * `t-3` (Gate-1 falsification test 3) — superseded by the
+  ;;     Gate 1 adjacency refresh (`decisions/gate1-adjacency-refresh.adoc`,
+  ;;     PR #77) which closed gate-1 work at 5/5 REFINED.
+  ;;   * `q2-4` (falsifier attempts) — partially absorbed into
+  ;;     `IntegrationAudit.agda` EI-2 negative result; further
+  ;;     falsifier attempts are now bookkeeping not load-bearing.
+  ;;   * `q2-1` (echo-not-prop generalisation) — still open.
+  ;;   * `q2-3` (RoleGraded as N5) — still open (low priority).
+  ;;   * `v0-2-recipe-extension` — still parked.
+  '(((id . q2-1)
      (title . "Generalisation of echo-not-prop")
      (status . open)
      (relevance . "n=2 special case proofs generalise to: for non-injective f with at least two distinct preimages of y, is-prop (Echo f y) → ⊥. Closing this also discharges the truncation-argument gap for refinement, IFC, and provenance adjacency notes.")
@@ -260,18 +261,98 @@
      (priority . low)
      (note . "Mostly bookkeeping post-EI-2 since the recipe is no longer the distinctness locus."))
 
-    ((id . integration)
-     (title . "Apply the seven-commit integration sequence")
-     (status . ready)
-     (relevance . "INTEGRATION_COMMITS.adoc has the full sequence. Commit 7 is the EI-2 termination. All artefacts are staged at /mnt/user-data/outputs/audit-output/.")
-     (priority . high))
+    ((id . owner-gated-paper-update)
+     (title . "Bounded new-contribution paragraph in paper.adoc / types-abstract.adoc / conservativity.adoc for F1+F3")
+     (status . owner-gated)
+     (relevance . "F1 + F3 (see META adr-007, adr-008) introduce a separate graded-comonad construction beside EchoGraded. The paper bodies are about EchoGraded's thin-poset structure — the title and central thesis should not move on these gates alone. Whether to add a bounded contribution paragraph mentioning the F1/F3 side-construction is an editorial decision.")
+     (priority . deferred))
+
+    ((id . ordinal-track-path-1)
+     (title . "Ordinal track Path-1 — Brouwer rank-mono into _<ᵇ⁻_")
+     (status . in-flight)
+     (relevance . "Brouwer arithmetic + rank-mono for _<ᵇ⁻_ are in a parallel-session worktree; this echo-types session stays clear of `proofs/agda/Ordinal/**` per `feedback_parallel_session_branch_drift` discipline.")
+     (priority . high)
+     (owner . other-session))
 
     ((id . v0-2-recipe-extension)
      (title . "Recipe extension exploration (parked)")
      (status . parked-v0.2)
      (relevance . "Coupled state across axes; multiple live positions per axis. New module work, not a re-investigation of EI-2.")
      (priority . deferred))))
 
+;;; ============================================================
+;;; Pillar F earn-back closure summary (2026-05-20)
+;;; ============================================================
+;;;
+;;; The Pillar F earn-back programme launched by R-2026-05-18 is now
+;;; CLOSED. All four gates passed at strictly-bounded strength; see
+;;; META.adr-{007,008,009} and docs/retractions.adoc follow-ups
+;;; F-2026-05-18a + F-2026-05-20a + F-2026-05-20b.
+
+(define earn-back-summary
+  '((status . closed)
+    (closing-date . "2026-05-20")
+    (gates
+     ((F4 (status . passed) (date . "2026-05-18")
+          (module . "proofs/agda/EchoPullbackUnivF4.agda")
+          (claim . "Terminal-cone universal property as a function of an explicit funext module parameter, never a postulate")
+          (retraction-followup . "F-2026-05-18a"))
+      (F2 (status . passed) (date . "2026-05-18")
+          (module . "proofs/agda/EchoStepNDModelF2.agda")
+          (claim . "Genuine second model of the bare Echo functor on the non-graph relation StepND; content-bearing agreement")
+          (retraction-followup . "F-2026-05-18a"))
+      (F1 (status . passed) (date . "2026-05-20")
+          (module . "proofs/agda/EchoGradedComonadF1.agda")
+          (claim . "Monoid-graded iterated-residue comonad at (ℕ, +, 0) with Echo as grade-unit object; nested δ; all three comonad laws; D2-nontrivial separating witness")
+          (retraction-followup . "F-2026-05-20a")
+          (adr . adr-007))
+      (F3 (status . passed) (date . "2026-05-20")
+          (modules . ("proofs/agda/EchoGradedComonadInterface.agda"
+                      "proofs/agda/EchoGradedComonadInstance1.agda"
+                      "proofs/agda/EchoGradedComonadInstance2.agda"))
+          (claim . "Abstract GradedComonadStructure record (no ⊑-prop-equivalent field) + two non-isomorphic-grade-monoid instances: nat-instance at commutative (ℕ, +, 0), list-instance at non-commutative free monoid (List Tag, ++, [])")
+          (retraction-followup . "F-2026-05-20b")
+          (adr . adr-008))))
+    (scope-qualifier . "F1+F3 earn back the graded-comonad and two-models claims FOR A NEW SIDE-CONSTRUCTION. EchoGraded remains a thin-poset reindexing modality per R-2026-05-18; EchoRelModel's two-models claim remains retracted. Different abstract interfaces; not interconvertible.")
+    (forbidden-rebrandings
+     . ("EchoGraded is a graded comonad"
+        "the F1 construction reinstates EchoGraded's retracted comonad claim"
+        "the F3 two-models result reinstates EchoRelModel's retracted two-models claim"
+        "the title or central thesis of paper.adoc moves on F1 or F3 alone"))
+    (unmoved-retractions
+     . ("R-2026-05-18 finding 5 (conservativity metatheorem) — stays retracted; no gate attempted to earn it back, no gate could (meta-statement over all propositions, not discharged by typechecking)"
+        "R-2026-05-18 finding 3 (\"Not two models\" for EchoRelModel/GCLaws) — stays retracted; F3 earned a different two-models claim at a different interface"))))
+
+;;; ============================================================
+;;; Theory-work closure summary (2026-05-20)
+;;; ============================================================
+;;;
+;;; The §"Theory work — no proof assistant needed" section in
+;;; docs/echo-types/roadmap.md is now empty. Every item is landed,
+;;; ruled out, or refreshed.
+
+(define theory-work-summary
+  '((status . closed)
+    (closing-date . "2026-05-20")
+    (closure-prs . (#67 #68 #69 #70 #71 #72 #74 #75 #76 #77 #78 #79 #82 #84 #86 #88 #90 #91 #92))
+    (axes-fully-mechanised
+     . ((axis-2-approximate-echo . "EchoApprox.agda + EchoApproxInstance.agda; Rung C BalancedTolerance at #78")
+        (axis-8-decidability    . "EchoDecidable.agda")
+        (axis-8-cost            . "EchoCost.agda + EchoCostInstance.agda (PR #85)")
+        (axis-8-access          . "EchoAccess.agda (PRs #68, #75)")
+        (axis-8-search          . "EchoSearch.agda + EchoSearchInstance.agda (PR #80)")
+        (negative-coecho        . "AntiEcho.agda (PR #69) + AntiEchoTropical.agda (PR #72) + AntiEchoTropicalGeneric.agda (PR #91) + antiecho-partition-dec (PR #90)")))
+    (ruled-out
+     . ((two-categorical-shape . "decisions/no-2-cat.adoc — every would-be 2-cell is refl or forced trivial")))
+    (refreshed
+     . ((presentation-dependence-cluster . "decisions/presentation-dependence.adoc — examples 5, 9, 10 cluster; meta-pattern only, no new module needed")
+        (gate-1-adjacency-refresh        . "decisions/gate1-adjacency-refresh.adoc — 5/5 REFINED, 0 RE-EVALUATE")))
+    (canonical-examples-cluster
+     . ((example-5-database-provenance . "EchoExampleProvenance.agda (PR #81)")
+        (example-9-parser              . "EchoExampleParser.agda (PR #83)")
+        (example-10-abstract-interp    . "EchoExampleAbsInt.agda (PR #82)")
+        (example-6-numeric             . "still unblocked, only remaining example item")))))
+
 ;;; ============================================================
 ;;; END OF STATE
 ;;; ============================================================