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| 1 | += Echo Types — Retraction Log |
| 2 | +:toc: macro |
| 3 | +:toclevels: 2 |
| 4 | +:sectnums: |
| 5 | +:sectnumlevels: 2 |
| 6 | +:icons: font |
| 7 | + |
| 8 | +[.lead] |
| 9 | +The canonical retraction log referenced by `roadmap-gates.adoc` |
| 10 | +("Failure is recorded in `docs/retractions.adoc` rather than silently |
| 11 | +revised"). Retractions are not failures of the repository; they are |
| 12 | +the mechanism by which its claims are made falsifiable. Append-only. |
| 13 | + |
| 14 | +toc::[] |
| 15 | + |
| 16 | +== Standing on retraction |
| 17 | + |
| 18 | +A retraction here means: a claim previously asserted in a repository |
| 19 | +artefact (README, paper, abstract, conservativity doc) is withdrawn |
| 20 | +or narrowed, with the reason recorded, the replacement stated, and |
| 21 | +the affected artefacts edited so no inflated claim survives in any |
| 22 | +document. The underlying Agda is *not* changed by a prose retraction |
| 23 | +unless separately noted — the mechanised content is whatever it was; |
| 24 | +only the description of it is corrected. |
| 25 | + |
| 26 | +== Entries |
| 27 | + |
| 28 | +[#R-2026-05-18] |
| 29 | +=== R-2026-05-18 — "graded comonad / two models / conservativity metatheorem / universal property / funext quarantine" |
| 30 | + |
| 31 | +==== Trigger |
| 32 | + |
| 33 | +An author-run adversarial review simulating three hostile referees |
| 34 | +(graded-modality skeptic in the Petriček–Orchard–Gaboardi–Katsumata |
| 35 | +lineage; LICS/MFPS semantics skeptic; CPP/ITP proof-assistant |
| 36 | +pragmatist), followed by a codebase pressure-test that searched for |
| 37 | +any in-repo defense of the strongest attacks. |
| 38 | + |
| 39 | +==== Finding |
| 40 | + |
| 41 | +Five central claims had no defense in the codebase; two were |
| 42 | +*contradicted by the repository's own Gate-2 audit* |
| 43 | +(`docs/characteristic.adoc`). Specifics: |
| 44 | + |
| 45 | +. *Not a graded comonad.* Tree-wide there is no `Comonad` record, no |
| 46 | + `δ : D_{r·s} ⇒ D_r D_s`, no nested `GEcho (GEcho …)`, no |
| 47 | + co-Kleisli. `gextract` is the identity coercion (`keep` is the |
| 48 | + definitional lattice bottom); `gduplicate` is the join-left |
| 49 | + *single-grade* reindex. The structure is a thin-poset reindexing |
| 50 | + action. The `CNO` modules are unrelated (a Clean-Null-Op / |
| 51 | + identity-program notion imported from the sister project |
| 52 | + `absolute-zero` as consumer evidence), not an alternative comonad. |
| 53 | +. *Content is exactly thinness.* The coherence equations collapse to |
| 54 | + `degrade-compose` + `≤g-prop`; the separating model shows the only |
| 55 | + content over generic Σ-functoriality is `≤g-prop` (the grade order |
| 56 | + is thin). `docs/characteristic.adoc` §"Honest qualifications" point |
| 57 | + 2 already states all four "characteristic" survivors are one recipe |
| 58 | + that "would weaken in parallel" under exactly this observation — |
| 59 | + i.e. the repository had already recorded the skeptic's case. |
| 60 | +. *Not two models.* `GCLaws` is instantiated only at `set-model` and |
| 61 | + `rel-model`; both fix the same grade poset (`_≤g_`, `≤g-prop`, |
| 62 | + `_⊔g_`, `keep`). `rel-model`'s carrier is the Set carrier with a |
| 63 | + `⊤` component (`RStep _ _ = ⊤`); `model-agreement` is `refl`. The |
| 64 | + `GradedLossModel` interface has `⊑-prop` as a *field*, baking in |
| 65 | + the only load-bearing hypothesis. This is carrier-parametricity |
| 66 | + over a fixed poset, not semantic model-independence. |
| 67 | +. *No universal property.* `echo-pullback-univ` proves only |
| 68 | + *pointwise* uniqueness `∀ v → m' v ≡ m v`. Full terminality |
| 69 | + (`m' ≡ m`) is neither stated nor provable here without funext. |
| 70 | + "A category theorist accepts echo as the limit of a cospan" does |
| 71 | + not follow from the mechanised content. |
| 72 | +. *No conservativity metatheorem.* Clause 2 ("any base proposition |
| 73 | + provable via `Echo` is provable without it") is a meta-statement |
| 74 | + over all propositions; it is not discharged by a typechecking run. |
| 75 | + `EchoFiberBridge.fiber` is a same-module restatement, so `echo↔fib` |
| 76 | + is the identity on a type — a triviality, not a grounding theorem. |
| 77 | +. *Funext story inverted.* There is no funext anywhere. |
| 78 | + `examples/Transport.agda` *avoids* funext via a first-order carrier; |
| 79 | + it does not "quarantine" a funext dependency. The genuine |
| 80 | + funext-relativity is the pointwise-only mediator property, which |
| 81 | + earlier drafts presented as a feature ("funext-free"). |
| 82 | + |
| 83 | +==== Action taken |
| 84 | + |
| 85 | +Per `roadmap-gates.adoc` §"Failure action" (record, then reframe — |
| 86 | +*not* silently revise). The following claims are *retracted* and the |
| 87 | +artefacts edited so no inflated form survives: |
| 88 | + |
| 89 | +[cols="2,3", options="header"] |
| 90 | +|=== |
| 91 | +| Retracted | Replaced by |
| 92 | + |
| 93 | +| "definitionally-grounded graded comonad of structured loss" (title, |
| 94 | + thesis, contribution 3) |
| 95 | +| "definitionally-grounded, loss-graded *reindexing modality*"; a |
| 96 | + thin-poset action, explicitly not a graded comonad |
| 97 | + |
| 98 | +| "terminal-cone universal property"; "category theorist accepts echo |
| 99 | + as the limit of a cospan" |
| 100 | +| funext-relative *pointwise mediator property*; terminality |
| 101 | + unstatable here without funext |
| 102 | + |
| 103 | +| "model independence across two agreeing models" |
| 104 | +| carrier-parametricity over a fixed grade poset; second model = first |
| 105 | + `× ⊤`, agreeing by `refl` |
| 106 | + |
| 107 | +| "conservativity metatheorem, discharged operationally by the build" |
| 108 | +| *postulate-free build* + definitional Σ-identity = *evidence for*, |
| 109 | + not a proof of, conservativity over MLTT+Σ |
| 110 | + |
| 111 | +| "funext boundary quarantined behind an isolated module; no result |
| 112 | + crosses it" |
| 113 | +| no funext anywhere; the pointwise-only mediator property is the |
| 114 | + real, now-disclosed funext boundary |
| 115 | +|=== |
| 116 | + |
| 117 | +Artefacts edited 2026-05-18: `docs/echo-types/paper.adoc` (title, |
| 118 | +thesis, contributions, §"loss-graded reindexing modality", §pullback |
| 119 | +presentation, §separating model, §carrier-parametricity, §methodology, |
| 120 | +§"Reframing note", conclusion); `docs/echo-types/conservativity.adoc` |
| 121 | +(statement, anchor table, scope, revision history); |
| 122 | +`docs/echo-types/types-abstract.adoc` (title, verdict, contributions, |
| 123 | +discipline; "submission-ready" status withdrawn pending re-review). |
| 124 | + |
| 125 | +==== Status of the underlying Agda |
| 126 | + |
| 127 | +Unchanged. No module was weakened or edited by this retraction. The |
| 128 | +mechanised content is exactly as strong as before; only the prose |
| 129 | +describing it is corrected downward to match it. The separating model, |
| 130 | +the postulate-free `--safe --without-K` build, the definitional |
| 131 | +Σ-identity, and the pointwise mediator property all stand as |
| 132 | +mechanised — they are simply now claimed at their true strength. |
| 133 | + |
| 134 | +==== Standing relationship to EI-2 |
| 135 | + |
| 136 | +This entry is consistent with, and does not reopen, the EI-2 negative |
| 137 | +result (`docs/next-questions.adoc`). EI-2 concerned cross-decoration |
| 138 | +integration narrowness; R-2026-05-18 concerns the graded-comonad / |
| 139 | +model-independence / conservativity framing. Both are calibration |
| 140 | +retractions, not invalidations of the mechanised artefacts. |
| 141 | + |
| 142 | +== Revision policy |
| 143 | + |
| 144 | +Append-only. New retractions get the next `R-YYYY-MM-DD` id. An entry |
| 145 | +is never edited after creation except to add a dated "follow-up" |
| 146 | +sub-section. Reframing of artefacts pursuant to an entry is logged in |
| 147 | +that entry's "Action taken". |
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