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| 1 | += Echo Types — Gates Protocol (Falsifiable Identity Claim) |
| 2 | +:toc: macro |
| 3 | +:toclevels: 2 |
| 4 | +:sectnums: |
| 5 | +:sectnumlevels: 2 |
| 6 | +:icons: font |
| 7 | + |
| 8 | +[.lead] |
| 9 | +The canonical gates protocol. Created 2026-05-18 to resolve a |
| 10 | +long-standing dangling reference: ~15 documents (including |
| 11 | +`docs/retractions.adoc`'s own lead, `next-questions.adoc`, |
| 12 | +`buchholz-plan.adoc`, the `EI2_*`/`gate-2-*` handoffs, and the |
| 13 | +`echo-types/*` papers) cited `roadmap-gates.adoc` as canonical while |
| 14 | +the file did not exist. This document states the protocol that was |
| 15 | +already being practised; it introduces no new claim and is faithful |
| 16 | +to the living instances in `next-questions.adoc`, `retractions.adoc`, |
| 17 | +and `echo-types/earn-back-plan.adoc`. |
| 18 | +
|
| 19 | +toc::[] |
| 20 | +
|
| 21 | +== The identity claim, made falsifiable |
| 22 | +
|
| 23 | +The repository asserts that "echo" (loss-with-residue, |
| 24 | +`Echo f y := Σ (x:A),(f x ≡ y)`) is a *distinct, characterisable |
| 25 | +type-theoretic phenomenon*. That assertion is held **falsifiable**: |
| 26 | +each gate below has an explicit pass condition *and an explicit |
| 27 | +retraction condition*. A gate whose retraction condition is met |
| 28 | +*retracts* the corresponding claim — it does not weaken into a hedge. |
| 29 | +Retraction is the mechanism by which the identity claim is made |
| 30 | +falsifiable, not a failure of the repository. |
| 31 | +
|
| 32 | +== The three gates |
| 33 | +
|
| 34 | +[#gate-1] |
| 35 | +=== Gate 1 — Distinct phenomenon |
| 36 | +
|
| 37 | +Echo is not a renaming of an existing construction (quotient, Galois |
| 38 | +connection, lens/optic, refinement type, modal/comonadic type, |
| 39 | +provenance semiring). *Pass:* a distinctness witness that survives |
| 40 | +reduction attempts to each neighbour. *Retract:* a neighbour |
| 41 | +construction expresses the characteristic family without importing |
| 42 | +echo-specific primitives. Living instances: `docs/next-questions.adoc` |
| 43 | +Gate 1; `docs/adjacency/*`. |
| 44 | +
|
| 45 | +[#gate-2] |
| 46 | +=== Gate 2 — Characteristic theorems |
| 47 | +
|
| 48 | +There exist theorems true of echo that *measure* its content rather |
| 49 | +than restate generic Σ-functoriality. *Pass:* a nominee that survives |
| 50 | +a sharpened falsifier of the shape that struck down earlier nominees |
| 51 | +(collapsing a pseudo-theorem to `proj₂` / a product of independent |
| 52 | +restatements). *Retract:* the nominee is shown to be such a product, |
| 53 | +or to reduce to thinness of the loss order alone (cf. |
| 54 | +`EchoSeparating`, `docs/characteristic.adoc` §"Honest |
| 55 | +qualifications"). |
| 56 | +
|
| 57 | +[#gate-2-nominees] |
| 58 | +.Gate 2 nominee table |
| 59 | +[cols="1,3,1", options="header"] |
| 60 | +|=== |
| 61 | +| Id | Candidate | Status |
| 62 | +
|
| 63 | +| N1–N4 |
| 64 | +| Earlier nominees (recipe family) |
| 65 | +| Audited; documented in `docs/characteristic.adoc` / |
| 66 | + `characteristic/IntegrationAudit.agda` — one recipe, "would weaken |
| 67 | + in parallel" (recorded, not hidden). |
| 68 | +| N3 |
| 69 | +| `knowledge-and-controlled-degradation` |
| 70 | +| *Struck down* by the sharpened falsifier |
| 71 | + (`characteristic.IntegrationAudit`). |
| 72 | +| N5 |
| 73 | +| `characteristic.RoleGraded.choreo-grade-commute` |
| 74 | +| *NOT adopted.* The falsifier attempt |
| 75 | + `characteristic/N5Falsifier.agda` is **known-broken** (unsolved |
| 76 | + metas; disclosed in `docs/foundation.adoc`). The "survives" verdict |
| 77 | + is *not mechanised*; N5 must not be cited as established. |
| 78 | +|=== |
| 79 | +
|
| 80 | +[#gate-3] |
| 81 | +=== Gate 3 — Canonical examples |
| 82 | +
|
| 83 | +The phenomenon has worked examples that are not toys. *Pass:* an |
| 84 | +example typechecking `--safe --without-K`, zero postulates, exercising |
| 85 | +the characteristic structure (e.g. `examples/Transport.agda` block |
| 86 | +averaging). *Retract:* every example collapses to a trivial instance. |
| 87 | +
|
| 88 | +== Failure action |
| 89 | +
|
| 90 | +*Failure is recorded in `docs/retractions.adoc` rather than silently |
| 91 | +revised.* When a gate's retraction condition is met: |
| 92 | +
|
| 93 | +. add a dated entry to `docs/retractions.adoc` (append-only) stating |
| 94 | + trigger, finding, what is retracted, and the replacement; |
| 95 | +. edit every affected artefact so *no inflated form survives* in any |
| 96 | + document — reframe to the mechanised strength, never delete history; |
| 97 | +. earn-back, if attempted, is gated and logged in |
| 98 | + `docs/echo-types/earn-back-plan.adoc`; a failed earn-back gate is a |
| 99 | + *second negative result*, logged, not a silent revert. |
| 100 | +
|
| 101 | +No postulates, no escape pragmas, `--safe --without-K`, ever — a gate |
| 102 | +"passed" by weakening these is failed (`tools/check-guardrails.sh` |
| 103 | +enforces this independently of any closure; see `docs/foundation.adoc`). |
| 104 | +
|
| 105 | +== Relationship to the other living documents |
| 106 | +
|
| 107 | +* `docs/next-questions.adoc` — the open questions, each with home |
| 108 | + gate, attack path, and explicit retraction condition (the |
| 109 | + operational instance of this protocol). |
| 110 | +* `docs/retractions.adoc` — the append-only failure log this |
| 111 | + protocol's *Failure action* writes to (R-2026-05-18 and its |
| 112 | + follow-ups). |
| 113 | +* `docs/echo-types/earn-back-plan.adoc` — the gated programme to |
| 114 | + convert retracted claims back into theorems (Pillar F). |
| 115 | +* `docs/foundation.adoc` — the trusted base and its enforcement. |
| 116 | +
|
| 117 | +== Revision policy |
| 118 | +
|
| 119 | +Append-only revision history. This document describes the protocol; |
| 120 | +it does not record results (those live in `retractions.adoc` / |
| 121 | +`next-questions.adoc`). |
| 122 | +
|
| 123 | +=== Revision history |
| 124 | +
|
| 125 | +* *2026-05-18 — created.* Faithful reconstruction of the |
| 126 | + already-practised protocol to resolve the dangling canonical |
| 127 | + reference. No new claim introduced. |
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