[WIP draft] F1 spike checkpoint — genuine graded comonad (feasibility positive, coassoc open)#48
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hyperpolymath merged 2 commits intoMay 18, 2026
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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>
…oassoc open
Gate F1 of 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). Monoid-graded iterated-residue candidate:
* D r = r nested informative residue layers; D 0 = Id, so
D 0 (Echo f y) IS the bare echo (Echo = grade-unit object).
* D r is non-collapsing — separating witness D2-nontrivial proves
D r is not ⊤/a prop (the old dev's fatal defect).
* NESTED comultiplication δ : D (m+n) A → D m (D n A) — the
structure the retracted dev never had.
* Functor laws (mapD-id/mapD-∘) proven.
* counit-right proven (definitional).
* counit-left proven (induction on grade; only non-structural tool
is ℕ-UIP, which is K-free via decidable equality).
DECISIVE FINDING: the make-or-break foundational question is answered
NO — Agda demanded no K, no funext, no postulate anywhere. The
obstruction F1 feared did not materialise.
OPEN (F1 not yet passed): gc-coassoc (coassociativity). Base case +
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's guardrail:
close-but-not-closed = failed-and-logged.
No reframed claim moves until F1 fully passes. Checkpoint only.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
hyperpolymath
merged commit 8682447
into
reframe/retraction-2026-05-18
7 of 8 checks passed
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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.agdatypechecks--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:
D r(separating witnessD2-nontrivial— not ⊤)δ : D (m+n) A → D m (D n A)(the structure the retracted dev never had)Open (F1 NOT passed)
gc-coassoc— base + skeleton close; inductive step has an isolated proof-engineering type-mismatch needing an explicit δ-naturality-over-Rlemma. Stated in-file as a precise OPEN obligation: not postulated, not softened, not wired intoAll.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