Add Agda echo/CNO bridge scaffold and integration pointers

Author: hyperpolymath

absolute-zero/README.adoc

@@ -48,6 +48,9 @@ absolute-zero/
 │   │
 │   ├── z3/                  # Z3 SMT verification (automated)
 │   ├── agda/                # Agda proofs (dependent types)
+│   │   ├── CNO.agda         # Main Agda CNO file (in-progress)
+│   │   ├── EchoBridgeScaffold.agda # Echo/CNO adapter interface scaffold
+│   │   └── README.adoc      # Agda bridge status + integration plan
 │   ├── isabelle/            # Isabelle/HOL (production-grade)
 │   └── mizar/               # Mizar proofs (mathematical library)
 │
@@ -204,6 +207,11 @@ For maximum confidence, we verify CNO properties in **six independent proof syst
 
 See [VERIFICATION.md](VERIFICATION.md) for detailed status and [PROOF-INSIGHTS.md](PROOF-INSIGHTS.md) for proof engineering knowledge.
 
+Agda bridge note:
+
+* `proofs/agda/EchoBridgeScaffold.agda` is now present as a compile-safe adapter layer to connect CNO identity witnesses to the echo/fiber shape used in `echo-types`.
+* Concrete import-level integration with `CNO.agda` remains gated until unfinished holes in `CNO.agda` are closed.
+
 **Coq Proof Status** (2026-02-05): 81 Qed / 19 Admitted / 6 Defined / 63 Axioms across 10 files. 4 files fully complete (CNO.v, CNOCategory.v, StatMech.v, StatMech_helpers.v).
 
 **Next Step**: Complete remaining 19 Admitted proofs, then build container for machine verification.

absolute-zero/ROADMAP.adoc

@@ -59,3 +59,4 @@ quantum verification, and standardization.
 * **ECHIDNA**: Security scanning - potential CNO verification integration
 * **Valence Shell**: Filesystem operations proved in FilesystemCNO.v
 * **echidnabot**: GitHub bot for automated proof checking in PRs
+* **echo-types**: Agda adapter scaffold now tracked at `proofs/agda/EchoBridgeScaffold.agda`; full cross-repo theorem alignment remains open

absolute-zero/proofs/agda/EchoBridgeScaffold.agda

@@ -0,0 +1,47 @@
+{-# OPTIONS --safe --without-K #-}
+
+-- Echo/CNO Agda bridge scaffold.
+--
+-- This module is intentionally independent from `CNO.agda` so it can
+-- stay typecheckable while that file is still being completed.
+
+module EchoBridgeScaffold where
+
+open import Agda.Primitive using (Level; lsuc; _⊔_)
+open import Agda.Builtin.Equality using (_≡_; refl)
+open import Agda.Builtin.Sigma using (Σ; _,_)
+open import Agda.Builtin.Unit using (⊤; tt)
+
+-- Canonical echo/fiber shape used by echo-types.
+Echo : ∀ {a b} {A : Set a} {B : Set b} → (A → B) → B → Set (a ⊔ b)
+Echo {A = A} f y = Σ A (λ x → f x ≡ y)
+
+-- Minimal interface needed to connect a CNO model to echoes.
+record CNOModel {ℓs ℓo : Level} (State : Set ℓs) : Set (lsuc (ℓs ⊔ ℓo)) where
+  field
+    Op           : Set ℓo
+    run          : Op → State → State
+    IsCNO        : Op → Set (ℓs ⊔ ℓo)
+    cno-identity : ∀ {op} → IsCNO op → (s : State) → run op s ≡ s
+
+open CNOModel public
+
+-- Any CNO witness yields an echo at any visible state.
+echo-from-cno :
+  ∀ {ℓs ℓo} {State : Set ℓs}
+  (M : CNOModel {ℓs} {ℓo} State)
+  (op : Op M) → IsCNO M op →
+  (s : State) → Echo (run M op) s
+echo-from-cno M op cno s = s , cno-identity M cno s
+
+-- A tiny closed model kept here as a local smoke witness.
+TrivialModel : CNOModel ⊤
+TrivialModel = record
+  { Op = ⊤
+  ; run = λ _ s → s
+  ; IsCNO = λ _ → ⊤
+  ; cno-identity = λ _ _ → refl
+  }
+
+trivial-echo : Echo (run TrivialModel tt) tt
+trivial-echo = echo-from-cno TrivialModel tt tt tt

absolute-zero/proofs/agda/README.adoc

@@ -0,0 +1,25 @@
+= Agda Proofs (absolute-zero)
+
+This directory currently contains:
+
+* `CNO.agda` — main Agda CNO development (currently includes unfinished holes).
+* `EchoBridgeScaffold.agda` — compile-safe interface layer for bridging CNO identity witnesses to the echo/fiber shape used in `echo-types`.
+
+== Purpose of `EchoBridgeScaffold.agda`
+
+The scaffold avoids importing `CNO.agda` directly so this bridge path can
+remain typecheckable while `CNO.agda` is still being completed.
+
+It provides:
+
+* `Echo` as `Σ x , f x ≡ y`.
+* `CNOModel` interface with `run`, `IsCNO`, and `cno-identity`.
+* `echo-from-cno` conversion from a CNO witness to an echo witness.
+
+== Integration plan
+
+1. Finish the remaining holes in `CNO.agda`.
+2. Add a concrete model instantiation from `CNO.Program` / `eval` into `CNOModel`.
+3. Add reciprocal consistency checks against:
+* `echo-types` (`proofs/agda/EchoCNOBridge.agda`)
+* this repository's Coq/Lean CNO statements.