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Add cross-repo bridge status ledger and canonical links
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README.md

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- bridge formalisms live in this repo (`EchoCNOBridge`, `EchoJanusBridge`, tropical-collapse witness work in `EchoTropical`)
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- Agda-side adapter slot now exists in `maa-framework/absolute-zero` at `absolute-zero/proofs/agda/EchoBridgeScaffold.agda`
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- end-to-end conformance against upstream codebases is a separate track and is not yet fully machine-checked here
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- current bridge ledger: `docs/echo-types/cross-repo-bridge-status.md`
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- see `docs/echo-types/roadmap.md` for staged cross-repo verification gates
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## What Echo Types Are For
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# Cross-Repo Bridge Status
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Last updated: 2026-04-23
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This file is the single status ledger for echo-type bridge work that touches
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other repositories.
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## Tracks
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| Track | echo-types side | Adjacent side | Current status | Main blocker |
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|---|---|---|---|---|
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| CNO bridge (Agda) | `proofs/agda/EchoCNOBridge.agda` | `maa-framework/absolute-zero/proofs/agda/EchoBridgeScaffold.agda` | Adapter slot landed on both sides | `absolute-zero/proofs/agda/CNO.agda` still has unfinished holes, so direct import-level instantiation is deferred |
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| CNO core theorem alignment | `EchoCNOBridge` theorem family | `absolute-zero/proofs/coq/common/CNO.v`, `absolute-zero/proofs/lean4/CNO.lean` | Paths identified; theorem-by-theorem alignment not yet done | Cross-prover statement normalization not written |
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| JanusKey bridge (reversibility/category/thermo context) | `proofs/agda/EchoJanusBridge.agda`, `EchoThermodynamics.agda` | `januskey/src/abi/*.idr`, `januskey/docs/wiki/theory/*.adoc` | Conceptual relation present; no formal checker bridge yet | JanusKey formal artifacts are mostly Idris + docs, not a synchronized Coq/Lean theorem surface |
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| Tropical alignment | `proofs/agda/EchoTropical.agda` | `tropical-resource-typing/*.thy`, `TropicalSessionTypes.lean` | Repo inventory complete; no theorem alignment yet | Adjacent repo not recently audited for this integration path |
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## Immediate next actions
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1. Close holes in `absolute-zero/proofs/agda/CNO.agda`.
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2. Add `EchoCNOBridgeConcrete.agda` in `absolute-zero/proofs/agda/` that instantiates `EchoBridgeScaffold.CNOModel` from concrete CNO semantics.
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3. Write a theorem correspondence table (name-by-name) for `EchoCNOBridge` vs Coq/Lean CNO statements.
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4. Decide JanusKey formal target layer (Idris ABI vs another prover) before writing an automated bridge.

docs/echo-types/roadmap.md

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**Status:** planning document. Partitions work by dependency on the
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two identified bottlenecks:
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For current cross-repo progress snapshots, see
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`cross-repo-bridge-status.md`.
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- **Bottleneck B1.** The `--without-K` shared-binder constructor
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block in the Buchholz `_<ᵇ_` order. `wf-<ᵇ` is landed for the
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currently admitted core, but full totality + full-constructor

readme.adoc

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* Bridge formalisms live in this repo (`EchoCNOBridge`, `EchoJanusBridge`, tropical-collapse witness work in `EchoTropical`).
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* Agda-side adapter slot now exists in `maa-framework/absolute-zero` at `absolute-zero/proofs/agda/EchoBridgeScaffold.agda`.
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* End-to-end conformance against upstream codebases is a separate track and is not yet fully machine-checked here.
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* Current bridge ledger: `docs/echo-types/cross-repo-bridge-status.md`.
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* See `docs/echo-types/roadmap.md` for staged cross-repo verification gates.
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== What Echo Types Are For

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