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Bridge Status

This document strictly tracks the status of experimental extensions and bridges between the minimal core of Echo Types and other domains.

Note: Bridge materials are speculative and exploratory. They do not affect the core identity or foundational theorems of the repository.

1. CNO Bridge (Absolute Zero)

  • Status: PARTIAL
  • Dependencies: Absolute Zero Framework
  • Blockers: End-to-end integration across repositories is not yet mechanically verified here.
  • Core Affect: NO

2. Thermodynamics

  • Status: EXPLORATORY
  • Dependencies: None
  • Blockers: The quantitative collapse functional on infinite carriers is negatively closed (collapse-cost-impossible).
  • Core Affect: NO

3. Tropical Semantics

  • Status: PARTIAL
  • Dependencies: None
  • Blockers: Witness residues under tropical collapse are established, but broader ecosystem mapping remains incomplete.
  • Core Affect: NO

4. Buchholz / Veblen Ordinals

  • Status: PARTIAL (11/13 constructors closed under WfCNF; 1 in flight)
  • Dependencies: Standard Agda
  • Blockers: <ᵇ-+1 joint-bplus is the single remaining open constructor. The head-Ω domination route (option A) has its abstraction + per-marker dominances at both branches + the option-(b) head-Ω inversion lemmas all landed across 2026-05-27 (PRs #124 / #130 / #131); only the WfCNF-carrier structural recursion (Slice 2-bplus) remains. The earlier shared-binder-self-lift blocker is resolved (RankAdm + RankLex slices, 2026-05-26/27). Live tracker: docs/echo-types/buchholz-rank-obstruction.adoc.
  • Core Affect: NO

5. JanusKey / Categorical

  • Status: EXPLORATORY
  • Dependencies: Categorical foundations
  • Blockers: Higher-level abstractions (monads, adjunctions) are still evolving; core functors are stable.
  • Core Affect: NO

6. Decoration bridge (conceptual, not cross-repo)

  • Status: EXPLORATORY (R5 deferred-research; cleanly abandonable)
  • Dependencies: EchoIntegration, EchoChoreo, EchoGraded (import only)
  • Blockers: Bridge is bounded by construction. Closes under any of the documented termination criteria: Track A/B/C failure, all candidate analogies retired, redundancy with retracted-prose graded-comonad framing, forbidden-rebrandings register addition, retraction-watch trip. Companion: docs/echo-types/explorations/decoration-bridge/README.adoc; module: proofs/agda/EchoDecorationBridge.agda (deliberately not in All.agda).
  • Core Affect: NO