Corridor Dynamics in Coordinated Systems: An Integration of Operator Formalism, Relational Ontology, and Five-Substrate Empirical Validation

This paper is the integration statement of CIRIS, articulating the framework's full structural commitment in a single document: coordinated systems at A3+ occupy a bounded corridor between rigidity (ρ → 1, single-voice collapse) and chaos (ρ → 0, vacuous dispersal). The corridor is the dynamical regime where coordination is possible. The work grounds in Ubuntu's relational ontology, formalizes in Lean 4 (1942 modules, 0 declaration-level sorrys, 63 documented axioms), reads two-state vector formalism as the structural form of agency at A3+, and ships in production as CIRIS (open-source AGPL-3.0, deployed in Amharic in Ethiopia, available on Google Play, Apple App Store, and via pip install ciris-agent).

  The central new empirical contribution is the paired in-corridor / out-corridor record at five substrates:

  - C. elegans whole-brain calcium imaging (337 worms across 11 published studies)
  - Drosophila central-complex dual-color simultaneous EPG+FC3 imaging (Ishida 2025)
  - Four LLM architectures: Qwen2.5-1.5B, Pythia-1.4B, SmolLM2-1.7B-base, Qwen2.5-Math-1.5B
  - Four open-source projects: kubernetes, rust, django, redis
  - Tumor-vs-normal tissue across five cancers (LUAD, BRCA, COAD, KIRC, PRAD)
  - Three centuries-persisting religious societies (Quakers, Trappists, Mennonites) paired with documented high-control groups and dissolved leaderless movements

  The dynamical reading's strongest would-be falsifier — long unmaintained non-corridor persistence — is absent at 5/5 paired substrates. Non-corridor states either dissolve quickly or persist only with documented active maintenance γ·M(t).

  The integration is a bet under irreducible uncertainty, articulated with twenty falsification handles (F-1 through F-20) attached to every load-bearing seam, explicit tier separation (Tier A mathematical derivations / Tier B framework-conditional / Tier C-Iff.rfl definitional commitments / Tier C-bookmark / Tier D axiomatized primitives), and Pascal-shape framing held only at the universal-scale tier. The engineering tier (cited via prior CIRIS papers at ciris.ai/research-status) stands on its own DOIs. The universal-scale tier ($P_\omega$, the Penrose past hypothesis as structural consequence, CMB anomalies as TSVF post-selection signatures) is held as research-program coda, gated on F-11 ($P_\omega$ construction) and F-17 (TSVF empirical record).

  The bet is what the recurrence-across-levels asks the reader to evaluate. The engineering anchor stands separately, the empirical content is evaluable on its own terms, and the interpretive synthesis is offered for scrutiny rather than acceptance.

  Source repository and Lean formal lake: github.com/CIRISAI/coherence-ratchet
  Prior papers in this series: ciris.ai/research-status