The EDP-Φ Bridge: A Computable Coordination Parameter for Integrated Systems Foundations and Two Proof-of-Concept. Validations

Abstract

The degree to which a complex adaptive system functions as an integrated whole — rather than as a population of locally autonomous components — is a quantity for which existing frameworks supply either qualitative profiles (the Epistemic Deficit Profile, EDP, of Kremenchutskiy 2026a–c) or formally elegant but computationally intractable measures (integrated information Φ^IIT of Tononi et al., 2016). We develop a computable coordination parameter Φ, defined as a four-component weighted composite of inter-component mutual information (I_mutual), phase synchrony (S_sync), graph integrity (G_int), and energetic coherence (E_coh), whose four dimensions are designed to instantiate operationally the four EDP axes (coherence, distributed representation, observability, capacity for revision). We name the resulting bridge between the qualitative EDP framework and the computable composite the EDP-Φ Bridge. We report two proof-of-concept validations on substrates that share no microscopic structure. First, in human prostate tissue (TCGA-PRAD), mutual information in a PCA-proxied cell-state space collapses 12.3-fold between matched normal and tumour samples (0.3376 → 0.0274 bits; p = 1.95 × 10⁻¹⁸; cluster-robust Cohen's d = 14.2, 95% CI 11.8–16.6), and a 256² FitzHugh–Nagumo lattice calibrated against this signal reproduces a coupling-driven phase transition with a hysteresis loop (A_Φ = 0.1434; recovery ratio 0.673; component hierarchy I_mutual > E_coh > G_int > S_sync). Second, in an eight-model ensemble of open-weight large language models performing knowledge-graph verification — using the corpus and verdict tables of Kremenchutskiy et al. (2026), Dynamic Calibration and Adversarial Verification in Eight-Model Ensembles: Parameter-Independent Acquiescence, Calibration Homeostasis, and the Wilson Gate Relaxation Threshold (Zenodo, doi:10.5281/zenodo.19639251; hereafter the DC paper) — we operationalise the same four components on verdict streams, recover three distinct collapse profiles (adversarial-axis hierarchy G_int > S_sync > E_coh > I_mutual; giant-component invariance under outsider-model addition; and zero composition-axis hysteresis robust across three stateless policy variants), and re-examine one model (DeepSeek-R1), previously characterised as an “extreme skeptic” in the DC paper, as a non-responder traceable to a parser–model interface. The cross-substrate measurement supports three working hypotheses. (H1) Tractability: Φ is an operationally useful, computable proxy for integration at scales (10⁵ cells; 10⁴ ensemble verdicts) where Φ^IIT is intractable. (H2) Provisional four-component mapping: the four components admit a one-to-one mapping to the four EDP axes; we treat this convergence as a working hypothesis rather than a derived result, pending independent replication and comparison with alternative decompositions. (H3) Hysteresis as a candidate substrate discriminator: the hysteresis signature of Φ — present in the FHN-model channel of the tissue substrate, absent on the composition axis of the stateless verifier ensemble under three orthogonal policy variants — is consistent with the hypothesis that hysteresis marks systems whose history is encoded in material state; the claim is based on N = 2 and awaits tests on state-carrying aggregation protocols. We frame this paper as the first quantitative instantiation of the EDP-Φ Bridge programme rather than its final adjudication; the Integration Atlas of §7 enumerates six further candidate domains as falsifiable predictions.