Topology-Dependent Coherence Cost in Dynamical Networks: The SDAT/TCE Research Program

Abstract This repository contains the complete SDAT/TCE research program, a computational investigation of topology-dependent coherence cost in dynamical networks. The central question is whether specific network structures can sustain coherent collective behavior at lower operational cost than alternative topologies — and how any such advantage evolves across scales, dynamical regimes, and validation conditions. The research is organized as a progressive falsification program. Rather than seeking confirmation of a predefined theory, each phase introduces increasingly stringent tests designed to identify the operational limits, robustness, and boundary conditions of the proposed framework. Falsification outcomes are treated as first-class scientific results. The initial phases (through Phase 5A) introduced and evaluated the Topological Coherence Efficiency Index (TCEI), a composite metric combining coherence, stability, signal transmission, coupling strength, and internal friction. Experiments spanned Kuramoto oscillator networks, Stuart–Landau oscillators, empirical networks, spectral intervention studies, congestion models, and large-scale scaling experiments. Key findings included a robust spectral invariant at peak performance (λ₂ ≈ 1. 59, spectral entropy ≈ 0. 97 at N=100), operational causality of spectral manipulation on friction (p < 10⁻⁸), and a scale-specific sign inversion of the λ₂–friction correlation at N=500. Subsequent work (Phase 5B) focused on post-publication validation under stricter methodological conditions, including scale-fair λ₂ matching, dynamic stationarity diagnostics, and a systematic audit of the TCEI signal-transmission estimator (Icorr). These investigations confirmed the structural matching procedure and identified a finite-sample bias in Icorr under noisy conditions: observed values tracked the statistical null floor, between-cell variance ratios reached only ~0. 07, and ranking robustness without Icorr yielded Spearman ρ ≈ 0. 56–0. 59. The full Phase 5B sweep was correctly paused pending estimator reassessment. These findings do not falsify SDAT/TCE; they define the conditions under which its composite ranking claims can and cannot be supported. The repository intentionally preserves both positive and negative results. The objective is to progressively refine the framework and clarify its domain of validity. Current contents — Topology-Dependent Coherence Cost in Dynamical Networks: A Progressive Falsification Study of SDAT/TCE through Phase 5A (v1. 4, Zenodo DOI: 10. 5281/zenodo. 20600201) — SDAT/TCE Phase 5B: Scale-Fair Validation and Metric Fragility Beyond Phase 5A— Supplementary materials and supporting documentation Keywordscomplex networks, synchronization, Kuramoto model, spectral graph theory, network topology, coherence cost, SDAT, TCE, Topological Coherence Efficiency Index, scale-fair validation, progressive falsification, metric robustness, ranking fragility, finite-sample bias, network scaling, hierarchical modularity, complex systems, computational modeling