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

Abstract This repository contains the SDAT/TCE research program, a progressive computational investigation of topology-dependent coherence cost, mesoscopic coherence transport, and boundary-domain characterization in dynamical networks. The central question is whether specific network structures and transport architectures can sustain coherent collective behavior at lower operational cost than alternative configurations — and how any such advantage changes across scale, topology, dynamical regime, metric choice, 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, fragility, and boundary conditions of the proposed framework. Positive, negative, mixed, and inconclusive outcomes are preserved 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. 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 while identifying 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 therefore 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. Phase 5C extends the program from topology-dependent coherence cost toward mesoscopic coherence transport and natural-flow-domain characterization. The primary branch, CCH, studies explicit inter-modular routing as a mechanism for transporting coherence across modular oscillator networks. The secondary ENV branch explores environment-mediated mean-field coupling as a contextual comparator, without replacing the CCH primary validation path. The Phase 5C/M10 work introduces the Natural Flow Domain Principle: CCH is not required to demonstrate universal traversal across every graph medium, stress level, routing condition, or parameter configuration. Its validation objective is to identify the domain in which coherence transport is structurally supported, declare that domain rigorously, and characterize what happens at its boundaries. Within the M10 branch, naive scaling from M=5 did not automatically preserve transport. A routing-recovery sequence identified a declared M10 operational corridor: 0→3→9→4→7→1→6→2→8→5→0 under M=10, Nₘ=100, ΔΩ=0. 30, ε=0. 60, and Kᵢntraₐbs=4. 00. Subsequent corridor confirmation, conductivity prefiltering, static descriptor auditing, and time-resolved phase-space mapping showed that the M10 domain is bounded rather than universal. A topological conductivity prefilter improved the tested operating envelope, increasing ER stationarity from 18/20 to 19/20 and Modular stationarity from 19/20 to 20/20. Static descriptors did not generalize as an explanation of residual ER failures, while phase-space mapping classified Seed 13 and Seed 14 as a partially shared 3→9 corridor vulnerability with class-specific release dynamics. The current Phase 5C interpretation is therefore not a claim of universal coherence transport. It is a bounded-domain result: M10 supports mesoscopic coherence transport inside a declared operational corridor, while residual boundary cases are characterized rather than erased. The M10 branch is consolidated at the current instrumentation level, but does not authorize extrapolation to M=20, a universal routing law, or automatic repair/intervention. The repository intentionally preserves the full research trajectory: successful results, failed extensions, methodological corrections, boundary audits, estimator fragilities, and decision checkpoints. The objective is to progressively refine SDAT/TCE, clarify its domain of validity, and make its limits scientifically explicit. Current contents — Phase 5A: 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) — Phase 5B: Scale-Fair Validation and Metric Fragility Beyond Phase 5A (Zenodo DOI: 10. 5281/zenodo. 20691518) — Phase 5C: Natural Flow Domains in Mesoscopic Coherence Transport — Routing Corridors, Conductivity Constraints, and Boundary Failure Modes at M=10 — Supplementary materials, consolidated research logs, computational outputs, CSV result tables, configuration files, and supporting documentation Keywordscomplex networks, synchronization, Kuramoto model, spectral graph theory, network topology, coherence cost, mesoscopic coherence transport, natural flow domain, routing corridors, graph-medium conductivity, boundary dynamics, phase-space mapping, CCH, ENV, SDAT, TCE, Topological Coherence Efficiency Index, scale-fair validation, progressive falsification, metric robustness, ranking fragility, finite-sample bias, network scaling, modular oscillator networks, hierarchical modularity, complex systems, computational modeling