Regulated Coordination Load and Conditional Logarithmic Hierarchy Scaling: A Minimal Phenomenological Model with Explicit Buffering and Setpoint Assumptions

Abstract

Coordination demand can outgrow primitive processing capacity, while buffering and hierarchy may reduce the remaining burden. The paper studies a regulated coordination-load representation through temporal regulation and cross-sectional sizing. A generalized-logistic activity controller approaches a prescribed setpoint; bounded capacity drift gives an attracting load band. A separate classical tracking law represents capacity actuation. Static sizing yields minimum integer depth, and positive residual logarithmic burden with positive finite average layer gain gives logarithmic growth. A residual-work realization and joint uncertainty bounds supply a measurement interpretation subject to every-tier service checks. The proposed contribution is a restricted synthesis: common coefficients must predict structural perturbations, size-by-depth separability and a cross-response relation between activity gain and required depth. Four prospective tests, matched rival models and noncircular measurement rules are specified. Published agent, social-group and production summaries constrain numerical mappings without fitting GGT coefficients. A separately calibrated companion bridge yields a further conditional cascade-response test. Synthetic and deterministic checks support the calculations; empirical adequacy, priority, physical criticality and universal hierarchy benefits are not established. Note on Version 2.0: this version revises the registered v1.0, titled "Self-Tuned Criticality and the Logarithmic Hierarchy Law" (about 3,600 to 10,700 words). The title and framing move from self-tuned criticality to regulated coordination load with explicit buffering and setpoint assumptions; literature integration is dated and a claim-level chronology is recorded in Appendix B.3. No independent domain experiment, raw-data fit or public prediction registration has been performed. Files: the v2.0 manuscript and a supplement archive with integrity and reproduction instructions, source ledgers, a manifest and SHA-256 checksums. The v1.0 simulation script remains available in the v1.0 record. Series Paper I of the Governance Geometry Theory (GGT) papers within the author's Deficit-Fractal Governance (DFG) framework.