Paper B-H1: The Cascade Exponent Is Regime-Bounded — A Cross-Substrate Test of DFG H1

This record contains Document 06 of the DFG Empirical Programme submission package: Paper B-H1 — The Cascade Exponent Is Regime-Bounded: A Cross-Substrate Test of DFG H1. This synthesis paper evaluates the DFG H1 cascade prediction across synthetic, digital, neural-culture, and in-vivo neural substrates. H1 originally predicted a Governance Cascading Universality Class (GCUC) in which cascade-size distributions follow P(s) ~ s-τ with τ ≈ 3/2. This paper refines that claim into a regime-bounded map rather than a universal exponent law. The paper separates two sub-claims:1. Operating-point criticality, measured by branching ratio σ ≈ 1.2. Exponent universality, measured by τ ≈ 3/2. Key findings include:- Neural operating-point criticality is strongly supported: σ ≈ 1 across 24 independent neural subjects spanning five substrates, with the in-vivo cortex cohort additionally tested under three avalanche-detection protocols for 44 subject × protocol observations.- Under LFP-band-equivalent detection on in-vivo cortex, σ = 1.00 exactly in 10/10 subjects.- The universal neural τ ≈ 3/2 claim is not supported in tested neural data: τ_tail never enters [1.3, 1.7] across the tested neural subject × protocol observations.- A targeted synthetic regime search locates the joint τ ≈ 1.5 and σ ≈ 0.87 criterion in a Manna conservative cascade rule on Watts-Strogatz small-world topology with low dissipation.- This Manna + Watts-Strogatz low-dissipation regime is finite-size robust across N = 1000–5000. The bounded conclusion is that DFG H1 is not a universal τ ≈ 3/2 law. Instead, H1 decomposes into an operating-point criticality claim, which is strongly supported in tested neural systems, and an exponent-universality claim, which is regime-bounded: incompatible in tested neural protocols, but located in a specific synthetic conservative-cascade small-world regime. This record is part of the DFG Empirical Programme submission package. It assumes the regime-atlas methodology established in Document 01, the Compatibility Atlas v1.3. Cell-level incompatibility should be interpreted as a regime-boundary marker rather than theory-level falsification.