The Density Clustering Computation Hypothesis: Computational Verification of Brain Science Signatures and a Unified Explanation Framework

This paper proposes the Density Clustering Computation Hypothesis: the brain's fundamental computation is density clustering of points in space, rather than numerical computation or symbolic manipulation. We construct a nonlinear oscillator network based on the Field Dynamic Number Equation (FDNE) as a computational model of density clustering, with a linear diffusion network as control, and systematically test 5 brain science signatures on a 2D grid (64x64=4096 nodes). Key findings: (1) FDNE networks produce avalanche -3/2 power law across all 11 parameter sets (exponent range [-1.71, -1.51], brain data: -1.5), while linear networks give -3.8 to -4.0 (2.5x deviation); (2) On regular grids, both FDNE and linear networks show 1/omega^4 spectra (beta~4), but introducing small-world topology causes FDNE networks to produce 1/f noise (beta=1.3-1.8, brain data: 1-2); (3) On the same small-world topology, both avalanche -3/2 and 1/f signatures are simultaneously satisfied (V10 dual-signature verification), while linear networks fail on both topologies; (4) FDNE networks qualitatively reproduce Weber's law and organized spatial patterns, while linear networks do not. We further classify density clustering computation from the field mathematics perspective, establishing a type space and positioning the brain's computation as 'multi-scale density clustering' (FDNE dynamics x small-world geometry x critical coupling), demonstrating that density clustering is not unique to brains but that brains employ a specific, experimentally distinguishable type. We then place 10 long-standing anomalies in brain science under the density clustering framework, obtaining self-consistent unified explanations. Based on experimental results and unified explanations, we propose a theoretical extension: perception is density clustering at full load, reasoning is the overflow effect of analytical pressure, and most brain energy consumption goes to perception rather than reasoning.