NHF Core v2.1: Formal Core for the Hypergraph Fractal Neuron

摘要

Description This deposit releases NHF Core v2.1, a technology-agnostic formal kernel for the Hypergraph Fractal Neuron (NHF). Unlike NHF v1—which is presented as an architectural implementation profile (packet-based signaling, meta-dendritic micro-processing, multiscale memory and decoding)—NHF Core v2.1 isolates the minimal mathematical structure required to define NHF as a governed, cost-aware adaptive system that can be instantiated across different stacks (ANN, SNN, hybrid, edge, robotics). The core formalizes a directed graph of units and introduces canonical state variables for both neurons and synapses: the neuron state ((\psi,\phi,\sigma,m)) captures latent content, phase/regime, epistemic uncertainty, and compressed fractal memory; the synapse state ((w, V^{(c)}, \tau)) captures strength, contextual modulation channels, and latency/energy cost. A unified objective functional (J) aggregates task performance, harmonic coherence, explicit latency/cost accounting, and normative penalties. Crucially, normative constraints are treated as first-class components of learning dynamics via projected updates onto an admissible set induced by an exogenous normative field (E(t)). This provides a principled mechanism for constraint-aware adaptation, budget-governed routing, and auditability-by-design (update traces, activated constraints, and per-edge cost contributions). This release includes a compatibility layer mapping NHF v1 modules (MPP/PIM/EAU/PD/MD/EAC) into the v2.1 core variables, an expanded glossary, and a compact taxonomy of potential uses. The document is intended as a reference “kernel/specification” for future implementations and empirical evaluations rather than a finalized benchmark claim. Included files Compiled PDF (primary artifact) LaTeX source package (reproducibility and future versions)