HγC W4: History-Biased Transition Paths in Morphology Space

This paper introduces the first controlled pathway description for structured near-critical reorganization in the HγC framework. Earlier W-series work established the temporal threshold for effective evolution, the temporal organization of occupied structured near-critical bands, and the fluctuation-dependent layer in which occupied mean morphology may display metastability, weak switching, and history-sensitive reorganization. W4 takes the next justified step by shifting the near-critical morphology sector from state description to path description. Departures from occupied mean morphology are re-read as partial traversals through morphology space, and a minimal vocabulary of reorganization paths is introduced. The paper distinguishes local drift paths, metastable detours, weak switching paths, and tail-mediated paths, and argues that such traversals need not be path-neutral once retained mesoscopic history is taken seriously. Nearby reorganization routes may differ in accessibility, and forward and backward local reorganization need not be dynamically equivalent. The scope of the paper is deliberately limited. W4 does not derive a microscopic kinetic equation, construct a full transition kernel, introduce a path-summing formalism, or enter a Schrödinger-type or QFT-type effective description. Instead, it establishes the first pre-kernel pathway layer of the near-critical morphology sector: the minimal framework in which structured mesoscopic bands may be said not only to persist and fluctuate, but also to reorganize through explicit history-biased transition paths across nearby morphology families.