HγC W5: Weighted and Linearized Transition Structure in Morphology Space

This paper introduces the first weighted and linearized local transition layer for the near-critical morphology sector of the HγC framework. Earlier W-series work established the temporal threshold for effective evolution, the temporal organization of occupied structured near-critical bands, the fluctuation-dependent reorganization layer, and the history-biased pathway layer for nearby morphology families. W5 takes the next justified step by lifting history-biased path organization into a weighted and linearized local transition structure. Effective accessibility weights, retention-biased coefficient organization, and local linear response are combined into a proto-kernel representation that organizes nearby reorganization as a unified weighted local transition sector without yet constructing a full path-summing kernel. Within this framework, local departures around occupied morphology families may be treated in controlled first-order form, and restoring, weakly retained, and switching-prone directions may be distinguished through local stability, relaxation, and switching-threshold language. The purpose of the paper is deliberately limited. W5 does not derive a microscopic kinetic equation, a canonical stochastic law, an amplitude formalism, or a Schrödinger-type effective evolution equation. Instead, it establishes the minimal weighted and linearized law-like layer that stands between the pathway layer fixed in W4 and the restricted quantum-effective threshold layer developed in W6.