HγC W6: A First Schrödinger-Type Effective Description for Near-Critical Fluctuation Modes

This paper introduces the first restricted quantum-effective threshold layer of the HγC framework. Earlier W-series work established that the microscopic update parameter τ is not physical time, that effective time becomes meaningful only after sufficient mesoscopic stabilization, that structured near-critical bands may undergo temporal organization and fluctuation-dependent reorganization, and that nearby morphology families may be connected through history-biased transition paths and weighted local transition structure. W6 takes the next justified step by asking whether part of this stabilized local transition sector may be lifted into a first quantum-effective description. The answer proposed here is deliberately restricted: such a lift applies not to primitive relational events or to the full microscopic substrate, but only to stabilized mesoscopic fluctuation modes within the local near-critical sector. Starting from the weighted and linearized local transition structure developed in W5, the paper introduces an amplitude-like rewriting of selected stabilized mode directions and formulates a minimal Schrödinger-type effective evolution law over emergent effective time. The scope of the paper is deliberately limited. W6 does not propose a microscopic quantization of the relational substrate, a universal Hilbert-space completion, a full path-integral construction, a quantum-field-theoretic description, a measurement theory, or a graviton theory. Instead, it establishes the minimal regime-limited bridge from weighted local transition structure to amplitude-like and Schrödinger-type mode description in a stabilized near-critical mesoscopic sector.