ΔΦ MASTER SPINE v5 ΔΦ CROSS-DOMAIN TRANSITION DESCRIPTOR Operator, Spectral, Topological, and Path-Integral Framework for Precursor Structure Detection in Transition Systems (v5.0)

This manuscript presents Version 5 of the ΔΦ Cross-Domain Transition Descriptor, proposing ΔΦ = ρ × v as a candidate measurable precursor structure descriptor for unstable transition systems. The framework integrates operator transport theory, spectral collapse dynamics, topological persistence evolution, and path-integral likelihood shift analysis into a unified adversarial testing structure.The document is intentionally structured to invite independent falsification and includes explicit calibration methods, null hypothesis testing batteries, domain proxy mappings, rejection criteria, and tiered acceptance thresholds. Partial validation is considered scientifically valuable even if cross-domain universality is rejected.This work is positioned as a transition detection synthesis framework rather than a replacement for domain-specific physical or biological models.