Quantum Structural Theory of Harmony (QSTH 6.0 Revised) — Born Set Invariants: From Probability Readout to Informational Admissibility

Abstract

QSTH 6.0 Revised — Born Set Invariants returns to the foundational role of the Born rule within the broader architecture of the Quantum Structural Theory of Harmony (QSTH). Rather than treating the Born rule solely as a probabilistic output of quantum measurement, the work examines its informational representation and its possible role as a bridge between quantum amplitude, effective entropic balance, record formation, and informational admissibility. The central observation is that the Born readout can be mapped into an informational representation through the relation ΔS_coh = −ln|ψ|². This provides a direct bridge between the standard quantum-mechanical probability readout and the later QSTH ledger quantities, including S_eff, TiM, Settlement Dynamics, and Entropic Zero. The publication introduces Born Set Invariants as a candidate class of informational quantities, relations, or structures whose meaning may survive admissible changes of representation, projection, or system readout. It further distinguishes probability from admissibility, asking whether a non-zero probability is sufficient for the formation of a stable physical record. Within this framework, S_eff is developed as an informational ledger between coherent and reductive contributions, while Ψ and κ(Γ) are retained respectively as candidate regime-signature and regime-sensitivity descriptors. These quantities are not proposed as new forces or fundamental constants. QSTH 6.0 Revised does not modify or replace the Born rule and does not propose a new quantum mechanics. The Born rule remains a CANON experimental and mathematical anchor. The purpose of the work is instead to construct a disciplined and auditable informational language linking probability → information → ledger → invariance → admissibility → regime. The publication forms the first pillar of the QSTH Revised Trilogy and provides the informational entry point for the subsequent treatment of temporal readability, settlement, and Entropic Zero. Part I of the QSTH Revised Trilogy: Probability → Readability → Settlement. QSTH 6.0 Revised establishes the Born Readout Ledger and provides the informational foundation for QSTH 5.0 Revised — The Entropic Clock Revisited and QSTH 6.1 Revised — Entropic Zero Revisited.