Ledger-Relative Probability and Born-Type Weight: A Bridge from Relative Determination to MOF–FDC–PFC (LRP v1)

This short theoretical note formulates a bridge between Relative Determination, the Minimal Ontological Foundation (MOF), Finite Distinguishability Closure (FDC), and Phase-Flow Coherence (PFC). The central claim is that probability need not be introduced as primitive global randomness. Instead, when a globally non-random structural realization is read through a finite internal ledger, multiple globally distinct realizations may be mapped to a single internal ledger state. If a later readout partitions this unresolved bundle into possible outcomes, the internal ledger is forced to represent the partition by normalized relative weights. The note first defines a ledger-relative probability representation using a finite ledger map from a structural closure domain to internal ledger states. It then shows that the domain is not a hidden-variable catalogue or an absolute classical value ledger, but a structural closure domain compatible with the relative-determination viewpoint. The second part specializes the abstract ledger-compatible measure to the PFC phase-bundle setting. Under phase invariance, orthogonal-sector additivity, non-negativity, and finite ledger closure, a functional-equation argument shows that the minimal admissible phase-bundle measure is proportional to the squared complex amplitude. This yields the Born-type weight as a specialization of ledger-relative probability. The paper does not claim that all physical probabilities are derived, nor that randomness is fundamental at the global level. Its purpose is to record a structural bridge: finite internal distinguishability forces probability representation, and PFC supplies the phase-measure specialization leading to Born-type weights.