IndisputableMonolith.Mathematics.ProbabilityTheoryFromRS
This module derives core probability concepts from the Recognition Science J-cost function. It establishes that zero J-cost corresponds to certain events with probability one and introduces related axioms. Researchers grounding probability in RS foundations would cite it. The module organizes definitions and relations built directly on the imported Cost module.
claimCertain events satisfy $J=0 \to P=1$, with Kolmogorov axioms holding for the probability measure induced by the cost function.
background
The module resides in the Mathematics domain and imports Mathlib together with the Cost module. The Cost module supplies the J-cost function and its algebraic properties, including the Recognition Composition Law. The module develops probability by linking cost values to event probabilities, with the central relation that zero cost implies unit probability for certain events.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the probabilistic layer required for higher RS derivations. It connects the J-cost to probability measures, enabling later steps that interpret physical structures through cost. No downstream uses are recorded yet.
scope and limits
- Does not extend to continuous or infinite probability spaces.
- Does not derive the full set of Kolmogorov axioms without further hypotheses.
- Does not address interpretations in quantum mechanics or statistical physics.