IndisputableMonolith.Measurement.BornRule
This module derives two-outcome measurement probabilities directly from recognition weights. Quantum foundations researchers would cite it when linking recognition costs to Born-rule statistics. The module imports the C=2A bridge and path-action interface, then normalizes weights into probabilities via sibling definitions and theorems.
claimFor a two-outcome measurement with recognition costs $C_1, C_2$, the probabilities are $p_1 = C_1/(C_1+C_2)$, $p_2 = C_2/(C_1+C_2)$, obtained by normalizing the weights that satisfy $C=2A$ for two-branch geodesic rotations.
background
The module belongs to the Measurement domain. It rests on two upstream modules. The C2ABridge states: 'This module proves the central equivalence between recognition cost C and the residual-model rate action A. Main theorem: For any two-branch geodesic rotation, C = 2A (exactly)'. The PathAction module supplies: 'Lightweight interface for recognition paths and their action/weights. Heavy measure-theoretic lemmas (piecewise additivity, domain shifts, etc.) are intentionally omitted to keep the build surface stable for paper exports.'
proof idea
This is a definition module with supporting theorems. It introduces TwoOutcomeMeasurement as the setup, defines prob and probabilities_normalized, then states born_rule_from_C and born_rule_normalized. The argument applies the imported C=2A equivalence and path weights to obtain the normalized probabilities.
why it matters in Recognition Science
The module supplies the explicit map from recognition weights to two-outcome probabilities, completing the measurement step that follows the C=2A bridge. It feeds the broader derivation of the Born rule inside Recognition Science by turning path actions into observable statistics. No downstream theorems are recorded yet.
scope and limits
- Does not treat measurements with more than two outcomes.
- Does not include full measure-theoretic lemmas on path additivity.
- Does not derive probabilities for continuous spectra or entangled states.
- Does not address time evolution or multi-particle extensions.