born_weight
plain-language theorem explainer
Born weight assigns to each recognition action C_I the unnormalized probability weight exp(-C_I). Researchers deriving Born's rule from gravitational coherence collapse cite it when converting recognition costs into outcome probabilities. The definition is a direct exponential mapping with no further reduction.
Claim. The Born weight for outcome I with recognition action $C_I$ is $w_I = e^{-C_I}$. The probability for that outcome is then $w_I$ divided by the sum of weights over all outcomes.
background
The Coherence Collapse module formalizes the link between gravitational recognition costs and quantum measurement. Recognition action is the path integral $C[γ] = ∫ J(r(t)) dt$ of the J-cost function. Residual rate action is defined as $A = -ln(sin θ_s)$ for geodesic separation angle θ_s, with the central identity C = 2A relating the two.
proof idea
The definition is a direct one-line assignment of the real exponential function to the negated input recognition action C_I.
why it matters
This definition supplies the weight map used by born_weight_is_sin_sq (which recovers sin²θ under C = 2A) and born_weight_pos, and appears inside the CoherenceCollapseCert structure. It realizes the module claim that P(I) = exp(-C_I)/Σ exp(-C_J) equals |α_I|², closing the recognition-to-Born-rule bridge in the Recognition Science framework.
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