bayesFactorThreshold
plain-language theorem explainer
bayesFactorThreshold defines the barely-convincing Bayes factor threshold as the golden ratio φ. Bayesian statisticians applying Recognition Science to belief revision cite this constant when marking the transition from negligible to detectable evidence in likelihood ratios. The definition is a direct assignment to the framework constant phi, with no further computation in the body.
Claim. The Bayes factor threshold is the constant $B = φ$, where $φ$ denotes the golden ratio.
background
The module develops Bayesian updating from J-cost, where posterior probability is proportional to likelihood times prior and information gain is measured by KL divergence. RS predicts that the minimum detectable update occurs at J-cost J(φ) ≈ 0.118, so the canonical barely-convincing threshold is the Bayes factor B = φ ≈ 1.618 while B = φ² ≈ 2.618 supplies moderate evidence, aligning with Kass-Raftery (1995) intervals for positive evidence. The module imports Cost for Jcost and Constants for phi, establishing the structural setting with zero axioms or sorrys.
proof idea
The declaration is a one-line definition that directly assigns the value phi.
why it matters
This supplies the numerical threshold required by BayesianUpdateCert (which records threshold_gt_one and moderate_gt_two) and by the theorems bayesFactorThreshold_cost (Jcost = phi - 3/2) and bayesFactorThreshold_gt_one. It realizes the module's RS prediction for the barely-convincing threshold and links to the self-similar fixed point phi from the forcing chain. The falsifier stated in the module is any empirical study placing the subjective threshold consistently outside (1.5, 4.0).
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