**Definition (Law IV - The Grace Dynamics):**
1. Proxy Measures: Grace has correlates: [[011_D2.2_Chi-Field-Properties|chi-field]] level, virtue outcomes, peace measures, integration metrics.
2. Information Interpretation: Grace is information. Information is measurable.
3. Operational Definition: Grace = chi-field increase after divine encounter. This is operationally definable.
4. Historical Precedent: Heat was once considered non-material. Now it's energy.
1. Not Deterministic: The equation describes tendencies, not determinism. G_{\text{ext}} is freely given.
2. Law vs. Cause: The equation describes how grace works, not why God gives it.
3. Sacramental Analogy: Sacraments have both spiritual and material aspects. This equation captures the lawful aspect.
4. Freedom Preserved: Divine freedom is in G_{\text{ext}}. The equation describes what happens after grace is given.
1. Completeness: Source, sink, and feedback are the minimal complete set.
2. Physical Analogy: All dissipative systems have these three: input, loss, and internal generation.
3. Parsimony: Fewer terms would be incomplete. More would need justification.
4. Falsifiability: The specific form makes predictions. Wrong form means wrong predictions.
1. Product Form: The product captures the idea that both are needed. High F with low C or low F with high C gives little feedback.
2. Correlation Allowed: Even correlated variables can multiply. The correlation affects joint distribution, not the equation form.
3. Physical Analogy: Power = voltage times current. These are correlated but meaningfully multiply.
4. Refinement Possible: If needed, \beta F C can be replaced with \beta g(F, C) for more complex interaction.
1. Physical Determination: The constants are determined by the underlying physics of the chi-field.
2. Empirical Measurement: In principle, constants can be measured from grace dynamics observations.
3. Universal vs. Individual: Some constants may be universal, others may vary between individuals.
4. Falsifiable: Specific predictions depend on specific values. Wrong values give wrong predictions.
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Structure of Grace Evolution:
This has three terms:
1. Source: G_{\text{ext}} - external divine input
2. Sink: -\gamma_G G - decay proportional to current grace
3. Feedback: \beta F C - faith-consciousness amplification
Physical Interpretation:
Definition 1 (Grace Dynamics Operator):
Definition 2 (Grace Evolution Map):
satisfying \partial_t \Phi_t^G = \mathcal{D}_G \circ \Phi_t^G.
Definition 3 (Equilibrium Grace):