parisLawExponent
plain-language theorem explainer
The declaration defines the Paris law exponent as the natural number 4 in the Recognition Science model of fracture mechanics. Materials researchers would cite it when writing the fatigue crack growth rate as da/dN = C (ΔK)^m with the exponent fixed by spatial symmetry. The definition is a direct constant assignment that matches configDim plus one.
Claim. The Paris law exponent is defined as $m = 4 = d + 1$, where $d = 3$ denotes the number of spatial dimensions.
background
The module develops fracture mechanics from the J-cost function. It recalls the Griffith criterion that a crack propagates when the strain energy release rate G meets or exceeds twice the surface energy per unit area. The Recognition Science model supplies the critical value G_c = 2 J(φ) E a_0, which evaluates numerically to roughly 14 J/m² for metals and lies inside the observed range of fracture toughness.
proof idea
The declaration is a direct definition that assigns the constant 4.
why it matters
It supplies the exponent field required by the FractureCert structure that certifies the full set of fracture properties. The value implements the Recognition Science prediction that the exponent equals configDim plus one, where the spatial dimension count of three follows from the eight-tick octave in the unified forcing chain. The module documentation links the choice to consistency with empirical KIc values between 10 and 100 J/m².
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