fractureCost
plain-language theorem explainer
fractureCost defines the J-cost applied to the ratio of strain energy to surface energy. Materials researchers deriving Griffith criteria within Recognition Science would cite this definition to normalize energy release against surface energy. It is a direct one-line wrapper around the Jcost function on the input ratio.
Claim. Let $e$ be strain energy and $s$ surface energy. The fracture cost is $J(e/s)$, where $J$ is the J-cost function satisfying the Recognition Composition Law.
background
The module derives fracture mechanics from the J-cost function at Tier B9. J-cost encodes the functional equation from the forcing chain (T5 J-uniqueness) and is applied here to the normalized ratio of strain energy release rate to surface energy per unit area. The module states the Griffith criterion: cracks propagate when $G$ exceeds $2γ$, with RS prediction $G_c = 2 J(φ) E a_0$ yielding approximately 14 J/m² for metals, consistent with observed KIc ranges.
proof idea
This is a one-line definition that applies Jcost to the quotient of the two real inputs.
why it matters
The definition feeds FractureCert, which certifies cost zero at equal energies, nonnegativity, surface factor positivity, and Paris exponent exactly 4. It fills the Tier B9 slot by connecting J-cost to material predictions via the phi-ladder and four-point symmetry (configDim + 1). It supports the surface energy factor J(φ) ≈ 0.118 and touches the falsifier of measurements outside the J(φ) E a0 band by more than 50%.
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