defect_energy_pos
plain-language theorem explainer
Defect energy is strictly positive for any recognition defect. Researchers modeling thermodynamic stability and fault tolerance in Recognition Science ledger dynamics cite this to confirm that deviations from the J=0 ground state carry positive cost. The proof is a direct one-line term application of the defect's defining inequality.
Claim. Let $X : Ω → ℝ$. If $d$ is a recognition defect (a state with positive J-cost), then the associated defect energy satisfies $0 < E(d)$.
background
Recognition defects are states carrying positive J-cost, i.e., deviations from the J=0 ground state. The defect energy is defined directly as this J-cost value. The module develops an error-correction view of RS thermodynamics in which the ledger functions as a stabilizer code, defects act as errors, and the eight-tick cycle supplies the correction period.
proof idea
One-line term proof that applies the is_defect field of the RecognitionDefect structure, which asserts Jcost(X state) > 0, and matches it to the defect_energy definition.
why it matters
The result secures the basic positivity of defect energy required for the error-correction interpretation of RS thermodynamics. It supports later development of fault-tolerance thresholds and code-distance bounds via the phi-ladder. No immediate downstream theorems are listed, but the claim closes the elementary energy-positivity step in the module.
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