structuralSafetyCert
plain-language theorem explainer
Structural safety is certified by instantiating the record with exactly five failure modes and a canonical safety threshold. This supplies the engineering application of the J-cost model in which the factor of safety equals phi. Civil engineers working inside the Recognition Science framework would cite the certificate to confirm that a design respects the five canonical modes of yielding, buckling, fatigue, fracture and creep. The construction is a direct record definition that pulls the mode count from the decide-proven failureModeCount lemma
Claim. The structural safety certificate asserts that the set of failure modes has cardinality five and that the safety threshold is supplied by CanonicalCert.
background
In the Recognition Science treatment of structural engineering the factor of safety is the reciprocal of the working-stress to ultimate-strength ratio. The associated J-cost is minimised when this ratio equals phi inverse, yielding the optimal factor phi that lies inside the empirical range of building codes. Five canonical failure modes are identified: yielding, buckling, fatigue, fracture and creep; their number equals the configuration dimension D = 5. The upstream theorem failureModeCount establishes that the cardinality of FailureMode is exactly five by direct decision. The module imports CanonicalJBand to supply the CanonicalCert type used for the threshold.
proof idea
The definition constructs the StructuralSafetyCert record by assigning the five_failure_modes field the result of failureModeCount and the safety_threshold field the value cert. No additional tactics are invoked; the cardinality proof is inherited verbatim from the decide tactic inside failureModeCount.
why it matters
This definition closes the engineering module by supplying the concrete certificate that links the J-cost formalism to practical structural safety. It inherits the five-mode count from parallel results in materials fatigue, institutional governance and sociology, confirming the universality of the configuration dimension across domains. The safety threshold implements the RS-optimal factor of safety phi, providing a direct bridge from the abstract forcing chain to civil-engineering practice. No downstream uses are recorded in the current graph.
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