Coherence as Strong Equationhood: Side-Failures, Facing Conditions, and the Equationhood License under Structural Flow

This artifact defines Coherence-licensed strong equationhood under Structural Flow. Its central discovery is that, in this universe as presented, the Coherence hinge itself licenses equationhood when a candidate relation has earned structurally distinct side-burdens, distinct side-failures, relation-level co-dependency, irreducible relation-failure, and a shared structural invariant that neither side carries alone. The artifact distinguishes strong equationhood from ordinary equality, identity, definition, convention, compatibility, analogy, accounting shorthand, Recognition-stable equivalence, Boundary-threshold relations, asymptotic convergence, symmetry-protected equivalence, relation packages, and side-completion terms. It does not replace ordinary mathematics, empirical testing, formal proof, domain expertise, or measured physical derivation. Its purpose is narrower: to provide a structural-warrant method for deciding when an equation-like relation has been earned under Structural Flow and when a weaker relation-status should be named instead.