PH-BC-002

Name: Boundary flux imbalance (divergence theorem)

Severity: warning

Input modes: adapter+dump

Scope separation (read first): PH-BC-002’s external validation separates (i) a harness-level Gauss-Green correctness fixture from (ii) the production rule’s Laplace and Poisson divergence-theorem verdict behavior. The production rule src/physics_lint/rules/ph_bc_002.py covers the scalar Laplace/Poisson divergence-theorem imbalance — narrower than the F1 mathematical anchor (the general Gauss-Green / divergence theorem for arbitrary C¹ vector fields). CITATION.md, README, and test docstrings do not imply broader production coverage than the rule provides.

Boundary flux imbalance check: for a Laplace-harmonic field u, the rule verifies ∫_Ω Δu dV ≈ 0 (equivalently ∫_{∂Ω} ∂u/∂n dS ≈ 0 by Gauss-Green); for a Poisson field (-Δu = f) it verifies ∫_Ω Δu dV + ∫_Ω f dV ≈ 0. Both compare against relative thresholds of 0.01 / 0.1 against ||u||_{L²}.