Functional Audit and Candidate-Coverage Diagnostics for Connection Dynamics

Under frozen criteria and in artificial environments, some relation combinations pass an existence gate, a task-synergy gate, and a limited set of control gates; offering identity opportunities to historically selected targets can raise retention rates on some seeds. This supports a coverage-and-opportunity diagnosis in specific models. It does not support blind discovery, full strong generalization, reflexive organization, phenomenal consciousness, or physical non-propagation. The paper also gives a sufficient condition for boundedness in an analytic model family, a convergence result for fixed structure, and counterexamples showing that positive task synergy implies neither state non-additivity nor topological specificity. v0.3 adds a post hoc structural decomposition of the archived synergy (Section 5.6): 423 of the 431 strong records (98.1%) are same-target pairs whose raw-weight effects are exactly additive and whose synergy is a threshold-crossing sum; the 8 records with genuine cross-identity interaction are about two orders of magnitude weaker. Scripts and per-record output are in case_study.zip. Unpublished discussion draft; not peer reviewed. Sections other than 5.6 are translated from the Chinese v0.2 draft.