structural-modifications-exhaust-topology-and-converge
OUT derived (depth 6)
All structural modifications to the belief network — additions, retractions, replacements, and bulk operations — both exhaust their effects through complete bidirectional graph traversal (reaching all transitively affected nodes in forward propagation and backward retraction) and converge to stable states with network topology fully preserved (all antecedent and outlist references correctly rewired)
Summary
When you add, remove, replace, or bulk-edit nodes in the network, the effects ripple out completely — nothing gets missed — and the system always settles into a consistent state with no broken links or dangling references. This is currently not held because one of its supporting claims has been retracted.
Justifications
SL — Bidirectional traversal completeness (depth-5) guarantees no affected node is missed while topology-preserving convergence (depth-5) guarantees the graph structure remains consistent — together they ensure structural modifications are both exhaustive and stable
Antecedents (all must be IN):
- graph-traversal-is-complete-and-terminating-in-both-directions — Both forward truth propagation and backward retraction cascades achieve complete graph traversal (reaching all transitively affected nodes through all relationship types including outlists) with guaranteed termination, ensuring the system converges from both assertion and retraction operations.
- all-belief-replacements-converge-with-topology-preservation — All mechanisms for replacing or restructuring beliefs — individual supersession with view-consistent gating, batch deduplication with bidirectional reference rewiring, and import reconciliation with dual convergent modes — both preserve network topology (no dangling references) and converge deterministically to stable states.
Dependents
These beliefs depend on this one:
- topology-soundness-is-accurate-and-convergent — All topology-modifying operations are simultaneously accurate (complete dependency tracking ensures dedup survivor selection reflects the true graph structure) and convergent (structural modifications exhaust their effects through complete traversal and reach deterministic stable states) — topology is both correctly measured and correctly maintained.