topology

11 beliefs (4 IN, 7 OUT)

• IN bidirectional-modification-achieves-topology-completeness
  Bidirectional belief modification — contradiction resolution through traceable backtracking and defeat reversal with guided recovery — achieves topology-complete truth changes that are robust across all graph states, ensuring both directions of modification propagate through the complete dependency graph including under adverse conditions.
• OUT bulk-operations-converge-and-preserve-topology
  All bulk modification operations — deduplication (rewiring both antecedent and outlist references to survivors) and import/sync (dual reconciliation modes with namespace isolation) — both preserve network topology invariants and converge deterministically to stable states through fixpoint iteration and idempotent operations.
• OUT bulk-operations-preserve-topology-and-reconcile
  Both bulk modification operations — deduplication and import/sync — preserve network topology by rewiring justification references (both antecedent and outlist) to survivors or updated targets, while providing distinct reconciliation strategies (dedup via user-editable keep/retract plans, import via dual additive/remote-wins modes)
• IN dedup-is-topology-preserving-and-auditable
  Deduplication preserves network topology (rewrites both antecedent and outlist references to survivors), selects structurally-optimal survivors (most dependents with lexicographic tiebreak), and supports human oversight (KEEP/RETRACT markers in a user-editable plan format).
• IN dedup-survivor-selection-is-topology-reliable
  Deduplication reliably selects the structurally-optimal survivor in each duplicate cluster by choosing the node with the most dependents, and this selection is correct because the dependents index accurately reflects the justification graph.
• OUT dispute-resolution-is-topology-accurate
  Both dispute resolution mechanisms — intentional dialectical challenge/defend and automated contradiction resolution — propagate their effects through an accurate convergent topology with complete dependency tracking, ensuring every transitively affected node reaches its correct truth state after any dispute.
• OUT growth-converges-with-topology-and-assurance
  Knowledge growth simultaneously preserves universal multidimensional assurance and converges deterministically with topology preservation and guided recovery — the expanding knowledge base reaches stable states where all structural relationships are maintained and all safety guarantees hold, regardless of the modification path taken.
• OUT knowledge-equilibria-are-correction-convergent-and-topology-accurate
  Knowledge growth converges to negation-transparent equilibria with complete propagation fidelity, where every correction that shapes that convergence operates on accurate topology — dependency completeness ensures corrections propagate through the true graph structure, not an approximation.
• IN migrated-retraction-bulk-operations-preserve-topology-and-reconcile-j0
  review-beliefs: The import antecedent establishes dual reconciliation modes and truth state handling but does not mention rewiring justification references (antecedent or outlist), which the claim attributes to both operations. (defeats bulk-operations-preserve-topology-and-reconcile justification 0)
• OUT structural-modifications-exhaust-topology-and-converge
  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)
• OUT 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.