system-reaches-equilibrium-from-all-modification-paths
OUT derived (depth 5)
The system converges to deterministic stable states through every modification path: import achieves ordered convergent reconciliation (add → propagate → retract sequencing with fixpoint convergence), retraction cascades terminate through BFS with stop-on-unchanged, and both addition and removal operations reach equilibrium — no modification can leave the system in a non-convergent state.
Summary
This claim says that no matter how the belief network is modified — whether through importing new data, adding individual claims, or retracting existing ones — the system always settles into a stable, predictable state and never gets stuck in a loop or lands in an ambiguous configuration. It is currently marked OUT, meaning one or more of its supporting claims has been retracted, so this guarantee is not currently established.
Justifications
SL — Convergence from addition/removal establishes directional equilibrium, while ordered import reconciliation establishes procedural equilibrium — together they guarantee the system reaches a stable state regardless of how beliefs enter, change, or leave.
Antecedents (all must be IN):
- system-converges-from-addition-and-removal — The system reaches deterministic stable states from both directions: import reconciliation converges through fixpoint iteration and dual reconciliation modes when beliefs are added, while retraction cascades terminate through BFS with stop-on-unchanged when beliefs are removed — bidirectional convergence guarantees that no sequence of additions or removals leaves the network in an oscillating or indeterminate state.
- import-achieves-ordered-convergent-reconciliation — Import achieves correct final state through two reinforcing mechanisms: deliberate ordering discipline (add → propagate → retract) ensures deferred retractions don't corrupt intermediate states, while deterministic convergence (dual reconciliation modes reaching stable states, propagation terminating via fixpoint) ensures the result is unique and reproducible regardless of input ordering within each phase.
Dependents
These beliefs depend on this one:
- all-modifications-converge-with-reporting-and-recovery — Every modification — addition, removal, or correction — converges to a deterministic stable state with complete effect reporting and guided recovery, ensuring the system's operational history is fully transparent and every change can be understood and reversed.
- system-autonomously-converges-and-self-corrects — The system autonomously reaches and maintains consistent states through two complementary mechanisms: passive convergence ensures every modification path (import, retraction, dedup) reaches a deterministic stable state, while active self-correction (contradiction resolution and staleness detection) ensures consistency is preserved over time — combining equilibrium-seeking with consistency-maintaining.