critical-operations-converge-to-fixed-points
OUT derived (depth 1)
The system's three critical reconciliation operations are all convergent: agent sync produces no changes on re-run with identical input, dependents index rebuilding yields identical results on repeated execution, and truth recomputation iterates to a fixpoint — ensuring the system reaches stable consistent state regardless of operation ordering.
Summary
The three core maintenance operations — syncing agent data, rebuilding dependency indexes, and recomputing truth values — all stabilize on their own, meaning running any of them a second time produces no further changes. This property is currently not established because one or more of its supporting claims have been retracted, so the system cannot currently guarantee that these operations reach a consistent steady state regardless of the order they run in.
Justifications
SL — Three independent convergence properties across sync, index maintenance, and truth computation establish system-wide fixed-point behavior
Antecedents (all must be IN):
- sync-agent-idempotent — Two consecutive `sync_agent` calls with identical file content produce zero additions, removals, and updates on the second call
- rebuild-dependents-is-idempotent — Calling `_rebuild_dependents()` twice in succession produces identical `dependents` sets on every node.
- recompute-all-uses-fixpoint — `recompute_all` iterates until no truth values change, bounded by `len(nodes) + 1` iterations, handling cascading dependencies from arbitrary node ordering.
Dependents
These beliefs depend on this one:
- all-reconciliation-converges-deterministically — All reconciliation operations converge deterministically to stable states: individual propagation terminates via BFS with stop-on-unchanged, while system-wide operations (sync, dependents rebuild, recompute) all reach idempotent fixed points — the system has no divergent operational paths.