convergence-produces-evaluation-invariant-equilibria
OUT derived (depth 7)
The system converges to equilibrium states where truth evaluation is transformation-invariant: regardless of the mutation path taken — order of additions, retractions, challenges, imports — the converged state evaluates all beliefs identically, because autonomous convergence reaches deterministic stable states and truth evaluation is agnostic to both temporal context and structural origin.
Summary
No matter what sequence of changes you make — adding, retracting, challenging, or importing — the system always settles into the same final state and evaluates every claim the same way once it gets there. This means the history of how the system arrived at its current configuration is irrelevant; only the current structure of justifications matters, making the system path-independent and deterministic.
Justifications
SL — Autonomous convergence (depth-6) reaching deterministic equilibria combined with transformation-invariant evaluation (depth-6) means the final state is path-independent
Antecedents (all must be IN):
- 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.
- truth-evaluation-is-transformation-invariant — Truth evaluation produces identical results regardless of both temporal context (when a justification was attached — at node creation vs. later addition) and structural transformation (premise → justified node via challenge) — all forms of node history and identity change are invisible to the evaluation function, making truth a pure function of current network state.
Dependents
These beliefs depend on this one:
- autonomous-convergence-produces-documented-equilibria — The system's autonomous convergence to evaluation-invariant equilibria generates consistently identifiable artifacts with deterministic traceable history at every step — every equilibrium state is not merely stable and transformation-invariant but fully explainable through its documented convergence path.
- canonical-equilibria-are-negation-transparent — The system converges to canonical evaluation-invariant equilibria where negative semantics are fully transparent — the final stable state is determined solely by the logical content of justifications, independent of both the transformation path taken and whether beliefs were established through positive assertion or negative defeat.
- convergent-equilibria-have-complete-propagation-fidelity — System convergence to evaluation-invariant equilibria achieves complete propagation fidelity — every truth change cascades to every transitively dependent node including outlist dependents — and topology preservation covers all reference types, provided the dependency tracking assumption holds.
- equilibrium-trajectory-is-deterministic-and-referenceable — Every convergence trajectory toward an evaluation-invariant equilibrium generates consistently identifiable artifacts with deterministic traceable events, enabling complete post-hoc reconstruction of how each stable state was reached.