DAG convergence monitor

First state what is converging. Replica-state convergence, numerical or editorial iteration progress, and DAG terminal completion are different claims with different evidence. A stable-looking score, a quiet replica, or a completed node does not establish the other two.

1. Declare the monitored object and stopping rule

Record the object identity/version, observations and clock source, goal or invariant, criterion, window, owner, resource budget, and action authority. For an iterative artifact, use a task-defined verifier or rubric and compare changes on a fixed evaluation set. For a DAG run, inspect declared completion predicates and blockers. For replicated data, identify merge semantics, delivery assumptions, and the validity invariant.

flowchart LR
  O[Monitored object and revision] --> K{Kind of claim}
  K -->|fixed evaluation set| I[Iterative artifact progress]
  K -->|declared predicates| D[DAG terminal completion]
  K -->|merge and delivery assumptions| R[Replica-state convergence]
  I --> C[Task-specific stopping criterion]
  D --> C
  R --> C
  C --> E[Evidence, uncertainty, and action]

2. Evaluate the right evidence

An iterative monitor may report improvement, regression, oscillation, or insufficient observations without using arbitrary iteration counts or universal slopes. A changed evaluation set, goal, or artifact contract starts a new monitored revision; do not compare it as a continuous trend. A DAG monitor traces blockers, retries, cancellation confirmation, and effect receipts rather than assuming nodes “converge.”

Strong eventual convergence for a CRDT is a claim about replicas with the same updates reaching equivalent state under the CRDT's merge semantics; it does not show agent consensus, quality improvement, or terminal workflow success. CALM-style coordination results also concern particular formal program properties, not a generic rule to stop agents.

flowchart TB
  R[Replica observations] --> M[Same update set and defined merge]
  M --> V{Equivalent state?}
  V -->|yes| C[Replica convergence evidence]
  V -->|no or unknown| H[Hold claim and inspect missing updates]
  A[Artifact revisions] --> Q[Fixed verifier or rubric]
  Q --> P[Progress evidence or unknown]
  D[DAG node receipts] --> T[Completion predicates and blockers]
  T --> W[Terminal-state evidence]

3. Stop, continue, or escalate by criterion

Stop only when the declared criterion is met and the responsible authority permits closure. Continue when a specified experiment or remediation is still justified by budget and policy. Escalate when evidence conflicts, the criterion is impossible to evaluate, the budget/authority boundary is reached, or the object has changed. State the alternative actions and what observation would resolve uncertainty.

Worked positive case

An editorial DAG run r7 produces artifact versions v1, v2, then v3. Its fixed lint-and-review verifier shows improvement, and v3 passes the declared criteria with all required approvals present. Report success for r7/output-v3 only; the failure of v1 remains recorded. Repeated tuning used the development verifier; any final generalization claim needs fresh evaluation. Do not call this CRDT convergence.

Worked negative case

Two CRDT replicas are quiet for ten minutes but their update-set digests differ. The monitor reports insufficient convergence evidence and requests reconciliation. It must not infer agreement from elapsed time, nor recommend a quality acceptance decision.

4. Limits and sources

Return object identity, claim kind, observations, criterion, decision, authority, known gaps, and next observation. Read convergence claim types. Cite Jagadeesan and Riely (2018) for CRDT convergence scope and Hellerstein and Alvaro (2020) for coordination context. These sources do not supply a universal iteration budget, quality metric, or agent-consensus guarantee.

Monitoring neither starts iterations nor synthesizes their feedback. Use dag-iteration-detector to decide when a loop is needed, dag-feedback-synthesizer for feedback measures, dag-dynamic-replanner for strategy changes, and dag-pattern-learner for historical analysis. Return a recommendation and evidence; the executor/owner retains action authority.