The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-directed-acyclic-graph-state-any-56e4

stable pending witness
2026-05-29 04:46:40 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a directed acyclic graph. State any key formula.
74 chars

Generation

A directed acyclic graph (DAG) is a graph consisting of vertices connected by directed edges, where it is impossible to start at any vertex and follow the directed edges back to that same vertex (no cycles). The "directed" aspect means edges have a specific direction, while "acyclic" means there are no loops. DAGs are commonly used in scheduling problems, dependency resolution, and representing hierarchical relationships. A key property is that every DAG has at least one **topological ordering**, which is a linear arrangement of vertices where for every directed edge (u,v), vertex u comes before vertex v in the ordering.
28 tokens in · 134 tokens out · 3490 ms · $0.0021

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
3498.4 ms
Base LLM
3490.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

04:46:40 received prompt_chars=74 verifiers=['scripture_anchors', 'theology_doctrine']
04:46:40 red_gate decision=pass reason=no disqualifying input patterns detected
04:46:43 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=134 latency_ms=3490.3 cost_usd=0.0021
04:46:43 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:46:43 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:46:43 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:46:43 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:46:43 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:46:43 signed hash_algo=sha256 hash=sha256:7dca4bb6e4498e4637e8ceba5f42e7990a1cb5413b70fc118e000890256a1f6d

Content hash

sha256:7dca4bb6e4498e4637e8ceba5f42e7990a1cb5413b70fc118e000890256a1f6d

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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