The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-minimum-spanning-tree-state-any-k-e569

stable pending witness
2026-05-29 03:43:32 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a minimum spanning tree. State any key formula.
73 chars

Generation

A minimum spanning tree (MST) is a subset of edges in a connected, weighted graph that connects all vertices together with the minimum total edge weight, while containing no cycles. It forms a tree structure with exactly **n - 1 edges** for n vertices. Common algorithms to find an MST include Kruskal's algorithm (which sorts edges and adds them if they don't create a cycle) and Prim's algorithm (which grows the tree from a starting vertex). The key formula is that an MST has exactly **|V| - 1 edges**, where |V| is the number of vertices.
26 tokens in · 133 tokens out · 3184 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
3190.2 ms
Base LLM
3184.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

03:43:32 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
03:43:32 red_gate decision=pass reason=no disqualifying input patterns detected
03:43:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=133 latency_ms=3184.0 cost_usd=0.0021
03:43:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:43:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:43:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:43:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:43:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:43:35 signed hash_algo=sha256 hash=sha256:9e424b1a3029cac15265c449e97c1fe9ff8eaaf9428724b352152b76dcc8fef6

Content hash

sha256:9e424b1a3029cac15265c449e97c1fe9ff8eaaf9428724b352152b76dcc8fef6

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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