The Mechanism · Gated-generation receipt

gen-state-a-minimum-spanning-tree-precisely-and-explain-why-it-m-719b

stable pending witness
2026-05-29 05:03:16 UTC · anthropic/claude-sonnet-4-5

Prompt

State a minimum spanning tree precisely and explain why it matters in 2-3 sentences.
84 chars

Generation

# Minimum Spanning Tree (MST) **Definition:** A minimum spanning tree of a weighted, connected graph is a subset of edges that connects all vertices together with no cycles, while minimizing the total sum of edge weights. **Why it matters:** MSTs solve critical real-world optimization problems like designing efficient telecommunication networks, road systems, and electrical grids where you need to connect all locations with minimum total cost. They form the foundation for approximation algorithms in harder problems like the traveling salesman problem and network clustering.
26 tokens in · 113 tokens out · 3629 ms · $0.0018

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
3643.9 ms
Base LLM
3629.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

05:03:16 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
05:03:16 red_gate decision=pass reason=no disqualifying input patterns detected
05:03:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=113 latency_ms=3629.4 cost_usd=0.0018
05:03:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:03:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:03:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:03:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:03:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:03:20 signed hash_algo=sha256 hash=sha256:9e584e33d633a2fcf1001a5e9a420aee60e60aa8b64be3f5d513eabbeb801429

Content hash

sha256:9e584e33d633a2fcf1001a5e9a420aee60e60aa8b64be3f5d513eabbeb801429

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.

Bring another teaching · Run a discernment