The Mechanism · Gated-generation receipt

gen-explain-the-centroid-of-a-triangle-as-you-would-to-a-capable-3f0b

stable pending witness
2026-05-29 07:38:26 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the centroid of a triangle as you would to a capable student, in 3-4 sentences.
87 chars

Generation

The centroid is the point where all three medians of a triangle intersect. A median is a line segment connecting a vertex to the midpoint of the opposite side, and remarkably, all three medians always meet at a single point. This point, the centroid, is located exactly 2/3 of the way along each median from any vertex to the opposite side's midpoint. You can think of the centroid as the triangle's "center of mass" or balance point—if you cut the triangle out of cardboard, it would balance perfectly on a pencil tip placed at the centroid.
31 tokens in · 130 tokens out · 3993 ms · $0.002

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
4000.3 ms
Base LLM
3992.7 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.002

Trail

07:38:26 received prompt_chars=87 verifiers=['scripture_anchors', 'theology_doctrine']
07:38:26 red_gate decision=pass reason=no disqualifying input patterns detected
07:38:30 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=130 latency_ms=3992.7 cost_usd=0.002
07:38:30 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:38:30 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:38:30 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:38:30 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:38:30 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:38:30 signed hash_algo=sha256 hash=sha256:2703e1509d2fe8388c4d3dbca0735769a2c9e43f60b4936c413b2898fd265587

Content hash

sha256:2703e1509d2fe8388c4d3dbca0735769a2c9e43f60b4936c413b2898fd265587

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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