The Mechanism · Gated-generation receipt

gen-state-the-centroid-of-a-triangle-precisely-and-explain-why-i-3dca

stable pending witness
2026-05-29 05:22:27 UTC · anthropic/claude-sonnet-4-5

Prompt

State the centroid of a triangle precisely and explain why it matters in 2-3 sentences.
87 chars

Generation

# Centroid of a Triangle **Definition:** The centroid is the point where the three medians of a triangle intersect. It is located at the average of the three vertices' coordinates: if the vertices are (x₁, y₁), (x₂, y₂), and (x₃, y₃), then the centroid is at ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). **Why it matters:** The centroid represents the triangle's center of mass or balance point—if you cut the triangle from uniform material, it would balance perfectly on a point placed at the centroid. This property makes it crucial in physics, engineering, and computer graphics for analyzing stability, calculating moments, and determining geometric centers.
28 tokens in · 179 tokens out · 3996 ms · $0.0028

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
4003.5 ms
Base LLM
3995.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0028

Trail

05:22:27 received prompt_chars=87 verifiers=['scripture_anchors', 'theology_doctrine']
05:22:27 red_gate decision=pass reason=no disqualifying input patterns detected
05:22:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=179 latency_ms=3995.9 cost_usd=0.0028
05:22:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:22:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:22:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:22:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:22:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:22:31 signed hash_algo=sha256 hash=sha256:13b2c30a97a088cf645081f5cb2588e32703853a04ddb59530a3da9e907c19b7

Content hash

sha256:13b2c30a97a088cf645081f5cb2588e32703853a04ddb59530a3da9e907c19b7

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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