The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-centroid-of-a-triangle-state-an-ddda

stable pending witness
2026-05-29 04:47:52 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the centroid of a triangle. State any key formula.
76 chars

Generation

The centroid of a triangle is the point where the three medians (lines from each vertex to the midpoint of the opposite side) intersect. It serves as the triangle's center of mass or balance point. The centroid divides each median in a 2:1 ratio, with the longer segment being closer to the vertex. If the vertices of a triangle are at coordinates (x₁, y₁), (x₂, y₂), and (x₃, y₃), the centroid is located at **G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)**.
28 tokens in · 154 tokens out · 2713 ms · $0.0024

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
2718.9 ms
Base LLM
2712.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

04:47:52 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
04:47:52 red_gate decision=pass reason=no disqualifying input patterns detected
04:47:55 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=154 latency_ms=2712.8 cost_usd=0.0024
04:47:55 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:47:55 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:47:55 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:47:55 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:47:55 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:47:55 signed hash_algo=sha256 hash=sha256:10480d0979cdce62a308d8b85d7621da7c13303ea0c3f861d551b9731a522f86

Content hash

sha256:10480d0979cdce62a308d8b85d7621da7c13303ea0c3f861d551b9731a522f86

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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