The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-law-of-cosines-answer-concis-1726

stable pending witness
2026-05-29 04:40:47 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the law of cosines? Answer concisely in 2-3 sentences.
82 chars

Generation

The law of cosines generalizes the Pythagorean theorem to work for any triangle, not just right triangles. It allows you to find unknown sides or angles in a triangle when you know either two sides and the included angle, or all three sides. This makes it essential for solving oblique triangles in fields like navigation, surveying, and engineering.
30 tokens in · 78 tokens out · 2365 ms · $0.0013

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
2377.4 ms
Base LLM
2364.8 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

04:40:47 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
04:40:47 red_gate decision=pass reason=no disqualifying input patterns detected
04:40:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=78 latency_ms=2364.8 cost_usd=0.0013
04:40:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:40:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:40:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:40:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:40:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:40:49 signed hash_algo=sha256 hash=sha256:6b27a123113471d67fe9507ae30ccf643c5ac49700ee46bc29ee84dece98d1a5

Content hash

sha256:6b27a123113471d67fe9507ae30ccf643c5ac49700ee46bc29ee84dece98d1a5

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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