The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-law-of-sines-answer-concisel-4de5

stable pending witness
2026-05-29 02:44:11 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

The law of sines establishes a proportional relationship between the sides of a triangle and the sines of their opposite angles, allowing us to solve for unknown sides or angles when given partial information. It's particularly significant because it works for any triangle (not just right triangles) and is essential for applications in surveying, navigation, astronomy, and engineering where indirect measurements are needed.
30 tokens in · 81 tokens out · 2586 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
2593.6 ms
Base LLM
2586.3 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0013

Trail

02:44:11 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
02:44:11 red_gate decision=pass reason=no disqualifying input patterns detected
02:44:13 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=81 latency_ms=2586.3 cost_usd=0.0013
02:44:13 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:44:13 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:44:13 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:44:13 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:44:13 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:44:13 signed hash_algo=sha256 hash=sha256:bd7e7377f5e39b8cf78fd7ef1b456770b9d8e629ea9ffd60b46e3f2b0969d6e4

Content hash

sha256:bd7e7377f5e39b8cf78fd7ef1b456770b9d8e629ea9ffd60b46e3f2b0969d6e4

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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