The Mechanism · Gated-generation receipt

gen-explain-the-law-of-sines-as-you-would-to-a-capable-student-i-495e

stable pending witness
2026-05-29 08:50:16 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the law of sines as you would to a capable student, in 3-4 sentences.
77 chars

Generation

The Law of Sines states that in any triangle, the ratio of each side length to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This means if you know two angles and one side, or two sides and an angle opposite one of them, you can find the unknown parts of the triangle. It's particularly useful for solving non-right triangles where the Pythagorean theorem doesn't apply. Think of it as a proportion that links each side to its opposite angle through the sine function.
30 tokens in · 125 tokens out · 3222 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
3230.8 ms
Base LLM
3222.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

08:50:16 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
08:50:16 red_gate decision=pass reason=no disqualifying input patterns detected
08:50:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=125 latency_ms=3222.3 cost_usd=0.002
08:50:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:50:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:50:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:50:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:50:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:50:19 signed hash_algo=sha256 hash=sha256:52e3d3aa01249fced5f9ab43aa354281c39e238d9187409e2e7eaad16d32bf11

Content hash

sha256:52e3d3aa01249fced5f9ab43aa354281c39e238d9187409e2e7eaad16d32bf11

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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