The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-law-of-sines-state-any-key-form-f933

stable pending witness
2026-05-29 07:50:53 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the law of sines. State any key formula.
66 chars

Generation

The law of sines states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant for all three sides. This relationship allows you to solve for unknown sides or angles in a triangle when you know either two angles and one side, or two sides and a non-included angle. **Key formula:** $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ where *a*, *b*, and *c* are the side lengths, and *A*, *B*, and *C* are their respective opposite angles.
27 tokens in · 141 tokens out · 3434 ms · $0.0022

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
3441.5 ms
Base LLM
3434.1 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0022

Trail

07:50:53 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
07:50:53 red_gate decision=pass reason=no disqualifying input patterns detected
07:50:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=141 latency_ms=3434.1 cost_usd=0.0022
07:50:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:50:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:50:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:50:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:50:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:50:56 signed hash_algo=sha256 hash=sha256:d2fbfcda4b2de25e59e0ac24cdb031fee2c94ef713b192be76657df59b50fd15

Content hash

sha256:d2fbfcda4b2de25e59e0ac24cdb031fee2c94ef713b192be76657df59b50fd15

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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