The Mechanism · Gated-generation receipt

gen-state-the-law-of-sines-precisely-and-explain-why-it-matters-d796

stable pending witness
2026-05-29 02:46:55 UTC · anthropic/claude-sonnet-4-5

Prompt

State the law of sines precisely and explain why it matters in 2-3 sentences.
77 chars

Generation

# Law of Sines For any triangle with sides of length *a*, *b*, *c* opposite to angles *A*, *B*, *C* respectively: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ Alternatively: $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ ## Why It Matters The Law of Sines allows us to solve triangles when we know either two angles and one side (AAS/ASA) or two sides and a non-included angle (SSA). It establishes a fundamental relationship between a triangle's angles and sides, making it essential for navigation, surveying, engineering, and any field requiring indirect distance or angle measurements.
27 tokens in · 193 tokens out · 4158 ms · $0.003

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
4165.7 ms
Base LLM
4158.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.003

Trail

02:46:55 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
02:46:55 red_gate decision=pass reason=no disqualifying input patterns detected
02:46:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=193 latency_ms=4158.4 cost_usd=0.003
02:46:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:46:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:46:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:46:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:46:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:46:59 signed hash_algo=sha256 hash=sha256:9329900f088b9054dce08bc931be74ff502497fc4097083dd53253777df4765a

Content hash

sha256:9329900f088b9054dce08bc931be74ff502497fc4097083dd53253777df4765a

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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