The Mechanism · Gated-generation receipt

gen-state-snell-s-law-of-refraction-precisely-and-explain-why-it-41e2

stable pending witness
2026-05-29 02:50:09 UTC · anthropic/claude-sonnet-4-5

Prompt

State Snell's law of refraction precisely and explain why it matters in 2-3 sentences.
86 chars

Generation

# Snell's Law **Precise Statement:** When light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction equals the ratio of the refractive indices: n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices and θ₁ and θ₂ are measured from the normal to the interface. **Why It Matters:** Snell's law is fundamental to all optical technologies, from designing eyeglasses and camera lenses to fiber optic communications. It explains everyday phenomena like why objects appear bent in water and enables us to precisely control how light bends through different materials, making modern optics possible.
30 tokens in · 178 tokens out · 4015 ms · $0.0028

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
4026.9 ms
Base LLM
4015.0 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0028

Trail

02:50:09 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
02:50:09 red_gate decision=pass reason=no disqualifying input patterns detected
02:50:13 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=178 latency_ms=4015.0 cost_usd=0.0028
02:50:13 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:50:13 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:50:13 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:50:13 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:50:13 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:50:13 signed hash_algo=sha256 hash=sha256:f2f22d87811d1658e11d3817eac0f260cee9874141a9267bdf161286b7759f5b

Content hash

sha256:f2f22d87811d1658e11d3817eac0f260cee9874141a9267bdf161286b7759f5b

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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