The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-snell-s-law-of-refraction-state-any-13b7

stable pending witness
2026-05-29 03:25:22 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain Snell's law of refraction. State any key formula.
75 chars

Generation

# Snell's Law of Refraction Snell's law describes how light bends when it passes from one transparent medium to another with a different optical density. The law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media. **Key Formula:** $$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$ where *n₁* and *n₂* are the refractive indices of the first and second media, and *θ₁* and *θ₂* are the angles of incidence and refraction measured from the normal to the surface.
30 tokens in · 162 tokens out · 3689 ms · $0.0025

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
3696.3 ms
Base LLM
3688.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

03:25:22 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
03:25:22 red_gate decision=pass reason=no disqualifying input patterns detected
03:25:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=162 latency_ms=3688.7 cost_usd=0.0025
03:25:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:25:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:25:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:25:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:25:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:25:26 signed hash_algo=sha256 hash=sha256:75577a7130b06338b839c3af9c2f8d6bb3c1dbadf1b258f2b47e1bc0e1eb2acb

Content hash

sha256:75577a7130b06338b839c3af9c2f8d6bb3c1dbadf1b258f2b47e1bc0e1eb2acb

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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