The Mechanism · Gated-generation receipt

gen-define-snell-s-law-of-refraction-and-give-one-short-worked-e-fa00

stable pending witness
2026-05-29 07:19:57 UTC · anthropic/claude-sonnet-4-5

Prompt

Define Snell's law of refraction and give one short worked example.
67 chars

Generation

# Snell's Law of Refraction ## Definition Snell's law describes how light bends when passing from one medium to another. It states: **n₁ sin θ₁ = n₂ sin θ₂** Where: - n₁ = refractive index of the first medium - θ₁ = angle of incidence (measured from the normal) - n₂ = refractive index of the second medium - θ₂ = angle of refraction (measured from the normal) ## Worked Example **Problem:** A light ray travels from air (n = 1.00) into water (n = 1.33) at an angle of 40° from the normal. Find the angle of refraction. **Solution:** Given: - n₁ = 1.00 (air) - θ₁ = 40° - n₂ = 1.33 (water) - θ₂ = ? Using Snell's law: n₁ sin θ₁ = n₂ sin θ₂ 1.00 × sin(40°) = 1.33 × sin θ₂ 0.643 = 1.33 × sin θ₂ sin θ₂ = 0.643/1.33 = 0.483 θ₂ = sin⁻¹(0.483) = **28.9°** The light bends toward the normal when entering the denser medium (water), refracting at 28.9° from the normal.
23 tokens in · 384 tokens out · 5865 ms · $0.0058

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
5872.3 ms
Base LLM
5865.3 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0058

Trail

07:19:57 received prompt_chars=67 verifiers=['scripture_anchors', 'theology_doctrine']
07:19:57 red_gate decision=pass reason=no disqualifying input patterns detected
07:20:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=23 tokens_out=384 latency_ms=5865.3 cost_usd=0.0058
07:20:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:20:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:20:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:20:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:20:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:20:03 signed hash_algo=sha256 hash=sha256:55638e018698bd4f2921703f3fa33a194214b74cb5d1516b696bcf18fe1839ce

Content hash

sha256:55638e018698bd4f2921703f3fa33a194214b74cb5d1516b696bcf18fe1839ce

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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