The Mechanism · Gated-generation receipt

gen-briefly-explain-the-diffraction-grating-equation-and-one-com-d8d4

stable pending witness
2026-05-29 05:05:42 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain the diffraction grating equation and one common misconception about it.
87 chars

Generation

## Diffraction Grating Equation The diffraction grating equation is: **d sin θ = mλ** Where: - **d** = spacing between adjacent slits - **θ** = angle of the diffracted light (measured from the normal) - **m** = order of diffraction (0, ±1, ±2, ...) - **λ** = wavelength of light This equation predicts the angles at which constructive interference produces bright fringes when light passes through a grating with many parallel slits. ## Common Misconception **Misconception**: *The angle θ is measured from the grating surface itself.* **Reality**: The angle θ is measured from the **normal** (perpendicular) to the grating surface, not from the grating plane. This is the same convention used in Snell's law. Measuring from the wrong reference line leads to completely incorrect predictions of where bright fringes will appear.
24 tokens in · 222 tokens out · 4448 ms · $0.0034

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
4455.9 ms
Base LLM
4448.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0034

Trail

05:05:42 received prompt_chars=87 verifiers=['scripture_anchors', 'theology_doctrine']
05:05:42 red_gate decision=pass reason=no disqualifying input patterns detected
05:05:47 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=222 latency_ms=4448.2 cost_usd=0.0034
05:05:47 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:05:47 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:05:47 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:05:47 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:05:47 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:05:47 signed hash_algo=sha256 hash=sha256:6956fa871d408bff124cb7c909b5742da5c69190cf3ea36a35c987431f50a725

Content hash

sha256:6956fa871d408bff124cb7c909b5742da5c69190cf3ea36a35c987431f50a725

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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