The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-diffraction-grating-equation-st-fd6c

stable pending witness
2026-05-29 05:58:13 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the diffraction grating equation. State any key formula.
82 chars

Generation

The diffraction grating equation describes how light is diffracted when it passes through a grating with many closely-spaced parallel slits. When monochromatic light hits the grating, constructive interference occurs at specific angles where the path difference between adjacent slits equals a whole number of wavelengths. The key formula is **d sin θ = mλ**, where *d* is the spacing between adjacent slits, θ is the diffraction angle, *m* is the order of the bright fringe (0, ±1, ±2, ...), and λ is the wavelength of light. This equation allows us to determine either the wavelength of light or the grating spacing by measuring the diffraction angles.
28 tokens in · 159 tokens out · 3740 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
3748.6 ms
Base LLM
3740.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

05:58:13 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
05:58:13 red_gate decision=pass reason=no disqualifying input patterns detected
05:58:17 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=159 latency_ms=3740.4 cost_usd=0.0025
05:58:17 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:58:17 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:58:17 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:58:17 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:58:17 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:58:17 signed hash_algo=sha256 hash=sha256:536b94ec5dba945388eb7505320675923cec0bc8229f5a88727a062285f9432f

Content hash

sha256:536b94ec5dba945388eb7505320675923cec0bc8229f5a88727a062285f9432f

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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