The Mechanism · Gated-generation receipt

gen-explain-the-diffraction-grating-equation-as-you-would-to-a-c-b06f

stable pending witness
2026-05-29 06:14:21 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the diffraction grating equation as you would to a capable student, in 3-4 sentences.
93 chars

Generation

# Diffraction Grating Equation When light passes through a diffraction grating (a surface with many equally-spaced slits), waves from different slits interfere with each other. Constructive interference occurs at specific angles where the path difference between adjacent slits equals a whole number of wavelengths, giving us the equation **d sin θ = mλ**, where *d* is the spacing between slits, *θ* is the angle of the bright fringe, *m* is the order number (0, ±1, ±2...), and *λ* is the wavelength. This equation tells us exactly where bright spots will appear, and because different wavelengths satisfy it at different angles, gratings can separate white light into its component colors—which is why they're so useful in spectroscopy.
31 tokens in · 183 tokens out · 4758 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
4765.0 ms
Base LLM
4758.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0028

Trail

06:14:21 received prompt_chars=93 verifiers=['scripture_anchors', 'theology_doctrine']
06:14:21 red_gate decision=pass reason=no disqualifying input patterns detected
06:14:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=183 latency_ms=4758.0 cost_usd=0.0028
06:14:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:14:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:14:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:14:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:14:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:14:26 signed hash_algo=sha256 hash=sha256:cf56a0bfe67cdd590da239f01272cf4f0875a51bad3af215aa806d466a899dbc

Content hash

sha256:cf56a0bfe67cdd590da239f01272cf4f0875a51bad3af215aa806d466a899dbc

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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