The Mechanism · Gated-generation receipt

gen-state-the-diffraction-grating-equation-precisely-and-explain-49a7

stable pending witness
2026-05-29 05:02:36 UTC · anthropic/claude-sonnet-4-5

Prompt

State the diffraction grating equation precisely and explain why it matters in 2-3 sentences.
93 chars

Generation

## Diffraction Grating Equation **d sin θ = mλ** where *d* is the spacing between grating lines, *θ* is the diffraction angle, *m* is the order of diffraction (integer), and *λ* is the wavelength of light. This equation matters because it allows different wavelengths of light to be separated at distinct angles, making it fundamental to spectroscopy for analyzing the composition of light sources. It's the principle behind spectrometers used everywhere from astronomy (analyzing starlight) to chemistry labs (identifying substances).
28 tokens in · 130 tokens out · 3425 ms · $0.002

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
3437.2 ms
Base LLM
3425.0 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.002

Trail

05:02:36 received prompt_chars=93 verifiers=['scripture_anchors', 'theology_doctrine']
05:02:36 red_gate decision=pass reason=no disqualifying input patterns detected
05:02:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=130 latency_ms=3425.0 cost_usd=0.002
05:02:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:02:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:02:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:02:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:02:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:02:39 signed hash_algo=sha256 hash=sha256:38b587d40353d099b29a457fa8d6831ab79bf349d083c7afadfaf9070f30798f

Content hash

sha256:38b587d40353d099b29a457fa8d6831ab79bf349d083c7afadfaf9070f30798f

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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