The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-diffraction-grating-equation-b214

stable pending witness
2026-05-29 04:35:30 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the diffraction grating equation? Answer concisely in 2-3 sentences.
96 chars

Generation

The diffraction grating equation (d sin θ = mλ) determines the specific angles at which constructive interference occurs when light passes through multiple parallel slits. It enables precise measurement of wavelengths and separation of light into its component colors, making it fundamental to spectroscopy and optical analysis. The equation shows that longer wavelengths diffract at larger angles and that multiple orders (m = 0, ±1, ±2...) of spectra can be observed.
31 tokens in · 105 tokens out · 3164 ms · $0.0017

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
3171.4 ms
Base LLM
3164.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0017

Trail

04:35:30 received prompt_chars=96 verifiers=['scripture_anchors', 'theology_doctrine']
04:35:30 red_gate decision=pass reason=no disqualifying input patterns detected
04:35:33 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=105 latency_ms=3164.1 cost_usd=0.0017
04:35:33 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:35:33 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:35:33 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:35:33 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:35:33 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:35:33 signed hash_algo=sha256 hash=sha256:55b15a05f16827fc2236a62b7aaa69ab2d5cd0dfdb451dd6924f1073d280a7e4

Content hash

sha256:55b15a05f16827fc2236a62b7aaa69ab2d5cd0dfdb451dd6924f1073d280a7e4

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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