The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-diffraction-through-a-single-slit-s-0499

stable pending witness
2026-05-29 08:40:58 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain diffraction through a single slit. State any key formula.
83 chars

Generation

# Diffraction Through a Single Slit When light passes through a narrow slit with width comparable to its wavelength, it spreads out rather than traveling in straight lines, creating a pattern of bright and dark fringes on a screen. This occurs because different parts of the wavefront within the slit interfere with each other—destructive interference produces dark fringes while constructive interference produces bright regions. **Key formula for dark fringes (minima):** $$a \sin\theta = m\lambda$$ where *a* is the slit width, θ is the angle from the central axis, *m* = ±1, ±2, ±3... is the order number, and λ is the wavelength of light. The central maximum is twice as wide as the other bright fringes.
29 tokens in · 183 tokens out · 4727 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
4734.5 ms
Base LLM
4727.2 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0028

Trail

08:40:58 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
08:40:58 red_gate decision=pass reason=no disqualifying input patterns detected
08:41:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=183 latency_ms=4727.2 cost_usd=0.0028
08:41:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:41:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:41:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:41:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:41:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:41:03 signed hash_algo=sha256 hash=sha256:45c8ab6cc2f778df249a4292dbef0acfeae285d1e3acc898a0dd61cd506e6981

Content hash

sha256:45c8ab6cc2f778df249a4292dbef0acfeae285d1e3acc898a0dd61cd506e6981

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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