The Mechanism · Gated-generation receipt

gen-state-the-inverse-square-law-for-lighting-precisely-and-expl-edbe

stable pending witness
2026-05-29 05:12:44 UTC · anthropic/claude-sonnet-4-5

Prompt

State the inverse-square law for lighting precisely and explain why it matters in 2-3 sentences.
96 chars

Generation

# Inverse-Square Law for Lighting **Precise statement:** The intensity (illuminance) of light at a surface is inversely proportional to the square of the distance from the point light source: I ∝ 1/r², or I = P/(4πr²), where I is intensity, P is power, and r is distance. **Why it matters:** This law means that doubling your distance from a light source reduces its brightness to one-quarter, not one-half—a dramatic falloff that's crucial for photographers, cinematographers, and lighting designers to understand when positioning lights. It explains why nearby objects appear much brighter than distant ones under the same light source, fundamentally affecting exposure, depth, and mood in visual work.
29 tokens in · 164 tokens out · 5664 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
5672.7 ms
Base LLM
5663.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

05:12:44 received prompt_chars=96 verifiers=['scripture_anchors', 'theology_doctrine']
05:12:44 red_gate decision=pass reason=no disqualifying input patterns detected
05:12:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=164 latency_ms=5663.7 cost_usd=0.0025
05:12:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:12:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:12:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:12:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:12:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:12:49 signed hash_algo=sha256 hash=sha256:e84333725ab8bec2312eafd7e4143ee2c06cd88960d270df6f65e11dab8bcc74

Content hash

sha256:e84333725ab8bec2312eafd7e4143ee2c06cd88960d270df6f65e11dab8bcc74

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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