The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-inverse-square-law-for-lighting-400e

stable pending witness
2026-05-29 03:21:57 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the inverse-square law for lighting. State any key formula.
85 chars

Generation

The inverse-square law states that the intensity of light decreases proportionally to the square of the distance from the source. This means that if you double the distance from a light source, the illumination becomes one-quarter as bright; triple the distance yields one-ninth the brightness. The key formula is: **I = P/(4πr²)** or simply **I ∝ 1/r²** where I is intensity, P is power, and r is the distance from the source.
29 tokens in · 111 tokens out · 2755 ms · $0.0018

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
2762.0 ms
Base LLM
2754.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

03:21:57 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
03:21:57 red_gate decision=pass reason=no disqualifying input patterns detected
03:22:00 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=111 latency_ms=2754.9 cost_usd=0.0018
03:22:00 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:22:00 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:22:00 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:22:00 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:22:00 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:22:00 signed hash_algo=sha256 hash=sha256:548b4ce00d8b02cc2cf6bbdfdbe4aab377bde6cb246a724a7e927723756097ab

Content hash

sha256:548b4ce00d8b02cc2cf6bbdfdbe4aab377bde6cb246a724a7e927723756097ab

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.

Bring another teaching · Run a discernment