The Mechanism · Gated-generation receipt

gen-explain-sound-intensity-and-the-inverse-square-law-as-you-wo-7ad1

stable pending witness
2026-05-29 07:40:17 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain sound intensity and the inverse-square law as you would to a capable student, in 3-4 sentences.
103 chars

Generation

# Sound Intensity and the Inverse-Square Law Sound intensity is the amount of sound energy passing through a given area per second, measured in watts per square meter (W/m²). As sound waves spread out from a source, they form an expanding sphere, so the same total energy gets distributed over an increasingly larger surface area. This leads to the **inverse-square law**: when you double your distance from a sound source, the intensity decreases to one-quarter (1/2² = 1/4) of its original value because the surface area of a sphere increases with the square of the radius. In practical terms, this is why a conversation sounds much quieter from across a room than up close—the sound energy spreads out and becomes less concentrated as it travels.
33 tokens in · 165 tokens out · 7599 ms · $0.0026

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
7607.0 ms
Base LLM
7599.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

07:40:17 received prompt_chars=103 verifiers=['scripture_anchors', 'theology_doctrine']
07:40:17 red_gate decision=pass reason=no disqualifying input patterns detected
07:40:25 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=33 tokens_out=165 latency_ms=7599.2 cost_usd=0.0026
07:40:25 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:40:25 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:40:25 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:40:25 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:40:25 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:40:25 signed hash_algo=sha256 hash=sha256:5f26c6fcbacfc7fded709586d0f14eccaa9ba7225af921ef265fb94f9bcdded9

Content hash

sha256:5f26c6fcbacfc7fded709586d0f14eccaa9ba7225af921ef265fb94f9bcdded9

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