The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-sound-intensity-and-the-inverse-squ-4648

stable pending witness
2026-05-29 05:49:36 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain sound intensity and the inverse-square law. State any key formula.
92 chars

Generation

Sound intensity is the power per unit area carried by a sound wave, measured in watts per square meter (W/m²). The inverse-square law states that sound intensity decreases proportionally to the square of the distance from the source: as you double the distance, the intensity becomes one-fourth as strong. The key formula is **I = P/(4πr²)** or **I ∝ 1/r²**, where I is intensity, P is power, and r is the distance from the source. This occurs because the same sound power spreads over an increasingly larger spherical area as the wave propagates outward.
30 tokens in · 137 tokens out · 3460 ms · $0.0021

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
3467.0 ms
Base LLM
3459.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

05:49:36 received prompt_chars=92 verifiers=['scripture_anchors', 'theology_doctrine']
05:49:36 red_gate decision=pass reason=no disqualifying input patterns detected
05:49:40 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=137 latency_ms=3459.8 cost_usd=0.0021
05:49:40 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:49:40 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:49:40 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:49:40 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:49:40 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:49:40 signed hash_algo=sha256 hash=sha256:38ff19ae1f03d3f7fcd789873d9e89e1235f2bc573520698a02bf4fdaeb32855

Content hash

sha256:38ff19ae1f03d3f7fcd789873d9e89e1235f2bc573520698a02bf4fdaeb32855

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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