The Mechanism · Gated-generation receipt

gen-state-sound-intensity-and-the-inverse-square-law-precisely-a-4e7c

stable pending witness
2026-05-29 04:43:52 UTC · anthropic/claude-sonnet-4-5

Prompt

State sound intensity and the inverse-square law precisely and explain why it matters in 2-3 sentences.
103 chars

Generation

# Sound Intensity and Inverse-Square Law **Sound intensity** is the acoustic power per unit area, measured in watts per square meter (W/m²), flowing through a surface perpendicular to the direction of sound propagation. **Inverse-square law**: Sound intensity decreases proportionally to the square of the distance from a point source: I ∝ 1/r², or I₁/I₂ = (r₂/r₁)². **Why it matters**: This law explains why sounds become rapidly quieter as you move away from the source—doubling your distance reduces intensity to one-quarter. It's crucial for architectural acoustics, noise control regulations, audio engineering, and understanding safe distances from loud sound sources to prevent hearing damage.
30 tokens in · 170 tokens out · 7263 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
7270.3 ms
Base LLM
7263.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

04:43:52 received prompt_chars=103 verifiers=['scripture_anchors', 'theology_doctrine']
04:43:52 red_gate decision=pass reason=no disqualifying input patterns detected
04:43:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=170 latency_ms=7263.2 cost_usd=0.0026
04:43:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:43:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:43:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:43:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:43:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:43:59 signed hash_algo=sha256 hash=sha256:59eca075bb9b18b5872535cfab25a556d53d0129641b377c4e78f76409242da1

Content hash

sha256:59eca075bb9b18b5872535cfab25a556d53d0129641b377c4e78f76409242da1

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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