The Mechanism · Gated-generation receipt

gen-define-the-decibel-scale-and-give-one-short-worked-example-db4e

stable pending witness
2026-05-29 05:48:11 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the decibel scale and give one short worked example.
59 chars

Generation

# The Decibel Scale The **decibel (dB)** is a logarithmic unit used to express the ratio between two values, most commonly power or intensity. ## Definition For sound intensity: **L = 10 log₁₀(I/I₀)** where: - L = sound level in decibels (dB) - I = intensity of the sound (W/m²) - I₀ = reference intensity = 10⁻¹² W/m² (threshold of human hearing) ## Worked Example **Question:** A sound has intensity I = 10⁻⁴ W/m². What is its level in decibels? **Solution:** L = 10 log₁₀(I/I₀) L = 10 log₁₀(10⁻⁴/10⁻¹²) L = 10 log₁₀(10⁸) L = 10 × 8 **L = 80 dB** This is roughly the loudness of heavy traffic or an alarm clock.
20 tokens in · 267 tokens out · 5715 ms · $0.0041

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
5721.7 ms
Base LLM
5714.5 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0041

Trail

05:48:11 received prompt_chars=59 verifiers=['scripture_anchors', 'theology_doctrine']
05:48:11 red_gate decision=pass reason=no disqualifying input patterns detected
05:48:17 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=20 tokens_out=267 latency_ms=5714.5 cost_usd=0.0041
05:48:17 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:48:17 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:48:17 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:48:17 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:48:17 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:48:17 signed hash_algo=sha256 hash=sha256:f761b435f48f49cc40f4e747db6e81aabc7948e8eea4b4a8268beb77a5920560

Content hash

sha256:f761b435f48f49cc40f4e747db6e81aabc7948e8eea4b4a8268beb77a5920560

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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