The Mechanism · Gated-generation receipt

gen-define-the-human-hearing-range-and-give-one-short-worked-exa-fc40

stable pending witness
2026-05-29 06:16:14 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the human hearing range and give one short worked example.
65 chars

Generation

# Human Hearing Range The **human hearing range** is approximately **20 Hz to 20,000 Hz (20 kHz)**. - **Lower limit (20 Hz)**: Below this, sounds become more felt as vibrations than heard - **Upper limit (20 kHz)**: Above this is ultrasound, inaudible to humans - This range decreases with age, especially the upper frequencies ## Worked Example **Question:** A sound wave travels at 343 m/s. What is the wavelength of the highest frequency sound a human can hear? **Solution:** Using the wave equation: v = fλ Where: - v = 343 m/s (speed of sound) - f = 20,000 Hz (highest audible frequency) - λ = ? Rearranging: λ = v/f λ = 343/20,000 = **0.017 m = 1.7 cm** This shows that the highest pitched sounds we can hear have very short wavelengths, about the width of a finger.
19 tokens in · 250 tokens out · 6176 ms · $0.0038

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
6183.6 ms
Base LLM
6176.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0038

Trail

06:16:14 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
06:16:14 red_gate decision=pass reason=no disqualifying input patterns detected
06:16:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=250 latency_ms=6176.1 cost_usd=0.0038
06:16:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:16:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:16:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:16:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:16:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:16:20 signed hash_algo=sha256 hash=sha256:90cf0ef77264e856f05c132803c386e4e9a2a9e996b303308d283a86a077a261

Content hash

sha256:90cf0ef77264e856f05c132803c386e4e9a2a9e996b303308d283a86a077a261

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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