The Mechanism · Gated-generation receipt

gen-define-the-speed-of-sound-versus-temperature-and-give-one-sh-0fe0

stable pending witness
2026-05-29 07:27:42 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the speed of sound versus temperature and give one short worked example.
79 chars

Generation

# Speed of Sound vs Temperature ## Definition The speed of sound in air varies with temperature according to: **v = 331.3 + 0.606T** Where: - v = speed of sound (m/s) - T = temperature (°C) Alternatively, using the more fundamental relationship: **v = √(γRT/M)** Where γ = heat capacity ratio, R = gas constant, T = absolute temperature (K), M = molar mass ## Key Point Speed of sound **increases** with temperature because warmer air molecules move faster and transmit vibrations more quickly. ## Worked Example **Question:** What is the speed of sound at 25°C? **Solution:** - v = 331.3 + 0.606T - v = 331.3 + 0.606(25) - v = 331.3 + 15.15 - **v = 346.5 m/s** (or approximately 347 m/s) **Note:** At 0°C, the speed is 331.3 m/s, and it increases by roughly 0.6 m/s for each degree Celsius increase.
21 tokens in · 277 tokens out · 6464 ms · $0.0042

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
6472.0 ms
Base LLM
6464.2 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0042

Trail

07:27:42 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
07:27:42 red_gate decision=pass reason=no disqualifying input patterns detected
07:27:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=21 tokens_out=277 latency_ms=6464.2 cost_usd=0.0042
07:27:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:27:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:27:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:27:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:27:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:27:49 signed hash_algo=sha256 hash=sha256:d1dacbb8fbd1e516f0d52d1bb7d07da43f0ea25b7af0ed5e60491fc135a9ad1c

Content hash

sha256:d1dacbb8fbd1e516f0d52d1bb7d07da43f0ea25b7af0ed5e60491fc135a9ad1c

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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