The Mechanism · Gated-generation receipt

gen-define-the-ideal-gas-law-and-give-one-short-worked-example-ad1b

stable pending witness
2026-05-29 06:42:04 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the ideal gas law and give one short worked example.
59 chars

Generation

# Ideal Gas Law ## Definition The **ideal gas law** describes the relationship between pressure, volume, temperature, and amount of gas: $$PV = nRT$$ Where: - **P** = pressure (Pa or atm) - **V** = volume (m³ or L) - **n** = number of moles (mol) - **R** = universal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K)) - **T** = absolute temperature (K) ## Worked Example **Problem:** What volume does 2.0 moles of nitrogen gas occupy at 25°C and 1.0 atm pressure? **Solution:** - Given: n = 2.0 mol, T = 25°C = 298 K, P = 1.0 atm - Using R = 0.0821 L·atm/(mol·K) $$V = \frac{nRT}{P} = \frac{(2.0\text{ mol})(0.0821\text{ L·atm/mol·K})(298\text{ K})}{1.0\text{ atm}}$$ $$V = 48.9\text{ L}$$ **Answer:** The nitrogen gas occupies approximately **49 L**.
19 tokens in · 318 tokens out · 5198 ms · $0.0048

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
5204.2 ms
Base LLM
5197.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0048

Trail

06:42:04 received prompt_chars=59 verifiers=['scripture_anchors', 'theology_doctrine']
06:42:04 red_gate decision=pass reason=no disqualifying input patterns detected
06:42:09 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=318 latency_ms=5197.6 cost_usd=0.0048
06:42:09 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:42:09 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:42:09 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:42:09 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:42:09 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:42:09 signed hash_algo=sha256 hash=sha256:1c92fff7cd7db4c5f842570370e31f0041c570003f1394b7e8f3ab9c7bbc0292

Content hash

sha256:1c92fff7cd7db4c5f842570370e31f0041c570003f1394b7e8f3ab9c7bbc0292

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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