The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-water-vapor-saturation-curve-st-761d

stable pending witness
2026-05-29 08:16:34 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the water vapor saturation curve. State any key formula.
82 chars

Generation

The water vapor saturation curve shows the maximum amount of water vapor air can hold at different temperatures, with warmer air capable of holding exponentially more moisture than cooler air. When air reaches this saturation point, it has 100% relative humidity and any additional cooling causes condensation. The key relationship is described by the **Clausius-Clapeyron equation**: **de_s/dT = (L_v × e_s)/(R_v × T²)** where e_s is saturation vapor pressure, T is temperature, L_v is latent heat of vaporization, and R_v is the gas constant for water vapor. This equation shows that saturation vapor pressure increases approximately exponentially with temperature (roughly doubling every 10°C near Earth-surface conditions).
28 tokens in · 176 tokens out · 5147 ms · $0.0027

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
5154.6 ms
Base LLM
5147.2 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0027

Trail

08:16:34 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
08:16:34 red_gate decision=pass reason=no disqualifying input patterns detected
08:16:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=176 latency_ms=5147.2 cost_usd=0.0027
08:16:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:16:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:16:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:16:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:16:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:16:39 signed hash_algo=sha256 hash=sha256:a2adda40b0908791b619cfd10c052263ff9a7de20f0311a342b5c06b3cfabe33

Content hash

sha256:a2adda40b0908791b619cfd10c052263ff9a7de20f0311a342b5c06b3cfabe33

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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