The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-boltzmann-distribution-state-an-afeb

stable pending witness
2026-05-29 07:40:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Boltzmann distribution. State any key formula.
76 chars

Generation

The Boltzmann distribution describes the probability of finding a system in a particular energy state at thermal equilibrium. It shows that states with lower energy are exponentially more probable than states with higher energy, with the probability decreasing as temperature decreases. The key formula is: **P(E) ∝ e^(-E/kT)** where P(E) is the probability of a state with energy E, k is Boltzmann's constant, and T is the absolute temperature. This distribution is fundamental to statistical mechanics and explains many thermal properties of matter.
28 tokens in · 126 tokens out · 3107 ms · $0.002

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
3113.3 ms
Base LLM
3106.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

07:40:42 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
07:40:42 red_gate decision=pass reason=no disqualifying input patterns detected
07:40:45 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=126 latency_ms=3106.6 cost_usd=0.002
07:40:45 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:40:45 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:40:45 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:40:45 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:40:45 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:40:45 signed hash_algo=sha256 hash=sha256:28196fb6fb2d48f8ec3733082fe37d2cf41715e4cc67896a1bbb0e351871efc6

Content hash

sha256:28196fb6fb2d48f8ec3733082fe37d2cf41715e4cc67896a1bbb0e351871efc6

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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