The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-boltzmann-distribution-answe-34ce

stable pending witness
2026-05-29 07:40:04 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the Boltzmann distribution? Answer concisely in 2-3 sentences.
90 chars

Generation

The Boltzmann distribution describes the probability of finding a system in a particular energy state at thermal equilibrium, showing that higher energy states are exponentially less likely to be occupied. It is fundamental to statistical mechanics, connecting microscopic particle behavior to macroscopic thermodynamic properties like temperature and entropy. This distribution explains countless phenomena, from chemical reaction rates to the behavior of gases and the distribution of molecular speeds.
31 tokens in · 87 tokens out · 3374 ms · $0.0014

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
3380.3 ms
Base LLM
3373.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

07:40:04 received prompt_chars=90 verifiers=['scripture_anchors', 'theology_doctrine']
07:40:04 red_gate decision=pass reason=no disqualifying input patterns detected
07:40:08 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=87 latency_ms=3373.6 cost_usd=0.0014
07:40:08 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:40:08 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:40:08 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:40:08 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:40:08 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:40:08 signed hash_algo=sha256 hash=sha256:149d108fef33610195164b6f3bc4f3cb4cc30b68dc0840ec6d321ccb72f109f0

Content hash

sha256:149d108fef33610195164b6f3bc4f3cb4cc30b68dc0840ec6d321ccb72f109f0

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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