The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-kullback-leibler-divergence-sta-e562

stable pending witness
2026-05-29 03:21:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Kullback-Leibler divergence. State any key formula.
81 chars

Generation

The Kullback-Leibler (KL) divergence is a measure of how one probability distribution differs from a reference probability distribution. It quantifies the expected number of extra bits required to encode data from the true distribution P using a coding scheme optimized for distribution Q. The KL divergence is given by the formula: **D_KL(P || Q) = Σ P(x) log(P(x)/Q(x))** for discrete distributions, or the integral equivalent for continuous distributions. Note that KL divergence is asymmetric (D_KL(P || Q) ≠ D_KL(Q || P)) and is always non-negative, equaling zero only when P and Q are identical.
32 tokens in · 165 tokens out · 5265 ms · $0.0026

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
5272.9 ms
Base LLM
5265.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

03:21:42 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
03:21:42 red_gate decision=pass reason=no disqualifying input patterns detected
03:21:47 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=165 latency_ms=5265.2 cost_usd=0.0026
03:21:47 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:21:47 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:21:47 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:21:47 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:21:47 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:21:47 signed hash_algo=sha256 hash=sha256:175eeeeae41d01281746b0b9ad55414ad6f264c60195303d24af0a61bd4b58e8

Content hash

sha256:175eeeeae41d01281746b0b9ad55414ad6f264c60195303d24af0a61bd4b58e8

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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