The Mechanism · Gated-generation receipt

gen-explain-the-kullback-leibler-divergence-as-you-would-to-a-ca-4b5f

stable pending witness
2026-05-29 04:24:59 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the Kullback-Leibler divergence as you would to a capable student, in 3-4 sentences.
92 chars

Generation

The Kullback-Leibler (KL) divergence measures how much one probability distribution differs from another reference distribution. You can think of it as quantifying the "surprise" or extra information needed when you use distribution Q to approximate the true distribution P—the more they differ, the higher the KL divergence. Mathematically, it's calculated as KL(P||Q) = Σ P(x) log(P(x)/Q(x)), summing over all possible outcomes. Importantly, KL divergence is asymmetric (KL(P||Q) ≠ KL(Q||P)), so the order matters when comparing distributions.
35 tokens in · 148 tokens out · 3969 ms · $0.0023

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
3976.9 ms
Base LLM
3969.2 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0023

Trail

04:24:59 received prompt_chars=92 verifiers=['scripture_anchors', 'theology_doctrine']
04:24:59 red_gate decision=pass reason=no disqualifying input patterns detected
04:25:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=35 tokens_out=148 latency_ms=3969.2 cost_usd=0.0023
04:25:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:25:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:25:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:25:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:25:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:25:03 signed hash_algo=sha256 hash=sha256:571f78414e50e31f3e4d6f40760c8ebdaf40535388c3c4cd9bd69068475bd53f

Content hash

sha256:571f78414e50e31f3e4d6f40760c8ebdaf40535388c3c4cd9bd69068475bd53f

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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