The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-chain-rule-of-entropy-answer-b1a2

stable pending witness
2026-05-29 05:08:11 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the chain rule of entropy? Answer concisely in 2-3 sentences.
89 chars

Generation

The chain rule of entropy allows us to decompose the joint entropy of multiple random variables into a sum of conditional entropies. This fundamental property reveals how uncertainty in a collection of variables can be broken down incrementally, showing that H(X₁, X₂, ..., Xₙ) = H(X₁) + H(X₂|X₁) + ... + H(Xₙ|X₁,...,Xₙ₋₁). It's essential for analyzing information flow in communication systems, data compression, and understanding dependencies between variables in information theory.
30 tokens in · 134 tokens out · 3099 ms · $0.0021

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
3107.3 ms
Base LLM
3098.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0021

Trail

05:08:11 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
05:08:11 red_gate decision=pass reason=no disqualifying input patterns detected
05:08:14 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=134 latency_ms=3098.7 cost_usd=0.0021
05:08:14 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:08:14 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:08:14 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:08:14 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:08:14 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:08:14 signed hash_algo=sha256 hash=sha256:44491d932414a5979922e5f4e8978ce7e63a9f69d1f1539798d5cea796e84f80

Content hash

sha256:44491d932414a5979922e5f4e8978ce7e63a9f69d1f1539798d5cea796e84f80

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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