The Mechanism · Gated-generation receipt

gen-state-conditional-entropy-precisely-and-explain-why-it-matte-d9df

stable pending witness
2026-05-29 06:35:56 UTC · anthropic/claude-sonnet-4-5

Prompt

State conditional entropy precisely and explain why it matters in 2-3 sentences.
80 chars

Generation

## Conditional Entropy **Definition:** The conditional entropy H(Y|X) is the expected entropy of Y given knowledge of X: H(Y|X) = ∑ₓ P(x) H(Y|X=x) = -∑ₓ ∑ᵧ P(x,y) log P(y|x) **Why it matters:** Conditional entropy quantifies the remaining uncertainty in one variable after observing another, measuring how much information is still "missing." It's fundamental to information theory because it enables the chain rule H(X,Y) = H(X) + H(Y|X) and defines mutual information I(X;Y) = H(Y) - H(Y|X), which measures how much knowing X reduces uncertainty about Y.
24 tokens in · 182 tokens out · 4325 ms · $0.0028

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
4334.5 ms
Base LLM
4325.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0028

Trail

06:35:56 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
06:35:56 red_gate decision=pass reason=no disqualifying input patterns detected
06:36:00 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=182 latency_ms=4325.3 cost_usd=0.0028
06:36:00 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:36:00 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:36:00 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:36:00 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:36:00 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:36:00 signed hash_algo=sha256 hash=sha256:7b80ddf0caa2af4792d63030fc1a6643023ddb6666c09c66bc820c7659986f21

Content hash

sha256:7b80ddf0caa2af4792d63030fc1a6643023ddb6666c09c66bc820c7659986f21

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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