The Mechanism · Gated-generation receipt

gen-state-mutual-information-precisely-and-explain-why-it-matter-1307

stable pending witness
2026-05-29 06:56:27 UTC · anthropic/claude-sonnet-4-5

Prompt

State mutual information precisely and explain why it matters in 2-3 sentences.
79 chars

Generation

# Mutual Information **Precise definition:** The mutual information I(X;Y) between random variables X and Y is: I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X) = ∑∑ p(x,y) log[p(x,y)/(p(x)p(y))] where H denotes entropy and H(X|Y) is conditional entropy. **Why it matters:** Mutual information quantifies how much knowing one variable reduces uncertainty about another, measuring the statistical dependence between variables in bits. It's fundamental to information theory, machine learning (feature selection), neuroscience (neural coding), and communication systems because it captures all types of relationships—not just linear correlations—and is zero if and only if the variables are independent.
24 tokens in · 189 tokens out · 4742 ms · $0.0029

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
4748.7 ms
Base LLM
4741.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0029

Trail

06:56:27 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
06:56:27 red_gate decision=pass reason=no disqualifying input patterns detected
06:56:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=189 latency_ms=4741.9 cost_usd=0.0029
06:56:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:56:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:56:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:56:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:56:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:56:32 signed hash_algo=sha256 hash=sha256:89e27c7198793c4b1f2a8a367b2d45ed10702e54694c0e85e76f97009150a167

Content hash

sha256:89e27c7198793c4b1f2a8a367b2d45ed10702e54694c0e85e76f97009150a167

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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