The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-mutual-information-state-any-key-fo-0007

stable pending witness
2026-05-29 06:42:01 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain mutual information. State any key formula.
68 chars

Generation

Mutual information measures the amount of information that one random variable contains about another, quantifying how much knowing one variable reduces uncertainty about the other. It is always non-negative and equals zero if and only if the variables are independent. The key formula is: **I(X;Y) = H(X) + H(Y) - H(X,Y)** where H(X) and H(Y) are the marginal entropies and H(X,Y) is the joint entropy. Equivalently, I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X), showing it measures the reduction in uncertainty.
24 tokens in · 153 tokens out · 3253 ms · $0.0024

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
3259.9 ms
Base LLM
3253.4 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0024

Trail

06:42:01 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
06:42:01 red_gate decision=pass reason=no disqualifying input patterns detected
06:42:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=153 latency_ms=3253.4 cost_usd=0.0024
06:42:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:42:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:42:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:42:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:42:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:42:04 signed hash_algo=sha256 hash=sha256:a99969f46fd29529700a637780b673d6886b9733718e44883dc3b0c3f43df781

Content hash

sha256:a99969f46fd29529700a637780b673d6886b9733718e44883dc3b0c3f43df781

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.

Bring another teaching · Run a discernment