The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-conditional-entropy-state-any-key-f-0759

stable pending witness
2026-05-29 07:53:23 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain conditional entropy. State any key formula.
69 chars

Generation

Conditional entropy H(Y|X) measures the average uncertainty remaining about random variable Y after observing random variable X. It quantifies how much additional information is needed to describe Y when X is already known. The key formula is: **H(Y|X) = ∑ₓ p(x) H(Y|X=x) = -∑ₓ ∑ᵧ p(x,y) log p(y|x)** Conditional entropy is always non-negative and satisfies H(Y|X) ≤ H(Y), with equality when X and Y are independent (knowing X provides no information about Y).
24 tokens in · 151 tokens out · 3380 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
3386.9 ms
Base LLM
3380.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0023

Trail

07:53:23 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
07:53:23 red_gate decision=pass reason=no disqualifying input patterns detected
07:53:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=151 latency_ms=3380.3 cost_usd=0.0023
07:53:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:53:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:53:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:53:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:53:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:53:26 signed hash_algo=sha256 hash=sha256:09abe34c018fbbe9edf424a6141e1085247dfa19c3c7785a0dde56517d75a460

Content hash

sha256:09abe34c018fbbe9edf424a6141e1085247dfa19c3c7785a0dde56517d75a460

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