The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-cross-entropy-state-any-key-formula-72a8

stable pending witness
2026-05-29 05:21:31 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain cross-entropy. State any key formula.
63 chars

Generation

Cross-entropy measures the difference between two probability distributions, commonly used as a loss function in classification tasks. It quantifies how well a predicted probability distribution Q matches the true distribution P. The key formula for cross-entropy is: **H(P,Q) = -∑ P(x) log(Q(x))** In binary classification, this simplifies to: **L = -[y log(ŷ) + (1-y) log(1-ŷ)]** where y is the true label and ŷ is the predicted probability. Lower cross-entropy indicates better model predictions.
25 tokens in · 140 tokens out · 3467 ms · $0.0022

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
3473.7 ms
Base LLM
3466.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

05:21:31 received prompt_chars=63 verifiers=['scripture_anchors', 'theology_doctrine']
05:21:31 red_gate decision=pass reason=no disqualifying input patterns detected
05:21:34 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=140 latency_ms=3466.6 cost_usd=0.0022
05:21:34 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:21:34 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:21:34 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:21:34 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:21:34 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:21:34 signed hash_algo=sha256 hash=sha256:27377863cbe99f6fbd274022cb803df92ee348308c8cc7838f9dd6db70dedcce

Content hash

sha256:27377863cbe99f6fbd274022cb803df92ee348308c8cc7838f9dd6db70dedcce

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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