The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-joint-entropy-state-any-key-formula-3324

stable pending witness
2026-05-29 07:12:06 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

Joint entropy measures the total uncertainty in two or more random variables considered together. It quantifies the average amount of information needed to describe the outcome of all variables simultaneously. The key formula for two random variables X and Y is: **H(X,Y) = -∑∑ p(x,y) log₂ p(x,y)** where p(x,y) is the joint probability distribution. Joint entropy satisfies H(X,Y) ≤ H(X) + H(Y), with equality when X and Y are independent.
24 tokens in · 126 tokens out · 3296 ms · $0.002

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
3305.4 ms
Base LLM
3295.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

07:12:06 received prompt_chars=63 verifiers=['scripture_anchors', 'theology_doctrine']
07:12:06 red_gate decision=pass reason=no disqualifying input patterns detected
07:12:10 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=126 latency_ms=3295.8 cost_usd=0.002
07:12:10 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:12:10 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:12:10 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:12:10 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:12:10 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:12:10 signed hash_algo=sha256 hash=sha256:cf06b00ed61b16d9eadfb3c17aacc1e1bea44bf6e3ecc9e65b647ab8b397eff2

Content hash

sha256:cf06b00ed61b16d9eadfb3c17aacc1e1bea44bf6e3ecc9e65b647ab8b397eff2

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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