The Mechanism · Gated-generation receipt

gen-state-shannon-entropy-precisely-and-explain-why-it-matters-i-eebe

stable pending witness
2026-05-29 05:32:05 UTC · anthropic/claude-sonnet-4-5

Prompt

State Shannon entropy precisely and explain why it matters in 2-3 sentences.
76 chars

Generation

# Shannon Entropy **Definition:** For a discrete random variable X with possible values {x₁, x₂, ..., xₙ} and probability mass function p(x), Shannon entropy is: H(X) = -∑ p(xᵢ) log₂ p(xᵢ) (measured in bits when using log base 2) **Why it matters:** Shannon entropy quantifies the fundamental limit on how much data can be compressed and the minimum number of bits needed to communicate information from a source. It forms the theoretical foundation for all of information theory, data compression, and digital communication, establishing fundamental bounds on what's physically possible in these domains.
24 tokens in · 154 tokens out · 4299 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
4309.5 ms
Base LLM
4299.5 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0024

Trail

05:32:05 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
05:32:05 red_gate decision=pass reason=no disqualifying input patterns detected
05:32:09 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=154 latency_ms=4299.5 cost_usd=0.0024
05:32:09 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:32:09 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:32:09 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:32:09 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:32:09 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:32:09 signed hash_algo=sha256 hash=sha256:66d4f5a8afa73b48310cc1c94fc757d180e1056a616a944fee271076f7130128

Content hash

sha256:66d4f5a8afa73b48310cc1c94fc757d180e1056a616a944fee271076f7130128

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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