The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-stirling-numbers-answer-concisel-b0f9

stable pending witness
2026-05-29 05:41:32 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Stirling numbers? Answer concisely in 2-3 sentences.
80 chars

Generation

Stirling numbers count fundamental combinatorial structures: Stirling numbers of the first kind count permutations by their number of cycles, while Stirling numbers of the second kind count ways to partition a set into non-empty subsets. They appear throughout mathematics, connecting permutation theory, polynomial algebra, and set partitions, and serve as essential tools in enumeration problems and the study of symmetric functions.
29 tokens in · 87 tokens out · 2882 ms · $0.0014

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
2889.5 ms
Base LLM
2882.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0014

Trail

05:41:32 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
05:41:32 red_gate decision=pass reason=no disqualifying input patterns detected
05:41:34 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=87 latency_ms=2882.2 cost_usd=0.0014
05:41:34 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:41:34 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:41:34 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:41:34 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:41:34 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:41:34 signed hash_algo=sha256 hash=sha256:984988d35fd5b83ea22097e11655f04fe79e8513eab5759cbbbdea94d782eea1

Content hash

sha256:984988d35fd5b83ea22097e11655f04fe79e8513eab5759cbbbdea94d782eea1

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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