The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-permutations-and-combinations-an-bc01

stable pending witness
2026-05-29 08:15:16 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of permutations and combinations? Answer concisely in 2-3 sentences.
93 chars

Generation

Permutations and combinations are fundamental counting principles used to determine the number of ways to arrange or select items from a set. They are essential in probability theory, statistics, and real-world applications like scheduling, lottery odds, password security, and experimental design. The key difference is that permutations consider order while combinations do not.
30 tokens in · 71 tokens out · 2760 ms · $0.0012

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
2771.9 ms
Base LLM
2759.8 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0012

Trail

08:15:16 received prompt_chars=93 verifiers=['scripture_anchors', 'theology_doctrine']
08:15:16 red_gate decision=pass reason=no disqualifying input patterns detected
08:15:18 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=71 latency_ms=2759.8 cost_usd=0.0012
08:15:18 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:15:18 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:15:18 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:15:18 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:15:18 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:15:18 signed hash_algo=sha256 hash=sha256:0f906a2d8626f8fa3dd0735586e759211ed5c5ab0610f318383747745136dae6

Content hash

sha256:0f906a2d8626f8fa3dd0735586e759211ed5c5ab0610f318383747745136dae6

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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