The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-inclusion-exclusion-principl-628e

stable pending witness
2026-05-29 04:42:50 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the inclusion-exclusion principle? Answer concisely in 2-3 sentences.
97 chars

Generation

The inclusion-exclusion principle is a fundamental counting technique that accurately calculates the size of unions of sets by systematically adding and subtracting overlapping regions to avoid double-counting. It's essential in probability theory, combinatorics, and computer science for solving problems involving multiple overlapping conditions or events. The principle generalizes to any number of sets, making it a powerful tool for complex counting problems.
31 tokens in · 86 tokens out · 3105 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
3112.5 ms
Base LLM
3105.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

04:42:50 received prompt_chars=97 verifiers=['scripture_anchors', 'theology_doctrine']
04:42:50 red_gate decision=pass reason=no disqualifying input patterns detected
04:42:53 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=86 latency_ms=3105.3 cost_usd=0.0014
04:42:53 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:42:53 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:42:53 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:42:53 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:42:53 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:42:53 signed hash_algo=sha256 hash=sha256:0736c29277fc5f07c1199b417081da4d06ebd6135d9d5e274522ff094ac8b133

Content hash

sha256:0736c29277fc5f07c1199b417081da4d06ebd6135d9d5e274522ff094ac8b133

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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