The Mechanism · Gated-generation receipt

gen-explain-the-inclusion-exclusion-principle-as-you-would-to-a-d75c

stable pending witness
2026-05-29 04:20:10 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the inclusion-exclusion principle as you would to a capable student, in 3-4 sentences.
94 chars

Generation

The inclusion-exclusion principle helps us count elements in overlapping sets without double-counting. The basic idea is: add up all the individual sets, then subtract the overlaps you counted twice, then add back the triple overlaps you subtracted too many times, and so on. For example, to count students taking math OR physics, you'd add (math students) + (physics students) - (students taking both), since those taking both were counted twice. The pattern alternates between adding and subtracting as you work through increasingly complex overlaps.
31 tokens in · 117 tokens out · 3928 ms · $0.0018

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
3935.7 ms
Base LLM
3928.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

04:20:10 received prompt_chars=94 verifiers=['scripture_anchors', 'theology_doctrine']
04:20:10 red_gate decision=pass reason=no disqualifying input patterns detected
04:20:14 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=117 latency_ms=3928.0 cost_usd=0.0018
04:20:14 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:20:14 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:20:14 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:20:14 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:20:14 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:20:14 signed hash_algo=sha256 hash=sha256:4eb061c221e6345d01286da5da34bf5c3b9056e3c7ff7a1f38371caf13957ae4

Content hash

sha256:4eb061c221e6345d01286da5da34bf5c3b9056e3c7ff7a1f38371caf13957ae4

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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