The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-pigeonhole-principle-answer-36a2

stable pending witness
2026-05-29 04:41:55 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the pigeonhole principle? Answer concisely in 2-3 sentences.
88 chars

Generation

The pigeonhole principle states that if you have more items than containers, at least one container must hold more than one item. This seemingly simple idea is a powerful tool in mathematics and computer science for proving existence—showing that certain situations *must* occur without necessarily finding them explicitly. It's used to prove results in number theory, combinatorics, probability, and algorithm analysis.
30 tokens in · 80 tokens out · 3751 ms · $0.0013

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
3758.9 ms
Base LLM
3751.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

04:41:55 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
04:41:55 red_gate decision=pass reason=no disqualifying input patterns detected
04:41:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=80 latency_ms=3751.3 cost_usd=0.0013
04:41:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:41:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:41:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:41:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:41:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:41:59 signed hash_algo=sha256 hash=sha256:431d16cb37c860633d2ad2f1beb77a283bc2fc5330f76598716cb1f60ca10235

Content hash

sha256:431d16cb37c860633d2ad2f1beb77a283bc2fc5330f76598716cb1f60ca10235

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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