The Mechanism · Gated-generation receipt

gen-briefly-explain-the-pigeonhole-principle-and-one-common-misc-250a

stable pending witness
2026-05-29 05:27:52 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain the pigeonhole principle and one common misconception about it.
79 chars

Generation

## The Pigeonhole Principle The pigeonhole principle states that if you have more objects than containers, at least one container must hold more than one object. For example, if 11 pigeons fly into 10 pigeonholes, at least one hole must contain 2 or more pigeons. ## Common Misconception Many people mistakenly think the principle tells you **which** container has multiple objects or **how many** objects are in it. In reality, the principle only guarantees that *some* container must have multiple objects—it doesn't identify which one or give precise counts. It's an **existence proof**, not a constructive one. For instance, knowing that two people in a group of 367 share a birthday doesn't tell you which two people or on what date.
23 tokens in · 178 tokens out · 5691 ms · $0.0027

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
5697.9 ms
Base LLM
5690.6 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0027

Trail

05:27:52 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
05:27:52 red_gate decision=pass reason=no disqualifying input patterns detected
05:27:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=23 tokens_out=178 latency_ms=5690.6 cost_usd=0.0027
05:27:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:27:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:27:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:27:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:27:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:27:58 signed hash_algo=sha256 hash=sha256:199f0e7efe0fb135757e4ca8135ec7990c16d75a22f8c24da2ff5931e5024ca7

Content hash

sha256:199f0e7efe0fb135757e4ca8135ec7990c16d75a22f8c24da2ff5931e5024ca7

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.

Bring another teaching · Run a discernment