The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-a-counterexample-answer-concisel-a78b

stable pending witness
2026-05-29 05:16:31 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of a counterexample? Answer concisely in 2-3 sentences.
80 chars

Generation

A counterexample is a specific case that disproves a general statement, conjecture, or theorem by showing it is false. Finding even a single counterexample is sufficient to invalidate a universal claim, making it a powerful tool in mathematics and logic for testing the validity of propositions.
29 tokens in · 63 tokens out · 2465 ms · $0.001

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
2473.9 ms
Base LLM
2464.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.001

Trail

05:16:31 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
05:16:31 red_gate decision=pass reason=no disqualifying input patterns detected
05:16:33 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=63 latency_ms=2464.6 cost_usd=0.001
05:16:33 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:16:33 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:16:33 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:16:33 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:16:33 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:16:33 signed hash_algo=sha256 hash=sha256:9480a3e59b41d82ff8232908f945eb181c031f82c1484e10021296524814c2c0

Content hash

sha256:9480a3e59b41d82ff8232908f945eb181c031f82c1484e10021296524814c2c0

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