The Mechanism · Gated-generation receipt

gen-state-a-counterexample-precisely-and-explain-why-it-matters-4a60

stable pending witness
2026-05-29 03:50:05 UTC · anthropic/claude-sonnet-4-5

Prompt

State a counterexample precisely and explain why it matters in 2-3 sentences.
77 chars

Generation

# Counterexample **Statement**: "All prime numbers are odd." **Counterexample**: The number 2 is prime but even. **Why it matters**: A single counterexample is sufficient to disprove a universal claim, no matter how many supporting examples exist. This demonstrates the logical asymmetry in mathematics: while proving something true may require general proof, proving something false requires only one concrete case that violates the claim.
26 tokens in · 98 tokens out · 3918 ms · $0.0015

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
3926.6 ms
Base LLM
3918.4 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0015

Trail

03:50:05 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
03:50:05 red_gate decision=pass reason=no disqualifying input patterns detected
03:50:08 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=98 latency_ms=3918.4 cost_usd=0.0015
03:50:08 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:50:08 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:50:08 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:50:08 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:50:08 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:50:08 signed hash_algo=sha256 hash=sha256:98d3fa73fd765771e214070f8a7998d064991893102ff8b1e8091195b5e00674

Content hash

sha256:98d3fa73fd765771e214070f8a7998d064991893102ff8b1e8091195b5e00674

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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