The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-counterexample-state-any-key-form-4689

stable pending witness
2026-05-29 06:19:12 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a counterexample. State any key formula.
66 chars

Generation

A counterexample is a specific example that disproves a mathematical statement or conjecture by showing at least one case where the statement is false. To disprove a universal statement of the form "For all x, P(x)," you only need to find one value of x where P(x) is false. For example, to disprove "all prime numbers are odd," the counterexample is 2, which is prime but even. **Key principle:** One counterexample is sufficient to disprove a universal claim.
26 tokens in · 116 tokens out · 3181 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
3188.6 ms
Base LLM
3181.2 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0018

Trail

06:19:12 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
06:19:12 red_gate decision=pass reason=no disqualifying input patterns detected
06:19:16 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=116 latency_ms=3181.2 cost_usd=0.0018
06:19:16 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:19:16 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:19:16 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:19:16 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:19:16 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:19:16 signed hash_algo=sha256 hash=sha256:cc8f3da0afe3b39589b6727420d6a1437c1c3b3680b73f0143200834cbd8dd69

Content hash

sha256:cc8f3da0afe3b39589b6727420d6a1437c1c3b3680b73f0143200834cbd8dd69

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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