The Mechanism · Gated-generation receipt

gen-explain-a-counterexample-as-you-would-to-a-capable-student-i-110c

stable pending witness
2026-05-29 08:07:58 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain a counterexample as you would to a capable student, in 3-4 sentences.
77 chars

Generation

A counterexample is a specific example that proves a general statement is false. To use one, you find just a single case where the claimed rule doesn't work—that's enough to show the statement isn't always true. For instance, if someone claims "all prime numbers are odd," you can disprove it with the counterexample of 2, which is prime but even. Counterexamples are powerful because one concrete instance of failure is all you need to reject a universal claim.
29 tokens in · 106 tokens out · 4725 ms · $0.0017

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
4730.0 ms
Base LLM
4724.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0017

Trail

08:07:58 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
08:07:58 red_gate decision=pass reason=no disqualifying input patterns detected
08:08:02 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=106 latency_ms=4724.5 cost_usd=0.0017
08:08:02 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:08:02 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:08:02 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:08:02 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:08:02 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:08:02 signed hash_algo=sha256 hash=sha256:ac550290a990e743fdba31f9f70d8256187e29c48b4ae929ef3cb365cd2e6936

Content hash

sha256:ac550290a990e743fdba31f9f70d8256187e29c48b4ae929ef3cb365cd2e6936

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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