The Mechanism · Gated-generation receipt

gen-explain-the-contrapositive-as-you-would-to-a-capable-student-7c46

stable pending witness
2026-05-29 03:36:21 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the contrapositive as you would to a capable student, in 3-4 sentences.
79 chars

Generation

The contrapositive of a statement "If P, then Q" is "If not Q, then not P"—and here's the key: **these two statements are logically equivalent**, meaning they're always either both true or both false. For example, "If it's raining, then the ground is wet" has the contrapositive "If the ground is not wet, then it's not raining"—notice how both must be true together. This is incredibly useful in proofs because sometimes proving the contrapositive is much easier than proving the original statement directly, yet it accomplishes exactly the same thing.
29 tokens in · 132 tokens out · 4706 ms · $0.0021

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
4712.9 ms
Base LLM
4705.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

03:36:21 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
03:36:21 red_gate decision=pass reason=no disqualifying input patterns detected
03:36:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=132 latency_ms=4705.6 cost_usd=0.0021
03:36:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:36:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:36:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:36:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:36:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:36:26 signed hash_algo=sha256 hash=sha256:e9805feca7605cdff86c0fdd2b5cd9b1c7b1ad82a88aa25a27f91fd7f5097840

Content hash

sha256:e9805feca7605cdff86c0fdd2b5cd9b1c7b1ad82a88aa25a27f91fd7f5097840

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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