The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-contrapositive-state-any-key-fo-6b88

stable pending witness
2026-05-29 04:32:38 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the contrapositive. State any key formula.
68 chars

Generation

The contrapositive of a conditional statement "if P, then Q" is the statement "if not Q, then not P." **Key formula:** (P → Q) ≡ (¬Q → ¬P) The contrapositive is logically equivalent to the original statement, meaning they always have the same truth value. This makes the contrapositive useful in mathematical proofs: proving the contrapositive is equally valid as proving the original statement directly.
26 tokens in · 105 tokens out · 2835 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
2842.6 ms
Base LLM
2835.0 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0017

Trail

04:32:38 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
04:32:38 red_gate decision=pass reason=no disqualifying input patterns detected
04:32:41 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=105 latency_ms=2835.0 cost_usd=0.0017
04:32:41 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:32:41 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:32:41 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:32:41 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:32:41 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:32:41 signed hash_algo=sha256 hash=sha256:9fb3eeac9f336ac556448bce59bafb02221c5fa59ef8f4703890c5cb826e6e60

Content hash

sha256:9fb3eeac9f336ac556448bce59bafb02221c5fa59ef8f4703890c5cb826e6e60

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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