The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-contrapositive-answer-concis-93ca

stable pending witness
2026-05-29 08:57:57 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the contrapositive? Answer concisely in 2-3 sentences.
82 chars

Generation

The contrapositive of a statement is logically equivalent to the original statement, meaning they always have the same truth value. This makes it significant in mathematical proofs because proving the contrapositive (if not Q, then not P) is often easier than proving the original statement (if P, then Q), yet it establishes the same result.
29 tokens in · 74 tokens out · 2277 ms · $0.0012

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
2284.1 ms
Base LLM
2277.0 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0012

Trail

08:57:57 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
08:57:57 red_gate decision=pass reason=no disqualifying input patterns detected
08:57:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=74 latency_ms=2277.0 cost_usd=0.0012
08:57:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:57:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:57:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:57:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:57:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:57:59 signed hash_algo=sha256 hash=sha256:ea87540df0a93ff23e835835cbce0d398952c46e20062761a7852e722232c174

Content hash

sha256:ea87540df0a93ff23e835835cbce0d398952c46e20062761a7852e722232c174

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.

Bring another teaching · Run a discernment