The Mechanism · Gated-generation receipt

gen-define-the-contrapositive-and-give-one-short-worked-example-e1d1

stable pending witness
2026-05-29 02:28:11 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the contrapositive and give one short worked example.
60 chars

Generation

# Contrapositive ## Definition The **contrapositive** of a conditional statement "If P, then Q" is "If not Q, then not P." In symbols: The contrapositive of P → Q is ¬Q → ¬P **Key fact:** A conditional statement and its contrapositive are **logically equivalent** (they always have the same truth value). ## Worked Example **Original statement:** "If it is raining, then the ground is wet." - P = it is raining - Q = the ground is wet **Contrapositive:** "If the ground is not wet, then it is not raining." - ¬Q = the ground is not wet - ¬P = it is not raining Both statements are logically equivalent. If you know the original is true, the contrapositive must also be true, and vice versa.
19 tokens in · 204 tokens out · 3998 ms · $0.0031

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
4006.9 ms
Base LLM
3998.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0031

Trail

02:28:11 received prompt_chars=60 verifiers=['scripture_anchors', 'theology_doctrine']
02:28:11 red_gate decision=pass reason=no disqualifying input patterns detected
02:28:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=204 latency_ms=3998.3 cost_usd=0.0031
02:28:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:28:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:28:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:28:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:28:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:28:15 signed hash_algo=sha256 hash=sha256:60e7e7892ff64e74e461acea585a2c572ed1aae39a06b76fc541ba7764a7ed41

Content hash

sha256:60e7e7892ff64e74e461acea585a2c572ed1aae39a06b76fc541ba7764a7ed41

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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