The Mechanism · Gated-generation receipt

gen-define-logical-consistency-and-give-one-short-worked-example-1450

stable pending witness
2026-05-29 06:37:14 UTC · anthropic/claude-sonnet-4-5

Prompt

Define logical consistency and give one short worked example.
61 chars

Generation

# Logical Consistency **Definition:** Logical consistency means that a set of statements, beliefs, or propositions do not contradict each other. A system is logically consistent if all its components can be simultaneously true without leading to a contradiction. ## Short Worked Example **Evaluate these statements for consistency:** 1. "All dogs are mammals." 2. "Rex is a dog." 3. "Rex is not a mammal." **Analysis:** - From statements 1 and 2, we can logically derive: "Rex is a mammal" - But statement 3 says: "Rex is not a mammal" - These conclusions contradict each other **Conclusion:** This set of statements is **logically inconsistent** because accepting all three as true leads to the contradiction that Rex both is and is not a mammal. --- *To make it consistent, we'd need to remove or change statement 3.*
17 tokens in · 208 tokens out · 5691 ms · $0.0032

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
5698.1 ms
Base LLM
5690.6 ms
Verifiers
0.4 ms
Gates
0.0 ms
Cost
$0.0032

Trail

06:37:14 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
06:37:14 red_gate decision=pass reason=no disqualifying input patterns detected
06:37:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=17 tokens_out=208 latency_ms=5690.6 cost_usd=0.0032
06:37:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:37:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:37:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:37:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:37:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:37:20 signed hash_algo=sha256 hash=sha256:f6bb6ef3121b59c6637f6b5e006c538c39a53776a6ae2aa3a8b96c118be67296

Content hash

sha256:f6bb6ef3121b59c6637f6b5e006c538c39a53776a6ae2aa3a8b96c118be67296

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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