The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-propositional-logic-state-any-key-f-b34e

stable pending witness
2026-05-29 06:59:16 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain propositional logic. State any key formula.
69 chars

Generation

Propositional logic is a formal system for reasoning about statements that are either true or false, using logical connectives like AND, OR, NOT, and IMPLIES. It represents arguments using propositional variables (p, q, r, etc.) combined with these operators to form compound propositions. A key formula is **modus ponens**: if p → q is true and p is true, then q must be true, written as ((p → q) ∧ p) → q. Propositional logic forms the foundation for more complex logical systems and is widely used in mathematics, computer science, and philosophy.
26 tokens in · 134 tokens out · 4021 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
4030.7 ms
Base LLM
4021.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

06:59:16 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
06:59:16 red_gate decision=pass reason=no disqualifying input patterns detected
06:59:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=134 latency_ms=4021.1 cost_usd=0.0021
06:59:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:59:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:59:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:59:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:59:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:59:20 signed hash_algo=sha256 hash=sha256:0b2c7deee1498b75a2eda750b96a51cec087d6f9e8afca763fc0d23f081570ba

Content hash

sha256:0b2c7deee1498b75a2eda750b96a51cec087d6f9e8afca763fc0d23f081570ba

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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