The Mechanism · Gated-generation receipt

gen-state-propositional-logic-precisely-and-explain-why-it-matte-6a4a

stable pending witness
2026-05-29 06:48:44 UTC · anthropic/claude-sonnet-4-5

Prompt

State propositional logic precisely and explain why it matters in 2-3 sentences.
80 chars

Generation

# Propositional Logic **Precise Definition:** Propositional logic is a formal system for reasoning about propositions (statements that are either true or false) using logical connectives (¬, ∧, ∨, →, ↔) and rules of inference to derive valid conclusions from premises. **Why It Matters:** Propositional logic forms the foundation for rigorous reasoning in mathematics, computer science, and philosophy by providing a precise framework to distinguish valid arguments from invalid ones. It underlies critical applications including circuit design, automated reasoning systems, programming language semantics, and artificial intelligence, making it essential for both theoretical understanding and practical problem-solving.
26 tokens in · 146 tokens out · 4260 ms · $0.0023

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
4270.5 ms
Base LLM
4259.7 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0023

Trail

06:48:44 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
06:48:44 red_gate decision=pass reason=no disqualifying input patterns detected
06:48:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=146 latency_ms=4259.7 cost_usd=0.0023
06:48:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:48:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:48:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:48:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:48:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:48:49 signed hash_algo=sha256 hash=sha256:20b0e89eef9dac4d9e5d4fc52cb5e72f06103df16ced207182003a87458d2025

Content hash

sha256:20b0e89eef9dac4d9e5d4fc52cb5e72f06103df16ced207182003a87458d2025

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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