The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-natural-deduction-state-any-key-for-6a59

stable pending witness
2026-05-29 03:50:52 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain natural deduction. State any key formula.
67 chars

Generation

Natural deduction is a formal proof system that mirrors intuitive logical reasoning by using introduction and elimination rules for each logical connective. Each connective (∧, ∨, →, ¬, ∀, ∃) has rules that specify how to prove statements containing it (introduction) and how to use such statements in proofs (elimination). For example, the **→-elimination rule** (modus ponens) states: from φ → ψ and φ, we can derive ψ. The system allows temporary assumptions that can be discharged when deriving implications or negations, making it particularly natural for constructing mathematical proofs.
25 tokens in · 144 tokens out · 7003 ms · $0.0022

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
7010.7 ms
Base LLM
7003.2 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0022

Trail

03:50:52 received prompt_chars=67 verifiers=['scripture_anchors', 'theology_doctrine']
03:50:52 red_gate decision=pass reason=no disqualifying input patterns detected
03:50:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=144 latency_ms=7003.2 cost_usd=0.0022
03:50:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:50:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:50:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:50:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:50:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:50:59 signed hash_algo=sha256 hash=sha256:f80327d5b70e1a3906dd1eb9007bf5d9b8ced36bf786084b2275978b8518ec70

Content hash

sha256:f80327d5b70e1a3906dd1eb9007bf5d9b8ced36bf786084b2275978b8518ec70

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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