The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-logical-consistency-state-any-key-f-ad5f

stable pending witness
2026-05-29 05:02:48 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain logical consistency. State any key formula.
69 chars

Generation

# Logical Consistency Logical consistency means that a set of statements or beliefs contains no contradictions—they can all be true simultaneously. A set of propositions is **consistent** if there exists at least one interpretation or model where all propositions are true together. **Key formula**: A set of formulas Γ is consistent if and only if **Γ ⊭ ⊥** (Γ does not entail a contradiction), or equivalently, there exists a model M such that **M ⊨ φ** for all φ ∈ Γ. Inconsistency arises when you can derive both a statement and its negation (P ∧ ¬P) from your set of assumptions.
24 tokens in · 170 tokens out · 5091 ms · $0.0026

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
5099.3 ms
Base LLM
5091.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

05:02:48 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
05:02:48 red_gate decision=pass reason=no disqualifying input patterns detected
05:02:53 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=170 latency_ms=5091.1 cost_usd=0.0026
05:02:53 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:02:53 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:02:53 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:02:53 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:02:53 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:02:53 signed hash_algo=sha256 hash=sha256:ce16d01d7c5ffde74c55e01bf1c872bfd2b6752d001f7acd5e1f73e5d0293944

Content hash

sha256:ce16d01d7c5ffde74c55e01bf1c872bfd2b6752d001f7acd5e1f73e5d0293944

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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