The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-predicate-logic-state-any-key-formu-262c

stable pending witness
2026-05-29 05:19:49 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain predicate logic. State any key formula.
65 chars

Generation

# Predicate Logic Explanation Predicate logic (also called first-order logic) extends propositional logic by allowing reasoning about objects, their properties, and relationships using variables, predicates, and quantifiers. It introduces predicates like P(x) meaning "x has property P" and quantifiers: the universal quantifier ∀x (for all x) and existential quantifier ∃x (there exists an x). **Key formulas:** - **Universal instantiation**: ∀x P(x) → P(a) (if P holds for all x, it holds for any specific a) - **Existential generalization**: P(a) → ∃x P(x) (if P holds for some specific a, then there exists an x for which P holds) This allows expressing statements like "All humans are mortal" as ∀x (Human(x) → Mortal(x)).
25 tokens in · 209 tokens out · 4573 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
4585.9 ms
Base LLM
4573.3 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0032

Trail

05:19:49 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
05:19:49 red_gate decision=pass reason=no disqualifying input patterns detected
05:19:53 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=209 latency_ms=4573.3 cost_usd=0.0032
05:19:53 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:19:53 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:19:53 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:19:53 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:19:53 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:19:53 signed hash_algo=sha256 hash=sha256:80e5bb2ec1c8e6afa1c1267362b59a56e8646c975fe6d447f29a1bb1d584d8db

Content hash

sha256:80e5bb2ec1c8e6afa1c1267362b59a56e8646c975fe6d447f29a1bb1d584d8db

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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