The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-logical-quantifiers-state-any-key-f-2498

stable pending witness
2026-05-29 06:22:43 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

# Logical Quantifiers Logical quantifiers are symbols used in predicate logic to express the quantity of objects that satisfy a given property. The two fundamental quantifiers are the **universal quantifier** (∀), meaning "for all," and the **existential quantifier** (∃), meaning "there exists." **Key formulas:** - ∀x P(x): "For all x, P(x) is true" - ∃x P(x): "There exists at least one x such that P(x) is true" These quantifiers can be negated using the equivalences: ¬∀x P(x) ≡ ∃x ¬P(x) and ¬∃x P(x) ≡ ∀x ¬P(x).
25 tokens in · 190 tokens out · 5663 ms · $0.0029

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
5670.8 ms
Base LLM
5663.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0029

Trail

06:22:43 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
06:22:43 red_gate decision=pass reason=no disqualifying input patterns detected
06:22:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=190 latency_ms=5663.4 cost_usd=0.0029
06:22:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:22:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:22:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:22:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:22:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:22:49 signed hash_algo=sha256 hash=sha256:61a87f7565d78d76a54f2903df85b73cdfc464c07a6e4ea67d7c17f183329a0d

Content hash

sha256:61a87f7565d78d76a54f2903df85b73cdfc464c07a6e4ea67d7c17f183329a0d

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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