The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-quantifier-negation-state-any-key-f-e903

stable pending witness
2026-05-29 07:13:15 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain quantifier negation. State any key formula.
69 chars

Generation

# Quantifier Negation Quantifier negation is the logical principle that negating a quantified statement converts universal quantifiers to existential quantifiers and vice versa. The key formulas are: - **¬∀x P(x) ≡ ∃x ¬P(x)** ("not all x satisfy P" means "some x doesn't satisfy P") - **¬∃x P(x) ≡ ∀x ¬P(x)** ("there is no x satisfying P" means "all x don't satisfy P") This principle is essential for working with negations in predicate logic and proves that denying "everything has property P" is equivalent to asserting "something lacks property P."
26 tokens in · 173 tokens out · 4198 ms · $0.0027

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
4209.8 ms
Base LLM
4198.4 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0027

Trail

07:13:15 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
07:13:15 red_gate decision=pass reason=no disqualifying input patterns detected
07:13:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=173 latency_ms=4198.4 cost_usd=0.0027
07:13:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:13:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:13:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:13:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:13:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:13:19 signed hash_algo=sha256 hash=sha256:dcc0f8c72bfa7b0f0a57650162269f8f6cd7bc9b16e50f4275b1ef90fd9ed264

Content hash

sha256:dcc0f8c72bfa7b0f0a57650162269f8f6cd7bc9b16e50f4275b1ef90fd9ed264

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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