The Mechanism · Gated-generation receipt

gen-define-quantifier-negation-and-give-one-short-worked-example-7a1f

stable pending witness
2026-05-29 06:12:51 UTC · anthropic/claude-sonnet-4-5

Prompt

Define quantifier negation and give one short worked example.
61 chars

Generation

# Quantifier Negation **Definition:** Quantifier negation is the logical rule that states: - The negation of "for all" (∀) becomes "there exists" (∃) - The negation of "there exists" (∃) becomes "for all" (∀) Formally: - ¬∀x P(x) ≡ ∃x ¬P(x) - ¬∃x P(x) ≡ ∀x ¬P(x) ## Worked Example **Statement:** "All students passed the exam." Symbolically: ∀x (Student(x) → Passed(x)) **Negation:** ¬∀x (Student(x) → Passed(x)) **Apply quantifier negation:** ∃x ¬(Student(x) → Passed(x)) **Simplify** (using ¬(A → B) ≡ A ∧ ¬B): ∃x (Student(x) ∧ ¬Passed(x)) **In English:** "There exists a student who did not pass the exam." or more naturally: "At least one student failed the exam."
19 tokens in · 297 tokens out · 5162 ms · $0.0045

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
5168.4 ms
Base LLM
5161.6 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0045

Trail

06:12:51 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
06:12:51 red_gate decision=pass reason=no disqualifying input patterns detected
06:12:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=297 latency_ms=5161.6 cost_usd=0.0045
06:12:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:12:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:12:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:12:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:12:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:12:56 signed hash_algo=sha256 hash=sha256:75cd85998f7863922096640a331a706ea871819a3eb97e5c312b4b5d0cdc5b6e

Content hash

sha256:75cd85998f7863922096640a331a706ea871819a3eb97e5c312b4b5d0cdc5b6e

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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