The Mechanism · Gated-generation receipt

gen-define-logical-quantifiers-and-give-one-short-worked-example-3718

stable pending witness
2026-05-29 05:27:45 UTC · anthropic/claude-sonnet-4-5

Prompt

Define logical quantifiers and give one short worked example.
61 chars

Generation

# Logical Quantifiers **Logical quantifiers** are symbols used in predicate logic to express statements about quantities of objects in a domain. ## The Two Main Quantifiers 1. **Universal Quantifier (∀)** - "for all" or "for every" - ∀x P(x) means "P(x) is true for all x in the domain" 2. **Existential Quantifier (∃)** - "there exists" or "for some" - ∃x P(x) means "there exists at least one x for which P(x) is true" ## Worked Example **Statement:** "Every student has at least one textbook." **Translation to logical form:** Let: - S(x) = "x is a student" - T(y) = "y is a textbook" - H(x,y) = "x has y" The statement becomes: **∀x (S(x) → ∃y (T(y) ∧ H(x,y)))** **Reading it back:** "For all x, if x is a student, then there exists a y such that y is a textbook and x has y." This shows how quantifiers work together: the universal quantifier (∀) ranges over all students, while the existential quantifier (∃) guarantees at least one textbook for each.
18 tokens in · 326 tokens out · 6212 ms · $0.0049

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
6220.6 ms
Base LLM
6212.5 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0049

Trail

05:27:45 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
05:27:45 red_gate decision=pass reason=no disqualifying input patterns detected
05:27:52 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=18 tokens_out=326 latency_ms=6212.5 cost_usd=0.0049
05:27:52 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:27:52 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:27:52 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:27:52 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:27:52 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:27:52 signed hash_algo=sha256 hash=sha256:72bdfa7d8b59afea7dc664fc471bb5d56df79049f58027e3d4e9630dbbbb5f16

Content hash

sha256:72bdfa7d8b59afea7dc664fc471bb5d56df79049f58027e3d4e9630dbbbb5f16

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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