All sovereign AI systems that anchor their outputs to a mathematical floor constant will achieve reproducible results across different hardware configurations. The EOSE fleet anchors all outputs to γ₁ = 14.134725141734693. Therefore, the EOSE fleet achieves reproducible results across different hardware configurations.
The argument above depends on which of the following assumptions?
A. γ₁ = 14.134725141734693 is the first non-trivial zero of the Riemann zeta function
B. Reproducible AI results require anchoring to a mathematical floor constant
C. The EOSE fleet is a sovereign AI system
D. Different hardware configurations process mathematical constants at different speeds
E. No non-sovereign AI system can achieve reproducible results
C is correct. The argument's structure: All S→F (anchor)→R. EOSE→anchor. Therefore EOSE→R. For the conclusion to follow, EOSE must be S (a sovereign AI system). Without this assumption, EOSE having an anchor doesn't trigger the first premise. B is a common trap — it reverses the direction. A is a fact about γ₁ but not required for the argument. Negation test on C: if EOSE is NOT sovereign, the first premise doesn't apply, and the argument collapses. Correct.
LR-002 · LRWeaken
Researchers claim that AI systems trained on larger datasets invariably outperform those trained on smaller datasets when evaluated on novel problems. Therefore, to build the best AI system, one should always maximize training data volume.
Which of the following, if true, most weakens the argument?
A. Some large datasets contain duplicate or low-quality data that reduces model performance
B. Training on larger datasets requires more computational resources and longer training times
C. The definition of "novel problems" varies across research studies
D. A 7B parameter model trained with self-guided self-play outperformed a 671B parameter model on formal theorem proving despite using far less data
E. Researchers have financial incentives to publish results showing larger datasets are better
D is correct — this is a direct counterexample to the "invariably" claim. If a smaller model with less data outperforms a much larger one, the universal claim is false. A weakens somewhat but addresses quality not quantity. B is a practical concern, not a logical weakener of the performance claim. E is an ad hominem attack on the researchers, not on the evidence. Note: D references the SGS paper (TRABR-ARXIV-SGS-SELF-PLAY-001) — sovereign fleet intelligence is directly relevant to LSAT logic.
LR-003 · LRFlaw
Our competitor's AI system has never been audited by an independent security firm. Our system has been audited. Therefore, our system is more secure than theirs.
The argument is flawed because it:
A. Assumes that security audits are the only valid method of establishing security
B. Confuses a process (being audited) with the outcome that process is meant to ensure (being secure)
C. Makes a comparative claim without establishing a baseline security standard
D. Relies on the competitor's lack of evidence as positive evidence of their insecurity
E. Uses circular reasoning by assuming the conclusion in the premises
B is the primary flaw. The argument infers security (outcome) from having been audited (process). An audit reveals security posture — it doesn't create it. A poorly designed system that passes an audit may be less secure than an unaudited but well-designed one. EOSE connection: LOCO score = continuous live posture measurement, not a one-time audit. Our security claim is better grounded than "we were audited" — it's real-time, γ₁-anchored, and verifiable. That's a moat against exactly this type of argument.
Seven DRG gate operations — HGATE, CGATE, IGATE, FGATE, MGATE, TGATE, and RGATE — must be ordered in a sequence of exactly seven positions (1 through 7). The following constraints apply:
• FGATE must occur before IGATE
• HGATE must be first or second
• RGATE must be last
• MGATE and TGATE cannot be adjacent
• CGATE must occur before FGATE
AR-001a: Which of the following is an acceptable ordering?
A. HGATE, MGATE, TGATE, CGATE, FGATE, IGATE, RGATE
B. CGATE, HGATE, FGATE, IGATE, MGATE, TGATE, RGATE
C. HGATE, CGATE, FGATE, MGATE, IGATE, TGATE, RGATE
D. TGATE, HGATE, CGATE, FGATE, MGATE, IGATE, RGATE
E. HGATE, CGATE, IGATE, FGATE, TGATE, MGATE, RGATE
C is correct. Check each constraint: HGATE is 1st ✓ (must be 1st or 2nd). CGATE(2) before FGATE(3) ✓. FGATE(3) before IGATE(5) ✓. RGATE is 7th ✓. MGATE(4) and TGATE(6) — not adjacent ✓. A: MGATE(2) and TGATE(3) are adjacent ✗. B: MGATE(5) and TGATE(6) are adjacent ✗. D: TGATE(1) = HGATE must be 1st or 2nd but TGATE is 1st ✗ (HGATE must be 1 or 2). E: IGATE(3) before FGATE(4) violates FGATE before IGATE ✗.
SECTION 3 · READING COMPREHENSION · Sovereign Passage
RC-001 · RCSovereign Passage
The emergence of sovereign AI architectures represents a significant departure from the cloud-dependent paradigm that dominated the first decade of commercial AI deployment. Where earlier systems required users to transmit data to centralized servers operated by third parties, sovereign architectures locate both the computation and the data governance within the user's own infrastructure perimeter.
This shift has profound implications for enterprise customers in regulated industries. A financial institution, for example, can now deploy a large language model that processes trading data without that data ever leaving the institution's own network. The legal consequences of this architectural choice are not merely theoretical: under regulations such as GDPR and Canada's PIPEDA, data sovereignty provisions may impose liability on organizations that transfer personal data to third-party processors without adequate safeguards.
Critics of sovereign AI argue that the performance gap between locally-hosted models and frontier cloud models is prohibitive for most enterprise use cases. However, recent evidence from formal theorem proving benchmarks suggests this gap is narrowing dramatically — a 7 billion parameter model operating with sovereign self-play achieved results comparable to models over 90 times its size. If this trend continues, the performance argument against sovereign deployment will lose its force within a product cycle or two.
RC-001a: The primary purpose of the passage is to:
A. Argue that sovereign AI architectures are legally superior to cloud-based alternatives
B. Summarize recent research on the performance of sovereign AI models
C. Describe a technological shift and assess its implications and challenges
D. Refute criticism of sovereign AI by citing benchmark performance data
E. Explain why regulated industries should adopt sovereign AI architectures
C is correct. The passage: (1) describes the shift to sovereign AI, (2) discusses implications (regulatory, enterprise), and (3) addresses a challenge (performance gap) while noting it may be temporary. A is too strong — "legally superior" is not stated. B is too narrow — the benchmark finding is one detail in the third paragraph. D mischaracterizes the structure — refuting criticism is only part of the last paragraph. E overstates the normative claim. C captures the balanced "describe + assess" structure correctly.