Chain-of-thought monitoring is proposed for AI oversight, yet evaluations often provide monitors with a trusted reference answer. We ask whether answer access improves reasoning verification or mainly exposes incorrect conclusions. We collected 237 step-numbered solutions to 79 Humanity's Last Exam physics questions from three frontier models, with no inserted errors, and independently labelled final-answer correctness and the first false step. The reference standard combined physicist annotations, an independent LLM debate, and source-masked adjudication. This yielded 24 critical traces in which the answer was correct but the trace contained a genuine error. 8 LLM monitors evaluated traces blind, with an unverified or certified answer, or after a blind commitment. Certification raised mean balanced accuracy from 0.637 to 0.796, while exact first-error localization rose from 0.261 to 0.379. Certification changed recall (the fraction of error traces flagged as erroneous) from 0.653 to 0.951 on wrong-answer traces but from 0.521 to 0.438 on critical traces; the contrast had the same direction for all 8 monitors (question-bootstrap 95% CI [+0.256, +0.506]). After blind commitment, monitors shown the answer newly flagged 93.8% of previously passed wrong-answer traces as erroneous, but only 18.0% of critical traces. Answer access therefore improves conclusion-consistency checking rather than independent verification of the supporting argument. For AI safety, these traces provide a benign analogue of reward hacking: an acceptable output does not establish that the process producing it was sound. Although the errors studied here were ordinary and mostly non-load-bearing rather than adversarial, trusted-answer evaluations may similarly overstate monitoring capability when acceptable outputs conceal unsound reasoning.
We propose claim-level falsification as a principle for test-time scaling and instantiate it through Claim-Level Reliability Assessment (CLR), a training-free framework that reallocates test-time compute from additional solution sampling to targeted verification. Since whole-trace evaluation often obscures decisive errors due to signal dilution from routine tokens, CLR condenses each reasoning trace into a compact set of decision-critical claims, thereby isolating its logical anchors. Furthermore, recognizing the inherent difficulty of generating entirely correct solutions under fixed model capabilities, CLR shifts the focus to semantic falsification. This approach exploits a fundamental asymmetry between solution construction and claim refutation. Constructing a valid solution requires a flawless reasoning path, whereas refuting an incorrect claim requires identifying only a single decisive flaw. This targeted search for negative evidence systematically compresses the survival space of high-confidence incorrect traces, effectively suppressing erroneous consensus via nonlinear reliability scoring. Across four LLMs and four reasoning benchmarks under matched budgets, CLR generally improves upon pass@1 and self-consistency. On GPT-OSS-20B/CMIMC25, for instance, CLR exceeds pass@1 by 27.15 percentage-points and raises self-consistency accuracy from 77.50\% to 82.19\% with 37.0\% fewer tokens.
Large language models have achieved impressive performance on reasoning tasks spanning mathematics, science, programming, and commonsense inference. Despite these advances, their reasoning processes remain largely latent, making them difficult to interpret, verify, replay, debug, and transfer across domains. Existing approaches such as chain-of-thought, tree-of-thoughts, graph-of-thoughts, and tool-augmented reasoning expose intermediate reasoning artifacts but typically lack explicit execution semantics, formal state representations, and verifiable reasoning structures. We introduce Theorem-Grounded Execution Ontologies (TGEO), a framework that models reasoning as an executable state-transition process rather than a sequence of generated tokens. Given an input problem, TGEO identifies relevant theorem families, binds the problem to a domain ontology, discovers semantic objects, instantiates states and operators, constructs predicates and contracts, and synthesizes an executable reasoning graph. The resulting graph provides an interpretable, replayable, and auditable representation of reasoning in which every state transition, operator application, and validation step is explicitly represented. TGEO integrates five architectural components: (1) theorem-grounded reasoning priors, (2) executable ontologies, (3) operator-mediated state transitions, (4) predicate and contract-based execution validation, and (5) architectural auditing and failure localization. We evaluate TGEO on theorem-intensive reasoning tasks derived from mathematical benchmark domains and a curated Golden Execution Suite. Our findings demonstrate the value of executable reasoning representations for interpretable, verifiable, and reproducible AI reasoning systems.