# Judging Is Not Enumerating: Silent Omissions in LLM-Authored Acceptable Sets

arXiv: https://arxiv.org/abs/2608.01000 · HTML: https://mlsanity.com/paper/2608.01000/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 62 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Builds on (most cited first, 30 of 36)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [LLM Critics Help Catch LLM Bugs](https://mlsanity.com/paper/2407.00215/) (2024)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Answer Matching Outperforms Multiple Choice for Language Model Evaluation](https://mlsanity.com/paper/2507.02856/) (2025)
- [RubricBench: Aligning Model-Generated Rubrics with Human Standards](https://mlsanity.com/paper/2603.01562/) (2026)
- [LLMs Gaming Verifiers: RLVR can Lead to Reward Hacking](https://mlsanity.com/paper/2604.15149/) (2026)
- [SELF-[IN]CORRECT: LLMs Struggle with Discriminating Self-Generated Responses](https://mlsanity.com/paper/2404.04298/) (2024)
- [TOGLL: Correct and Strong Test Oracle Generation with LLMs](https://mlsanity.com/paper/2405.03786/) (2024)
- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [From Accuracy to Robustness: A Study of Rule- and Model-based Verifiers in Mathematical Reasoning](https://mlsanity.com/paper/2505.22203/) (2025)
- [TinyV: Reducing False Negatives in Verification Improves RL for LLM Reasoning](https://mlsanity.com/paper/2505.14625/) (2025)
- [Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Models](https://mlsanity.com/paper/2412.02674/) (2024)
- [Rethinking Verification for LLM Code Generation: From Generation to Testing](https://mlsanity.com/paper/2507.06920/) (2025)
- [Do LLMs generate test oracles that capture the actual or the expected program behaviour?](https://mlsanity.com/paper/2410.21136/) (2024)

## Built on by (most cited first, 2 of 2)

- [LLM Judges Verify Presence, Not Absence: Omission Blindness in AI Clinical Notes and What Recovers It](https://mlsanity.com/paper/2608.31016/) (2026)
- [The Architect, the Adversary, and the Judge: Closed-Loop Generation of Standards-Aligned Assessment Items at Scale](https://mlsanity.com/paper/2609.26087/) (2026)

## Abstract (arXiv)

Language models are increasingly promoted from examinees to examiners: they write the test suites, answer keys, rubrics, and reward functions that define correctness for other systems. We measure the capability that role assumes and find it lacking under the protocol the role is usually deployed with, one-shot greedy authoring with no test-time reasoning. Across four reference constructions - two with complete finite truth, one with a hardened executable reference (HumanEval+/MBPP+), one with an explicitly incomplete lexical reference (WordNet) - models judge whether a candidate belongs far better than they author the set itself. On the incompleteness-proof algorithmic construction the gap is +0.34 to +0.29 F1 over a 24x parameter range and does not close; on executable code, models judging at F1 0.74-0.90 author suites admitting only 19-42% of oracle-correct solutions. A control locates the deficit: asked to emit the predicate rather than its extension, the same models reach F1 about 0.99. The failure is not missing knowledge or an inability to specify, but an inability to materialise the region a specification induces. The dominant error is omission, which resists audit: an over-inclusion is a token a reviewer can challenge, a missing member an absence whose discovery is the authoring problem itself. Models detect planted over-inclusions 6-7x more often than planted omissions, and a production deployment of 43,227 items fails omission-first at 10:1. Wired into RLVR, an authored key costs 1.9 points of accuracy against an exact oracle and 18.5 WordNet-relative (six paired seeds, p=0.031). Gating authored verifiers on a known-correct probe cuts false rejection from 58-92% to at most 5%, but keeps only 5-39% of suites. Repairing them instead, by rewriting each wrong expected value to what a reference execution returns, raises yield 3.3-10.6x across four author families.