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The mathematical thesis, executable system, benchmark surface, and public claims must mature together, yet often drift apart. We identify two LM-specific failure modes: hallucination accumulation, in which claims exceed what code or theory supports and unsupported assertions propagate across sessions; and desynchronization, in which code, theory, or the model's own world model fall out of alignment.\n  We propose Comet-H, an iterative prompt automaton that orchestrates ideation, implementation, evaluation, grounding, and paper-writing as coupled coordinates of a single workspace state. At each step, a controller selects the next prompt by scoring it against what the workspace currently lacks, carries unfinished follow-up work forward with a half-life, and re-checks the paper and","title":"Theory Under Construction: Orchestrating Language Models for Research Software Where the Specification Evolves","url":"https://arxiv.org/abs/2604.27209","vendor":"arxiv_cs_ai"},"summary":"arXiv:2604.27209v2 Announce Type: replace-cross \nAbstract: Large language models can now generate substantial code and draft research text, but research-software projects require more than either artifact alone. The mathematical thesis, executable system, benchmark surface, and public claims must mature together, yet often drift apart. 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