What a Cross-Model Fixed-Point Census Can and Cannot Arbitrate About Repetition

Two accounts of neural text degeneration coexist. One locates the cause in the training data -- repetition in the corpus produces repetition in the output, established by training on repetition-sorted data -- the other in the trained network, in copying circuits and repetition features. Neither has been arbitrated across a broad cohort of pretrained models: the causal work trains its own. We report an observational measurement in a different currency: the fixed-point structure of a model's own short-window argmax map, censused from 96 random two-token starts over 17 off-the-shelf models, always unprompted -- a companion paper shows nine tokens of conditioning move this readout across most of its range. The four-way class is stable across census seeds on 17 of 17. Three exhibits. At fixed corpus (The Pile), fixed scale and that fixed domain, the class is not determined: across two size-matched tiers, pythia is a funnel while RWKV, Mamba and a second transformer family are not, and both hold their class across an order of magnitude of scale. Six of seven models in that ladder reach the same endpoint token, and those concentrating on it most strongly are among those that never stay there -- what varies is not where trajectories go but whether the destination self-continues. The deduplicated Pythia suite does not change the class. And the corpus-side inflow term proposed for this phenomenon does not select our endpoints once frequency is controlled, in English and three other languages. This is observational and cannot refute a training intervention. Funnels are common: eight of seventeen models, seven families, five corpora -- so the limit is not that the phenomenon is one model's peculiarity, but that within the one corpus where training data can be held fixed only one available family funnels; that subset cannot show the split is corpus-independent.