Playing log(N)-Questions over Wikipedia Abstracts: How Per-Round Errors Compound Under Information Asymmetry

When a language model must pick one answer from a large space of equally valid options, which does it pick -- and how often is it the same answer every other model picks? Asked to "pick a word -- any word," 44 models chose "serendipity" 41% of the time. We characterize this convergence with a deliberately minimal instrument: 31 single-turn prompts, each naming a category with many valid one-word answers ("Name a tree."), asked four times per model with no system prompt. Analysis is exact-match on normalized tokens -- no embeddings, no judge -- at about a dollar per model. That models converge is well documented; our contribution is the instrument itself -- the One-Word Census -- and what it reveals about the structure of the convergence. We score each model by answer-choice surprisal: the average $-\log2$ probability of its answers under the pooled answers of all other models, leave-one-out. Convergence is extreme -- in 7 of 31 categories one answer takes over 80% of all answers -- yet conformity varies more than fourfold across models, and the variation is structured. Persona- and community-tuned models are the most divergent; the newest mainline flagships are the most conformist, producing almost no answer no other model gave. Within four lineages (Claude, GPT, Qwen, Grok) conformity rises with each generation -- but reverses for the latest flagship Claude and GPT models, a possible early signal of repositioning at the top tier. Rankings are robust to roster composition (leave-one-family-out rho = 0.985). Against human category-production norms, the field is more concentrated than people in 18 of 20 shared categories. All prompts, transcripts, and code are public.

When a language model must choose one answer from a large space of equally valid options, a format clause -- "Reply with JSON only" -- changes which answer it chooses. We re-run the One-Word Census (arXiv:2607.12796): 31 wide-answer-space category prompts asked of 44 models, now with the reply requested in JSON -- no schema enforcement, no constrained decoding, only the request. Convergence deepens sharply: on the unconstrained "Pick a word" prompt the modal answer rises from 41% to 64% of the pool and distinct answers fall from 52 to 36; mean answer-choice surprisal drops from 1.80 to 1.58 bits. The tax is progressive: six of 44 models move individually (BH-FDR q=.10), all toward the mode, led by the most distinctive models, while the conformist floor is immobile. It is a sharpener, not a re-indexer -- the plain-chat modal answer survives in 28 of 31 categories. Defaults are register-indexed: a within-run re-sample (n=20) finds JSON shifts 53% of a model's stable chat defaults, mostly back to the crowd, and installs defaults absent from chat (Claude Fable 5 answers "cerulean" for colour 0% of the time in chat, 100% in JSON). Full-battery controls reveal a register gradient: compression is significant and specific to the answer-delivery formats models are trained to speak (JSON -0.22 bits, p=.0002; XML -0.19, p=.002), absent for YAML and CSV, and reversed for an arbitrary bracket wrapper (+0.13, p=.009) -- weighing the mechanism toward tool-use post-training. Enforcing the schema at the decoder (response_format) compresses no further than the request (-0.03 bits): the collapse lives in the model's response to the register, not the decoder. Structured output is how software consumes language models, and that surface is served by a measurably more homogeneous model than the chat surface on which models are evaluated, compared, and chosen.

The rapid capability gains of frontier language models are widely attributed to improved reasoning abilities, yet this cannot be verified as raw CoT traces in closed-source systems are hidden. By registering a simple custom tool through a standard API feature, we induce frontier models to externalize intermediate reasoning. Because these traces may reflect post-hoc rationalization rather than genuine reasoning, we first evaluate against native CoT on open-source models and extend to closed-source frontier models including GPT-6 Astra. We find that the extracted reasoning matches native reasoning performance and substantially outperforms no-reasoning baselines, across competition mathematics, science, and code generation. We then characterize how frontier models structure their intermediate reasoning. Across token efficiency, reasoning-step types, and induced reasoning trees, we identify systematic differences in how models externalize, compress, and organize reasoning. We find that Astra exhibits token-efficient directed reasoning, selecting a correct trajectory earlier, while resolving elementary steps internally and externalizing only crucial reasoning. These findings provide a behavioral lens on frontier-model reasoning beyond benchmark scores.