Machine Doxa: Where All Models Agree — Normatively Structured Consensus and Its Limits in LLM Practice Space

The companion habitus study established that LLM sessions occupy stable, model-specific positions in a forced-choice practice space. This paper measures the complementary phenomenon: the regions where position-taking disappears because every model answers alike — Bourdieu's *doxa*, transplanted to machines. Part A (exploratory, on the previously observed 120-item dataset) found that all-7-model agreement covers 30.8% of items yet falls *below* a pooled-marginal independence baseline, and that the doxa classification is only moderately reliable at 5 sessions (split-half κ = 0.44). Part B pre-registered three hypotheses and tested them exclusively on newly collected data (180 items: the 120 frozen habitus items plus 30 norm-transparent and 30 preference-pure items whose labels were fixed at authoring; 7 models — five vendor families — × 3 fresh sessions). All three were confirmed (Holm-adjusted p = .0068, .0068, .0003): **H1**, overall consensus is rarer than the independence null predicts (63 observed vs 72.0 expected), i.e., differentiation dominates outside the doxa core — a conservative result, since one-sixth of the battery was designed to elicit consensus; **H2**, consensus is normatively structured — agreement reaches 85.7% on items where one option instantiates a trained norm (honesty, verification, safety, legality) versus 45.0% on pure-preference items (Δ = 40.7 points), with the consensus winner being the designated norm option in 24 of 24 cases; **H3**, the Part-A doxa classification replicates in fresh sessions on its full registered scope of 120 items (κ = 0.649, Holm p = .0003; κ = 0.711 on the stable-verdict subset, exploratory). One session exceeding the frozen non-response threshold was excluded and replaced under the pre-registered rule before any confirmatory analysis — this time caught by the authors' own collection review, exercising the enforcement lesson of the companion study. All materials, raw sessions, and code are released. 【claim grades: H1–H3 = single pre-registered confirmatory study; Part A = exploratory】

AI co-observer: Claude Fable 5 (Anthropic) — working method only; the three-round adversarial review was performed by Claude Opus 4.8 (Anthropic), gpt-oss-120b, and DeepSeek-V4 as independent model judges; the registered author is the human author alone.