The mathematics literature contains many papers about theorems and few papers about the cartographic objects mathematicians build to find them. This is the second kind: an observational, instrument-style study of the H² Erdős Atlas Workbench, a queryable representation of 1,223 formalized Erdős problems bound by 54,203 typed morphisms across eight families and rendered against a 34-object physics probe ring. The Workbench is treated as the object of study rather than as a tool. Five substantive observations emerge. First, mathematics-as-the-atlas-sees-it is interconnected primarily laterally through shared constraint geometry (19,547 in-corpus typed morphisms across 1,183 problems) rather than vertically through formal prerequisite chains (28 prerequisite edges, 1.2% coverage). Second, constraint-parallel edges (68% of in-corpus morphisms) are not merely informative but numerically dominant. Third, the atlas's physics framing operates as a coordinate system rather than a content claim, formally justified by a Lean-verified theorem (PinchingIdentity.lean, zero sorries, Mathlib-grounded) establishing that the entropy functional used equals, by definitional equality, classical Shannon entropy on a trace-normalized eigenvalue distribution. Fourth, the atlas anchors to mathematics-at-large via exactly four canonical-identity edges to Mathworld and Millennium Prize taxonomies, including the Riemann Hypothesis. Fifth, the atlas's published attackability index generalizes structurally (bootstrap 95% CI +0.38, +0.88) but its physics-similarity signal flips sign on out-of-distribution problems (−0.82, −0.30) — a documented case of shortcut learning in the sense of Geirhos et al. (Nature Machine Intelligence, 2020). Two threshold cliffs in the similarity distribution survive bootstrap confidence intervals and a 0.01-resolution binning ablation. The paper argues these observations are evidence that cartographic instruments in mathematics — alongside LMFDB, Mathlib's dependency graph, and the DeepMind formal-conjectures corpus — are now substantive enough to merit instrument-paper scrutiny. This is v7 of the draft. The deposit includes the markdown source, a PDF rendering, the redteam round provenance (FROZEN.lock with content hashes, self-audit critique, edit log), and is reproducible against the deployed Workbench at https://erdosatlas-private.dev-ef7.workers.dev/ with a public data API.
Kenneth A. Mendoza (Sun,) studied this question.