Cartographic Infrastructure in Mathematics: Field notes from the Erdős Atlas Workbench

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.