{"paper":{"title":"Edge-Span Chern Algebras of Graphical Configuration Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Jackson Walters","submitted_at":"2026-07-31T14:48:50Z","abstract_excerpt":"Place the vertices of a finite graph at projective points. Each edge defines a span map to $\\mathrm{Gr}(2,n)$; the pulled-back Chern classes generate a graded algebra $A_G^{(n)}$. This assignment is a covariant graph functor, so the abstract graded-algebra type is a graph invariant. In ambient dimension four, the Hilbert series is incomparable with the chromatic and Tutte polynomials. On five vertices in dimension three, the $34$ graph classes yield $33$ algebra types, strictly refining both classical polynomials. For every tree $T$, we obtain a closed Hilbert-series formula depending only on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29483","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29483/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}