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We define a tangent class \\(T_{M,\\G}\\) in the \\(K\\)-ring \\(K(M,\\G)\\), which extends the tangent bundle class of the de Concini--Procesi wonderful model from realizable matroids to arbitrary matroids with building sets.\n  The class \\(T_{M,\\G}\\) satisfies a matroidal Hirzebruch--Riemann--Roch package. More precisely, its Hirzebruch class \\[ \\operatorname{ch}(\\lambda_y T_{M,\\G}^{\\vee})\\operatorname{td}(T_{M,\\G}) \\] specializes to the Todd class and computes the Chow polyno"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.22650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-21T19:50:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9321a299f746887f277264222cc14cb8200a57428c0ec5fbcba74213a29a22ac","abstract_canon_sha256":"a25ec9ac3685f9878ebb14eb11ef5e1348bebc649f47e22814434ac61b4d51ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:43.973403Z","signature_b64":"LN6DaUjHtIWp3+LRvqe8RHSXhRUxnjf84TFGV7q6KKBMZphkXFUwpm7WPwAS3+8nyGXJHLhyJ9a6LSXrrEzxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88008c08a8e1321741a07227a161edc1ad4f202dbc311029246531a110a1952b","last_reissued_at":"2026-06-23T02:13:43.973015Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:43.973015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tangent classes for matroid building sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Ronnie Cheng","submitted_at":"2026-06-21T19:50:44Z","abstract_excerpt":"Let \\(M\\) be a loopless matroid on a finite ground set \\(E\\), and let \\(\\G\\) be a building set containing the top flat \\(E\\). We define a tangent class \\(T_{M,\\G}\\) in the \\(K\\)-ring \\(K(M,\\G)\\), which extends the tangent bundle class of the de Concini--Procesi wonderful model from realizable matroids to arbitrary matroids with building sets.\n  The class \\(T_{M,\\G}\\) satisfies a matroidal Hirzebruch--Riemann--Roch package. More precisely, its Hirzebruch class \\[ \\operatorname{ch}(\\lambda_y T_{M,\\G}^{\\vee})\\operatorname{td}(T_{M,\\G}) \\] specializes to the Todd class and computes the Chow polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22650","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/2606.22650/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.22650","created_at":"2026-06-23T02:13:43.973076+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22650v1","created_at":"2026-06-23T02:13:43.973076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22650","created_at":"2026-06-23T02:13:43.973076+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAAIYCFI4EZB","created_at":"2026-06-23T02:13:43.973076+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAAIYCFI4EZBOQNA","created_at":"2026-06-23T02:13:43.973076+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAAIYCFI","created_at":"2026-06-23T02:13:43.973076+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2607.05835","citing_title":"Tangent classes of matroids and wonderful compactifications","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2607.06447","citing_title":"Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2607.05835","citing_title":"Tangent classes of matroids and wonderful compactifications","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2607.06447","citing_title":"Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG","json":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG.json","graph_json":"https://pith.science/api/pith-number/RAAIYCFI4EZBOQNAOIT2CYPNYG/graph.json","events_json":"https://pith.science/api/pith-number/RAAIYCFI4EZBOQNAOIT2CYPNYG/events.json","paper":"https://pith.science/paper/RAAIYCFI"},"agent_actions":{"view_html":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG","download_json":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG.json","view_paper":"https://pith.science/paper/RAAIYCFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22650&json=true","fetch_graph":"https://pith.science/api/pith-number/RAAIYCFI4EZBOQNAOIT2CYPNYG/graph.json","fetch_events":"https://pith.science/api/pith-number/RAAIYCFI4EZBOQNAOIT2CYPNYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG/action/storage_attestation","attest_author":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG/action/author_attestation","sign_citation":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG/action/citation_signature","submit_replication":"https://pith.science/pith/RAAIYCFI4EZBOQNAOIT2CYPNYG/action/replication_record"}},"created_at":"2026-06-23T02:13:43.973076+00:00","updated_at":"2026-06-23T02:13:43.973076+00:00"}