{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Z2Z7YBBPMLYWXRZ4LNCVQJY6OF","short_pith_number":"pith:Z2Z7YBBP","schema_version":"1.0","canonical_sha256":"ceb3fc042f62f16bc73c5b4558271e716f2a9468e502525a574471967a84c262","source":{"kind":"arxiv","id":"2507.01412","version":2},"attestation_state":"computed","paper":{"title":"Coarse cone quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Ulrich Bunke","submitted_at":"2025-07-02T07:05:27Z","abstract_excerpt":"We study the coarse motive of the quotient $\\mathcal{O}^{\\infty}(X)//G$ of the cone of a uniform bornological coarse space $X$ with $G$-action. If $X$ admits a sufficiently ergodic probability measure, then we show that the coarse assembly map for $\\mathcal{O}^{\\infty}(X)//G$ is not an equivalence. The main ideas are taken from a recent paper by C. Kitsios, T. Schick and F. Vigolo (arXiv:2504.21811) and adapted to the formalism of coarse homotopy theory based on bornological coarse spaces developed by A. Engel and the author."},"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":"2507.01412","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-07-02T07:05:27Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"1797fb8b891b4cd88d9007b7889fb176a4839a946ce5d47a83b8b1492dca9477","abstract_canon_sha256":"100b2cd745f2bec81d38600909ed7a6d59f9b860455eabe2bde1e0cb2ce1aae0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:28.938252Z","signature_b64":"jh5l3HJlMRMZcBXY/mzzkFp36YWmGD+i0WnvOfec2NZAlET8ve+Uk+8dDqp56QFCeB0j6ESDBy5yu4lzzE34BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceb3fc042f62f16bc73c5b4558271e716f2a9468e502525a574471967a84c262","last_reissued_at":"2026-05-28T01:04:28.937569Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:28.937569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coarse cone quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Ulrich Bunke","submitted_at":"2025-07-02T07:05:27Z","abstract_excerpt":"We study the coarse motive of the quotient $\\mathcal{O}^{\\infty}(X)//G$ of the cone of a uniform bornological coarse space $X$ with $G$-action. If $X$ admits a sufficiently ergodic probability measure, then we show that the coarse assembly map for $\\mathcal{O}^{\\infty}(X)//G$ is not an equivalence. The main ideas are taken from a recent paper by C. Kitsios, T. Schick and F. Vigolo (arXiv:2504.21811) and adapted to the formalism of coarse homotopy theory based on bornological coarse spaces developed by A. Engel and the author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01412","kind":"arxiv","version":2},"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/2507.01412/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":"2507.01412","created_at":"2026-05-28T01:04:28.937662+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.01412v2","created_at":"2026-05-28T01:04:28.937662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.01412","created_at":"2026-05-28T01:04:28.937662+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2Z7YBBPMLYW","created_at":"2026-05-28T01:04:28.937662+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2Z7YBBPMLYWXRZ4","created_at":"2026-05-28T01:04:28.937662+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2Z7YBBP","created_at":"2026-05-28T01:04:28.937662+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF","json":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF.json","graph_json":"https://pith.science/api/pith-number/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/graph.json","events_json":"https://pith.science/api/pith-number/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/events.json","paper":"https://pith.science/paper/Z2Z7YBBP"},"agent_actions":{"view_html":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF","download_json":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF.json","view_paper":"https://pith.science/paper/Z2Z7YBBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.01412&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/action/storage_attestation","attest_author":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/action/author_attestation","sign_citation":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/action/citation_signature","submit_replication":"https://pith.science/pith/Z2Z7YBBPMLYWXRZ4LNCVQJY6OF/action/replication_record"}},"created_at":"2026-05-28T01:04:28.937662+00:00","updated_at":"2026-05-28T01:04:28.937662+00:00"}