{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HKHI264B7SXOPSFVXTWBAZJHUN","short_pith_number":"pith:HKHI264B","schema_version":"1.0","canonical_sha256":"3a8e8d7b81fcaee7c8b5bcec106527a372d951c61ffc9d31ac8a96a11a0c54a9","source":{"kind":"arxiv","id":"2605.20008","version":1},"attestation_state":"computed","paper":{"title":"Central idempotents in group-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert","submitted_at":"2026-05-19T15:39:19Z","abstract_excerpt":"Let $G$ be a group and let $R$ be a $G$-graded ring. We show that a nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain one-sided non-annihilation condition on nonzero homogeneous elements. In particular, under the respective hypotheses, if $G$ is torsion-free, then every central idempotent lies in the principal component of the grading. Our results generalize those of H. Bass and R. G. Burns from group rings to non-commutative, possibly non-unital, group-graded rings. We demonstrat"},"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":"2605.20008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-19T15:39:19Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"911b5fb7d6557d3c860edf76f8826678375d5b04ecf93d9e89a9015a7da5edd1","abstract_canon_sha256":"3bc9b07df59a65d80c6feb383dc9c7ef45b1ec631962ecc86211ede8fbef2174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:05:58.768528Z","signature_b64":"eYEygHGEb2swipoAEGZ4cl/r26tz7nIKN0KvUWcag17sPLK3mKH7iX9x52o13MXCch2GcGC1bVruDgLJ84lFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a8e8d7b81fcaee7c8b5bcec106527a372d951c61ffc9d31ac8a96a11a0c54a9","last_reissued_at":"2026-05-20T02:05:58.767948Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:05:58.767948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central idempotents in group-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert","submitted_at":"2026-05-19T15:39:19Z","abstract_excerpt":"Let $G$ be a group and let $R$ be a $G$-graded ring. We show that a nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain one-sided non-annihilation condition on nonzero homogeneous elements. In particular, under the respective hypotheses, if $G$ is torsion-free, then every central idempotent lies in the principal component of the grading. Our results generalize those of H. Bass and R. G. Burns from group rings to non-commutative, possibly non-unital, group-graded rings. We demonstrat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20008","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/2605.20008/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":"2605.20008","created_at":"2026-05-20T02:05:58.768047+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20008v1","created_at":"2026-05-20T02:05:58.768047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20008","created_at":"2026-05-20T02:05:58.768047+00:00"},{"alias_kind":"pith_short_12","alias_value":"HKHI264B7SXO","created_at":"2026-05-20T02:05:58.768047+00:00"},{"alias_kind":"pith_short_16","alias_value":"HKHI264B7SXOPSFV","created_at":"2026-05-20T02:05:58.768047+00:00"},{"alias_kind":"pith_short_8","alias_value":"HKHI264B","created_at":"2026-05-20T02:05:58.768047+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/HKHI264B7SXOPSFVXTWBAZJHUN","json":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN.json","graph_json":"https://pith.science/api/pith-number/HKHI264B7SXOPSFVXTWBAZJHUN/graph.json","events_json":"https://pith.science/api/pith-number/HKHI264B7SXOPSFVXTWBAZJHUN/events.json","paper":"https://pith.science/paper/HKHI264B"},"agent_actions":{"view_html":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN","download_json":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN.json","view_paper":"https://pith.science/paper/HKHI264B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20008&json=true","fetch_graph":"https://pith.science/api/pith-number/HKHI264B7SXOPSFVXTWBAZJHUN/graph.json","fetch_events":"https://pith.science/api/pith-number/HKHI264B7SXOPSFVXTWBAZJHUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN/action/storage_attestation","attest_author":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN/action/author_attestation","sign_citation":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN/action/citation_signature","submit_replication":"https://pith.science/pith/HKHI264B7SXOPSFVXTWBAZJHUN/action/replication_record"}},"created_at":"2026-05-20T02:05:58.768047+00:00","updated_at":"2026-05-20T02:05:58.768047+00:00"}