{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WLJEGYL3VSPYKUPHVN2MJYVNHM","short_pith_number":"pith:WLJEGYL3","schema_version":"1.0","canonical_sha256":"b2d243617bac9f8551e7ab74c4e2ad3b36edc9c16802ac73fe9ecdc234d5c368","source":{"kind":"arxiv","id":"1709.09289","version":3},"attestation_state":"computed","paper":{"title":"Smash products of group weighted bound quivers and Brauer graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hideto Asashiba","submitted_at":"2017-09-27T00:10:41Z","abstract_excerpt":"Let $\\Bbbk$ be a field, $G$ a group, and $(Q, I)$ a bound quiver. A map $W\\colon Q_1 \\to G$ is called a $G$-weight on $Q$, which defines a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$, and $W$ is called homogeneous if $I$ is a homogeneous ideal of the $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$. Then we have a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, I, W):= \\Bbbk(Q, W)/I$. We can then form a smash product $\\Bbbk(Q, I, W)\\# G$ of $\\Bbbk(Q, I, W)$ and $G$, which canonically defines a Galois covering $\\Bbbk(Q, I, W)\\# G \\to \\Bbbk(Q, I)$ with group $G$ (we will see that all such Galois coverings to $\\Bbb"},"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":"1709.09289","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-27T00:10:41Z","cross_cats_sorted":[],"title_canon_sha256":"8adb9a6081bd373a1894b0867e9f320222f36d24abd5e5da56c41da0cffdf894","abstract_canon_sha256":"18a9fa19a317225a04d2680aaefa7d2ccad13c589ff2b2e6ad5148e6985623d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:11.301911Z","signature_b64":"uaHPwLmVd+QdgmBnq4B4sP5JCteh7/ZY5im0r/ylpjtFnQyYzNnqVADBhdnXCbqxgQQOSGceWdM1YYL28TtZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2d243617bac9f8551e7ab74c4e2ad3b36edc9c16802ac73fe9ecdc234d5c368","last_reissued_at":"2026-05-18T00:10:11.301232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:11.301232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smash products of group weighted bound quivers and Brauer graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hideto Asashiba","submitted_at":"2017-09-27T00:10:41Z","abstract_excerpt":"Let $\\Bbbk$ be a field, $G$ a group, and $(Q, I)$ a bound quiver. A map $W\\colon Q_1 \\to G$ is called a $G$-weight on $Q$, which defines a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$, and $W$ is called homogeneous if $I$ is a homogeneous ideal of the $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$. Then we have a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, I, W):= \\Bbbk(Q, W)/I$. We can then form a smash product $\\Bbbk(Q, I, W)\\# G$ of $\\Bbbk(Q, I, W)$ and $G$, which canonically defines a Galois covering $\\Bbbk(Q, I, W)\\# G \\to \\Bbbk(Q, I)$ with group $G$ (we will see that all such Galois coverings to $\\Bbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09289","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1709.09289","created_at":"2026-05-18T00:10:11.301333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09289v3","created_at":"2026-05-18T00:10:11.301333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09289","created_at":"2026-05-18T00:10:11.301333+00:00"},{"alias_kind":"pith_short_12","alias_value":"WLJEGYL3VSPY","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WLJEGYL3VSPYKUPH","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WLJEGYL3","created_at":"2026-05-18T12:31:53.515858+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/WLJEGYL3VSPYKUPHVN2MJYVNHM","json":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM.json","graph_json":"https://pith.science/api/pith-number/WLJEGYL3VSPYKUPHVN2MJYVNHM/graph.json","events_json":"https://pith.science/api/pith-number/WLJEGYL3VSPYKUPHVN2MJYVNHM/events.json","paper":"https://pith.science/paper/WLJEGYL3"},"agent_actions":{"view_html":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM","download_json":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM.json","view_paper":"https://pith.science/paper/WLJEGYL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09289&json=true","fetch_graph":"https://pith.science/api/pith-number/WLJEGYL3VSPYKUPHVN2MJYVNHM/graph.json","fetch_events":"https://pith.science/api/pith-number/WLJEGYL3VSPYKUPHVN2MJYVNHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM/action/storage_attestation","attest_author":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM/action/author_attestation","sign_citation":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM/action/citation_signature","submit_replication":"https://pith.science/pith/WLJEGYL3VSPYKUPHVN2MJYVNHM/action/replication_record"}},"created_at":"2026-05-18T00:10:11.301333+00:00","updated_at":"2026-05-18T00:10:11.301333+00:00"}