{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LMSSSJZG4TISLVUAXTITKPDGLE","short_pith_number":"pith:LMSSSJZG","canonical_record":{"source":{"id":"1304.0482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-01T21:09:16Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d403abe9a82cab6beeb6533ef0eb8db591e988435f93ab2917fefda3a072cf2b","abstract_canon_sha256":"c92a74230559e653c923d720fea0a20ecc08e3d302e82f52f388d9acfeb7a745"},"schema_version":"1.0"},"canonical_sha256":"5b25292726e4d125d680bcd1353c66592625d781e2bd76af243e0e9cf9b4e0b4","source":{"kind":"arxiv","id":"1304.0482","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0482","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0482v2","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0482","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"LMSSSJZG4TIS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LMSSSJZG4TISLVUA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LMSSSJZG","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LMSSSJZG4TISLVUAXTITKPDGLE","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-01T21:09:16Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d403abe9a82cab6beeb6533ef0eb8db591e988435f93ab2917fefda3a072cf2b","abstract_canon_sha256":"c92a74230559e653c923d720fea0a20ecc08e3d302e82f52f388d9acfeb7a745"},"schema_version":"1.0"},"canonical_sha256":"5b25292726e4d125d680bcd1353c66592625d781e2bd76af243e0e9cf9b4e0b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.252695Z","signature_b64":"sgLmdsdU5OkakHMmoLJkfp0YP7evh6y2Mv0Yq12tTRBsQI0Wh9qtzApYWb52qoaSJXksoYb4L+AyK2wMy55MAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b25292726e4d125d680bcd1353c66592625d781e2bd76af243e0e9cf9b4e0b4","last_reissued_at":"2026-05-18T02:54:05.251960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.251960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0482","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3iGaShWaUW24meixNgD4CDDJ/GODh3Hg71mEXLIGGgJghfBR3iHerGapoIlPFkhUw4Pd8zKL5eR9Jx0dJhiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:21:45.280617Z"},"content_sha256":"b93adefaba6dd5484729c1d5b8c5eba0b10e1547ec20e210713f9b23068a57ee","schema_version":"1.0","event_id":"sha256:b93adefaba6dd5484729c1d5b8c5eba0b10e1547ec20e210713f9b23068a57ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LMSSSJZG4TISLVUAXTITKPDGLE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finitistic dimensions and piecewise hereditary property of skew group algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Liping Li","submitted_at":"2013-04-01T21:09:16Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra and $G$ be a finite group whose elements act on $\\Lambda$ as algebra automorphisms. Under the assumption that $\\Lambda$ has a complete set $E$ of primitive orthogonal idempotents, closed under the action of a Sylow $p$-subgroup $S \\leqslant G$. If the action of $S$ on $E$ is free, we show that the skew group algebra $\\Lambda G$ and $\\Lambda$ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra $\\Lambda^S$ is a direct summand of the $\\Lambda^S$-bimodule $\\Lambda$. Using a homological characterization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0482","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ko1G5TkY6E8zrvsWEKGxOaKwINzXHJrSrMygAh+GHury8sVJ8ZFDl127kJf92vZ7WJYjQo+7D3UrFw/4oOwSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:21:45.281241Z"},"content_sha256":"ad02d316c3179528452ee36145ff5f7b505319a17d4974083a335379e5942d4f","schema_version":"1.0","event_id":"sha256:ad02d316c3179528452ee36145ff5f7b505319a17d4974083a335379e5942d4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMSSSJZG4TISLVUAXTITKPDGLE/bundle.json","state_url":"https://pith.science/pith/LMSSSJZG4TISLVUAXTITKPDGLE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMSSSJZG4TISLVUAXTITKPDGLE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T10:21:45Z","links":{"resolver":"https://pith.science/pith/LMSSSJZG4TISLVUAXTITKPDGLE","bundle":"https://pith.science/pith/LMSSSJZG4TISLVUAXTITKPDGLE/bundle.json","state":"https://pith.science/pith/LMSSSJZG4TISLVUAXTITKPDGLE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMSSSJZG4TISLVUAXTITKPDGLE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LMSSSJZG4TISLVUAXTITKPDGLE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c92a74230559e653c923d720fea0a20ecc08e3d302e82f52f388d9acfeb7a745","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-01T21:09:16Z","title_canon_sha256":"d403abe9a82cab6beeb6533ef0eb8db591e988435f93ab2917fefda3a072cf2b"},"schema_version":"1.0","source":{"id":"1304.0482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0482","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0482v2","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0482","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"LMSSSJZG4TIS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LMSSSJZG4TISLVUA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LMSSSJZG","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:ad02d316c3179528452ee36145ff5f7b505319a17d4974083a335379e5942d4f","target":"graph","created_at":"2026-05-18T02:54:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra and $G$ be a finite group whose elements act on $\\Lambda$ as algebra automorphisms. Under the assumption that $\\Lambda$ has a complete set $E$ of primitive orthogonal idempotents, closed under the action of a Sylow $p$-subgroup $S \\leqslant G$. If the action of $S$ on $E$ is free, we show that the skew group algebra $\\Lambda G$ and $\\Lambda$ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra $\\Lambda^S$ is a direct summand of the $\\Lambda^S$-bimodule $\\Lambda$. Using a homological characterization of ","authors_text":"Liping Li","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-01T21:09:16Z","title":"Finitistic dimensions and piecewise hereditary property of skew group algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0482","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b93adefaba6dd5484729c1d5b8c5eba0b10e1547ec20e210713f9b23068a57ee","target":"record","created_at":"2026-05-18T02:54:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c92a74230559e653c923d720fea0a20ecc08e3d302e82f52f388d9acfeb7a745","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-01T21:09:16Z","title_canon_sha256":"d403abe9a82cab6beeb6533ef0eb8db591e988435f93ab2917fefda3a072cf2b"},"schema_version":"1.0","source":{"id":"1304.0482","kind":"arxiv","version":2}},"canonical_sha256":"5b25292726e4d125d680bcd1353c66592625d781e2bd76af243e0e9cf9b4e0b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b25292726e4d125d680bcd1353c66592625d781e2bd76af243e0e9cf9b4e0b4","first_computed_at":"2026-05-18T02:54:05.251960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.251960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sgLmdsdU5OkakHMmoLJkfp0YP7evh6y2Mv0Yq12tTRBsQI0Wh9qtzApYWb52qoaSJXksoYb4L+AyK2wMy55MAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.252695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b93adefaba6dd5484729c1d5b8c5eba0b10e1547ec20e210713f9b23068a57ee","sha256:ad02d316c3179528452ee36145ff5f7b505319a17d4974083a335379e5942d4f"],"state_sha256":"ef5b62dd1bb6588be8db52437dd5c22e5113238c2363703c7ede550633c6d872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/p+2N4ZiIORXewLRo9kq/NVvJwk6w8Uj7f7loeWIC3POVP/3U5qQaCwcvg2H9s3AEYFyuy7OXxPWweoGIKzQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T10:21:45.284448Z","bundle_sha256":"6ec9d3ceb56afc0c33ead05b023af6598aeedbc0db3e0065714225b04ba393ad"}}