{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:L6QIAJEKIZWGRME5TNOI5PD7NH","short_pith_number":"pith:L6QIAJEK","canonical_record":{"source":{"id":"1202.2479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-11T23:33:21Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"1e8167fc004debaacc52771be2fc7600fe0b47e11f251d21c995583a53f2a121","abstract_canon_sha256":"e5a97d857f2036bad65d33acb5f9a44ccdfa5ac5252569836c141879ca00624f"},"schema_version":"1.0"},"canonical_sha256":"5fa080248a466c68b09d9b5c8ebc7f69f509312136074bc2fb0444a4bd21f0fd","source":{"kind":"arxiv","id":"1202.2479","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2479","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2479v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2479","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"L6QIAJEKIZWG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L6QIAJEKIZWGRME5","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L6QIAJEK","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:L6QIAJEKIZWGRME5TNOI5PD7NH","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-11T23:33:21Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"1e8167fc004debaacc52771be2fc7600fe0b47e11f251d21c995583a53f2a121","abstract_canon_sha256":"e5a97d857f2036bad65d33acb5f9a44ccdfa5ac5252569836c141879ca00624f"},"schema_version":"1.0"},"canonical_sha256":"5fa080248a466c68b09d9b5c8ebc7f69f509312136074bc2fb0444a4bd21f0fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:39.337426Z","signature_b64":"htqjp2+wWuwzsrnDoe6bRV918wxqeqe++laOB4MopgcrxgIWLvLQ9Wo7+fgNsUTCO+SBMtmez9tuGsn2m1OjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fa080248a466c68b09d9b5c8ebc7f69f509312136074bc2fb0444a4bd21f0fd","last_reissued_at":"2026-05-18T03:58:39.336714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:39.336714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2479","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Let2uTajYfzTyo8drtQ57nGipmitI7H30qMd43D/ambjFEG05wzm2oWQQWa+nZEbJd/k8tpTY93INuQCoWJ5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:44:53.901661Z"},"content_sha256":"7412cc27b79eed4690e9fca0bcb49755a5d601213976f58310e8721c99bc88cb","schema_version":"1.0","event_id":"sha256:7412cc27b79eed4690e9fca0bcb49755a5d601213976f58310e8721c99bc88cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:L6QIAJEKIZWGRME5TNOI5PD7NH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A classification of algebras stratified for all preorders by Koszul theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Liping Li","submitted_at":"2012-02-11T23:33:21Z","abstract_excerpt":"Let $A = \\bigoplus_{i \\geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing many classical results, and use it to classify algebras stratified for all preorders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2479","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oihTbaG/su7Sqd16SEtm7DBLzjeHgrPTEvxGVPC/+lH1RABzH6fFwwRN0lAAX16Jaz6QADzml+c0rzhCXOLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:44:53.902377Z"},"content_sha256":"fa6384cdb884823347653edff39be12219b20dd5243307350fec049030fdd458","schema_version":"1.0","event_id":"sha256:fa6384cdb884823347653edff39be12219b20dd5243307350fec049030fdd458"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/bundle.json","state_url":"https://pith.science/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/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":"2026-05-25T20:44:53Z","links":{"resolver":"https://pith.science/pith/L6QIAJEKIZWGRME5TNOI5PD7NH","bundle":"https://pith.science/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/bundle.json","state":"https://pith.science/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6QIAJEKIZWGRME5TNOI5PD7NH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L6QIAJEKIZWGRME5TNOI5PD7NH","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":"e5a97d857f2036bad65d33acb5f9a44ccdfa5ac5252569836c141879ca00624f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-11T23:33:21Z","title_canon_sha256":"1e8167fc004debaacc52771be2fc7600fe0b47e11f251d21c995583a53f2a121"},"schema_version":"1.0","source":{"id":"1202.2479","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2479","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2479v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2479","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"L6QIAJEKIZWG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L6QIAJEKIZWGRME5","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L6QIAJEK","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:fa6384cdb884823347653edff39be12219b20dd5243307350fec049030fdd458","target":"graph","created_at":"2026-05-18T03:58:39Z","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 $A = \\bigoplus_{i \\geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing many classical results, and use it to classify algebras stratified for all preorders.","authors_text":"Liping Li","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-11T23:33:21Z","title":"A classification of algebras stratified for all preorders by Koszul theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2479","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":"sha256:7412cc27b79eed4690e9fca0bcb49755a5d601213976f58310e8721c99bc88cb","target":"record","created_at":"2026-05-18T03:58:39Z","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":"e5a97d857f2036bad65d33acb5f9a44ccdfa5ac5252569836c141879ca00624f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-11T23:33:21Z","title_canon_sha256":"1e8167fc004debaacc52771be2fc7600fe0b47e11f251d21c995583a53f2a121"},"schema_version":"1.0","source":{"id":"1202.2479","kind":"arxiv","version":2}},"canonical_sha256":"5fa080248a466c68b09d9b5c8ebc7f69f509312136074bc2fb0444a4bd21f0fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fa080248a466c68b09d9b5c8ebc7f69f509312136074bc2fb0444a4bd21f0fd","first_computed_at":"2026-05-18T03:58:39.336714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:39.336714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"htqjp2+wWuwzsrnDoe6bRV918wxqeqe++laOB4MopgcrxgIWLvLQ9Wo7+fgNsUTCO+SBMtmez9tuGsn2m1OjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:39.337426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2479","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7412cc27b79eed4690e9fca0bcb49755a5d601213976f58310e8721c99bc88cb","sha256:fa6384cdb884823347653edff39be12219b20dd5243307350fec049030fdd458"],"state_sha256":"901754319d699bd1ca83d174240ee8b077795ef08a1f4e30ae74e0a1542f5d79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQ81UABYQWMtaGsa9qEqDat4I0j7YDkh3jMYC0twpXy65xb4sHBzTGclAKViwNX8GaBm3RArNGdAVjfPXNs0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:44:53.906035Z","bundle_sha256":"d810c5b0c2b844ae5b42e4714900c4dc5dda849bd8659434cc2dd2c946293a9e"}}