{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OINKRMMJI26M4DS2UIGXGEHV54","short_pith_number":"pith:OINKRMMJ","canonical_record":{"source":{"id":"1605.05458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-05-18T06:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"dd140998d4802c578ad96b4b0cfe48c19cae8a735f16bb87b21d576822653ad1","abstract_canon_sha256":"9bfd598f90a1b0c5ada666be3d0c8edf1391974bfe225e748ec51eea0e22f163"},"schema_version":"1.0"},"canonical_sha256":"721aa8b18946bcce0e5aa20d7310f5ef0386cab441384a095e48c2c892b57406","source":{"kind":"arxiv","id":"1605.05458","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05458","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05458v1","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05458","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"OINKRMMJI26M","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OINKRMMJI26M4DS2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OINKRMMJ","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OINKRMMJI26M4DS2UIGXGEHV54","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-05-18T06:43:19Z","cross_cats_sorted":[],"title_canon_sha256":"dd140998d4802c578ad96b4b0cfe48c19cae8a735f16bb87b21d576822653ad1","abstract_canon_sha256":"9bfd598f90a1b0c5ada666be3d0c8edf1391974bfe225e748ec51eea0e22f163"},"schema_version":"1.0"},"canonical_sha256":"721aa8b18946bcce0e5aa20d7310f5ef0386cab441384a095e48c2c892b57406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:34.899274Z","signature_b64":"pvbyjGuDS37qRM7g25zv9PLj5jjUcOhpxn11YUgFGu58kXSlQF9xU+EaNUIOEo1AetCBVMKVv6NNY+vQxASnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"721aa8b18946bcce0e5aa20d7310f5ef0386cab441384a095e48c2c892b57406","last_reissued_at":"2026-05-18T01:14:34.898731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:34.898731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05458","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBzjoN8GU5e7wLHWl0hqclxLoc6T937gg/sOEsiOFZyQMivGgwfeaCRI3J1LsWbwWY7zNufKrZWOGtWoaqPfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:05:54.592952Z"},"content_sha256":"723e95e6b8fab1aa194b9d76f3b61da6f4f14b58180eeca3c87044d8c4b2374b","schema_version":"1.0","event_id":"sha256:723e95e6b8fab1aa194b9d76f3b61da6f4f14b58180eeca3c87044d8c4b2374b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OINKRMMJI26M4DS2UIGXGEHV54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Koszulity of Finite Posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Adrian Manea, Drago\\c{s} \\c{S}tefan","submitted_at":"2016-05-18T06:43:19Z","abstract_excerpt":"We prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of $\\Tor_n^A(R,R)$. As an application of these characterizations we investigate the Koszulity of the incidence rings for finite graded posets. Based on these results, we describe an algorithm to produce new classes of Koszul posets (i.e. graded posets whose incidence rings are Koszul). Specific examples of Koszul posets are included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05458","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":""},"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":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btGNWGvdB/TZzsizZ5C5zVbx3dyQi5GLnInHOJH9UpHriN315aaLHQA+AmWf0HiZ1cr+gZ7tlXlLiFbwVUZ0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:05:54.593332Z"},"content_sha256":"665408674dbd5702e86af563bbcb64e1dbaa4f5453df2d0b86104d7e47be62a5","schema_version":"1.0","event_id":"sha256:665408674dbd5702e86af563bbcb64e1dbaa4f5453df2d0b86104d7e47be62a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OINKRMMJI26M4DS2UIGXGEHV54/bundle.json","state_url":"https://pith.science/pith/OINKRMMJI26M4DS2UIGXGEHV54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OINKRMMJI26M4DS2UIGXGEHV54/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":"2026-06-05T18:05:54Z","links":{"resolver":"https://pith.science/pith/OINKRMMJI26M4DS2UIGXGEHV54","bundle":"https://pith.science/pith/OINKRMMJI26M4DS2UIGXGEHV54/bundle.json","state":"https://pith.science/pith/OINKRMMJI26M4DS2UIGXGEHV54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OINKRMMJI26M4DS2UIGXGEHV54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OINKRMMJI26M4DS2UIGXGEHV54","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":"9bfd598f90a1b0c5ada666be3d0c8edf1391974bfe225e748ec51eea0e22f163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-05-18T06:43:19Z","title_canon_sha256":"dd140998d4802c578ad96b4b0cfe48c19cae8a735f16bb87b21d576822653ad1"},"schema_version":"1.0","source":{"id":"1605.05458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05458","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05458v1","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05458","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"OINKRMMJI26M","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OINKRMMJI26M4DS2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OINKRMMJ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:665408674dbd5702e86af563bbcb64e1dbaa4f5453df2d0b86104d7e47be62a5","target":"graph","created_at":"2026-05-18T01:14:34Z","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":"We prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of $\\Tor_n^A(R,R)$. As an application of these characterizations we investigate the Koszulity of the incidence rings for finite graded posets. Based on these results, we describe an algorithm to produce new classes of Koszul posets (i.e. graded posets whose incidence rings are Koszul). Specific examples of Koszul posets are included.","authors_text":"Adrian Manea, Drago\\c{s} \\c{S}tefan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-05-18T06:43:19Z","title":"On Koszulity of Finite Posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05458","kind":"arxiv","version":1},"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":"sha256:723e95e6b8fab1aa194b9d76f3b61da6f4f14b58180eeca3c87044d8c4b2374b","target":"record","created_at":"2026-05-18T01:14:34Z","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":"9bfd598f90a1b0c5ada666be3d0c8edf1391974bfe225e748ec51eea0e22f163","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-05-18T06:43:19Z","title_canon_sha256":"dd140998d4802c578ad96b4b0cfe48c19cae8a735f16bb87b21d576822653ad1"},"schema_version":"1.0","source":{"id":"1605.05458","kind":"arxiv","version":1}},"canonical_sha256":"721aa8b18946bcce0e5aa20d7310f5ef0386cab441384a095e48c2c892b57406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"721aa8b18946bcce0e5aa20d7310f5ef0386cab441384a095e48c2c892b57406","first_computed_at":"2026-05-18T01:14:34.898731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:34.898731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pvbyjGuDS37qRM7g25zv9PLj5jjUcOhpxn11YUgFGu58kXSlQF9xU+EaNUIOEo1AetCBVMKVv6NNY+vQxASnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:34.899274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:723e95e6b8fab1aa194b9d76f3b61da6f4f14b58180eeca3c87044d8c4b2374b","sha256:665408674dbd5702e86af563bbcb64e1dbaa4f5453df2d0b86104d7e47be62a5"],"state_sha256":"e83a6f11a0f791ffc14a4c61039d653f5e04f892399615c38d7c5f05f81cfd8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eh17WImc+Yb8yGbzEpXjrCzIHKdQRQuhXyA2F/fwlsfqEsljbfvzQDKmRbroJFZKiiheviaVRXKcTkZRGQhTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:05:54.595838Z","bundle_sha256":"7e02ae48c2f46940e493d5800453f4e9551e9f4d46a8dcfab7adbe07da20e4b4"}}