{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U7ABFSDQOZTQ5ZACK76OLNOPXA","short_pith_number":"pith:U7ABFSDQ","canonical_record":{"source":{"id":"1203.5545","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","cross_cats_sorted":["math.CO","math.CT"],"title_canon_sha256":"31b4e758b9ce9f93e3c039b1f12d9e098aae8bdf9bb461d112622dea7f71689d","abstract_canon_sha256":"558bf56edc3db2ec48e149fe0603bf2ba4b06740da2a23eff83e0576bfd0ba61"},"schema_version":"1.0"},"canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","source":{"kind":"arxiv","id":"1203.5545","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5545","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5545v4","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5545","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"U7ABFSDQOZTQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7ABFSDQOZTQ5ZAC","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7ABFSDQ","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U7ABFSDQOZTQ5ZACK76OLNOPXA","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5545","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","cross_cats_sorted":["math.CO","math.CT"],"title_canon_sha256":"31b4e758b9ce9f93e3c039b1f12d9e098aae8bdf9bb461d112622dea7f71689d","abstract_canon_sha256":"558bf56edc3db2ec48e149fe0603bf2ba4b06740da2a23eff83e0576bfd0ba61"},"schema_version":"1.0"},"canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:03.564864Z","signature_b64":"KBbh76tmRcc7ZQyu2eRsEONF84O7u58QttlW3u9Sd7IRB3oL6HFkRmK8z3gN2TBhSoB8eEH531bC7lApDFiyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","last_reissued_at":"2026-05-18T02:40:03.564427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:03.564427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5545","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ot6Ct8j404hvKCMvTSqlQhpmV/MzOoNuLlvalJ0IcDGmcxqMvbWn97baWb2b+AvrRZECMbiAoHQkrmFO3CgUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:57:11.388240Z"},"content_sha256":"17d7035689d4b7a55fa6bf9c6836e730e5002ee2afa98db48020d58fad093e99","schema_version":"1.0","event_id":"sha256:17d7035689d4b7a55fa6bf9c6836e730e5002ee2afa98db48020d58fad093e99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U7ABFSDQOZTQ5ZACK76OLNOPXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Highest weight sl_2-categorifications II: structure theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.RT","authors_text":"Ivan Losev","submitted_at":"2012-03-25T21:13:54Z","abstract_excerpt":"This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the refined sense. Then we prove that any highest weight sl_2-categorification can be filtered in such a way that the successive quotients are so called basic highest weight sl_2-categorifications. For a basic highest weight categorification we determine minimal projective resolutions of standard objects. We use this, in particular, to examine the structure of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5545","kind":"arxiv","version":4},"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":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMxxPeufHO86R9X9//IpDE6g3oIWJmZupBPm8sQw23pQjgUhtREGgFFcT6vWob2Xp3hix8ySNGeuE6PScEDkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:57:11.389071Z"},"content_sha256":"7ba9509bca9423f4c9e3e4509c1fc52ea111aa40982203e76cfc0fb2540363c4","schema_version":"1.0","event_id":"sha256:7ba9509bca9423f4c9e3e4509c1fc52ea111aa40982203e76cfc0fb2540363c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/bundle.json","state_url":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/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":"2026-05-31T12:57:11Z","links":{"resolver":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA","bundle":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/bundle.json","state":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U7ABFSDQOZTQ5ZACK76OLNOPXA","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":"558bf56edc3db2ec48e149fe0603bf2ba4b06740da2a23eff83e0576bfd0ba61","cross_cats_sorted":["math.CO","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","title_canon_sha256":"31b4e758b9ce9f93e3c039b1f12d9e098aae8bdf9bb461d112622dea7f71689d"},"schema_version":"1.0","source":{"id":"1203.5545","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5545","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5545v4","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5545","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"U7ABFSDQOZTQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7ABFSDQOZTQ5ZAC","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7ABFSDQ","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:7ba9509bca9423f4c9e3e4509c1fc52ea111aa40982203e76cfc0fb2540363c4","target":"graph","created_at":"2026-05-18T02:40:03Z","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":"This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the refined sense. Then we prove that any highest weight sl_2-categorification can be filtered in such a way that the successive quotients are so called basic highest weight sl_2-categorifications. For a basic highest weight categorification we determine minimal projective resolutions of standard objects. We use this, in particular, to examine the structure of ","authors_text":"Ivan Losev","cross_cats":["math.CO","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","title":"Highest weight sl_2-categorifications II: structure theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5545","kind":"arxiv","version":4},"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":"sha256:17d7035689d4b7a55fa6bf9c6836e730e5002ee2afa98db48020d58fad093e99","target":"record","created_at":"2026-05-18T02:40:03Z","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":"558bf56edc3db2ec48e149fe0603bf2ba4b06740da2a23eff83e0576bfd0ba61","cross_cats_sorted":["math.CO","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","title_canon_sha256":"31b4e758b9ce9f93e3c039b1f12d9e098aae8bdf9bb461d112622dea7f71689d"},"schema_version":"1.0","source":{"id":"1203.5545","kind":"arxiv","version":4}},"canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","first_computed_at":"2026-05-18T02:40:03.564427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:03.564427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBbh76tmRcc7ZQyu2eRsEONF84O7u58QttlW3u9Sd7IRB3oL6HFkRmK8z3gN2TBhSoB8eEH531bC7lApDFiyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:03.564864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5545","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17d7035689d4b7a55fa6bf9c6836e730e5002ee2afa98db48020d58fad093e99","sha256:7ba9509bca9423f4c9e3e4509c1fc52ea111aa40982203e76cfc0fb2540363c4"],"state_sha256":"4160371a4bc327c4e747dc66d5f190514a6e07399842ee8ba0736c54297bad12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lL2Ia8dWAQFtfGjHlKnIaeDM9DwYAL+JPsfVc/NX4kraQymP+GLl0Wg0nrUjDjqq76wx18036FE4rR6vZM+OAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:57:11.392938Z","bundle_sha256":"89ef2ec7c25404eed05064c471fe717e7475897cecc288a642c1a73ac826099b"}}