{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NFGL2NZKGFHJE6ZX677BDFTPCF","short_pith_number":"pith:NFGL2NZK","canonical_record":{"source":{"id":"1502.00479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-02T13:53:33Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a86897df71cfa3347b4f7334474b338628b1910357ead1b241f59702a8bb63cd","abstract_canon_sha256":"e4ca8699ecc70e0e4b5c2d407623d6bd7016dbbb98b4a097701785a29bb1e9b4"},"schema_version":"1.0"},"canonical_sha256":"694cbd372a314e927b37f7fe11966f117f7f2a2230ba29c780bd07c953cebda2","source":{"kind":"arxiv","id":"1502.00479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00479","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00479v1","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00479","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"NFGL2NZKGFHJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFGL2NZKGFHJE6ZX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFGL2NZK","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NFGL2NZKGFHJE6ZX677BDFTPCF","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-02T13:53:33Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a86897df71cfa3347b4f7334474b338628b1910357ead1b241f59702a8bb63cd","abstract_canon_sha256":"e4ca8699ecc70e0e4b5c2d407623d6bd7016dbbb98b4a097701785a29bb1e9b4"},"schema_version":"1.0"},"canonical_sha256":"694cbd372a314e927b37f7fe11966f117f7f2a2230ba29c780bd07c953cebda2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:05.943360Z","signature_b64":"GaYuJxrs/wCNp41HAiGs+2jka59fR9AEK3lmwln+8XEh+OmoHNF32/P5xqJPxmVI91JpFwk6SVc0c8vVdeGxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"694cbd372a314e927b37f7fe11966f117f7f2a2230ba29c780bd07c953cebda2","last_reissued_at":"2026-05-18T02:28:05.943011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:05.943011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00479","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":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eVSCy5NSTXCwfZFaRdm4yUli5lMbYb43zHBSOnBqjjV2hfAapAQcVq5JV5awkp6Ayhuv1PTUjgBqx9XPTb83DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:36:17.268294Z"},"content_sha256":"dda33295b8ca9a8df6be33d2f98c7cc3245f4e750d93ef682145d5070890a0ef","schema_version":"1.0","event_id":"sha256:dda33295b8ca9a8df6be33d2f98c7cc3245f4e750d93ef682145d5070890a0ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NFGL2NZKGFHJE6ZX677BDFTPCF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recollement of additive quotient categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Minxiong Wang, Zengqiang Lin","submitted_at":"2015-02-02T13:53:33Z","abstract_excerpt":"In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by mutation pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00479","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":"2026-05-18T02:28:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"604InP5Hfm4G2Jj2ryr9yHLrumFq5+1ELmt8rwk2ViPZnPAiDeSMzsCPxtsppW+9PsXGxEr9jvKj7lEUC6qiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:36:17.268658Z"},"content_sha256":"d319dfd5e0f04cc090b8a6cdddb36eac87c624106fd91959a5f1f1d2e3dfa929","schema_version":"1.0","event_id":"sha256:d319dfd5e0f04cc090b8a6cdddb36eac87c624106fd91959a5f1f1d2e3dfa929"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/bundle.json","state_url":"https://pith.science/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/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":"2026-06-20T21:36:17Z","links":{"resolver":"https://pith.science/pith/NFGL2NZKGFHJE6ZX677BDFTPCF","bundle":"https://pith.science/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/bundle.json","state":"https://pith.science/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFGL2NZKGFHJE6ZX677BDFTPCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NFGL2NZKGFHJE6ZX677BDFTPCF","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":"e4ca8699ecc70e0e4b5c2d407623d6bd7016dbbb98b4a097701785a29bb1e9b4","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-02T13:53:33Z","title_canon_sha256":"a86897df71cfa3347b4f7334474b338628b1910357ead1b241f59702a8bb63cd"},"schema_version":"1.0","source":{"id":"1502.00479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00479","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00479v1","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00479","created_at":"2026-05-18T02:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"NFGL2NZKGFHJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFGL2NZKGFHJE6ZX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFGL2NZK","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d319dfd5e0f04cc090b8a6cdddb36eac87c624106fd91959a5f1f1d2e3dfa929","target":"graph","created_at":"2026-05-18T02:28:05Z","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":"In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by mutation pairs.","authors_text":"Minxiong Wang, Zengqiang Lin","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-02T13:53:33Z","title":"Recollement of additive quotient categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00479","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:dda33295b8ca9a8df6be33d2f98c7cc3245f4e750d93ef682145d5070890a0ef","target":"record","created_at":"2026-05-18T02:28:05Z","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":"e4ca8699ecc70e0e4b5c2d407623d6bd7016dbbb98b4a097701785a29bb1e9b4","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-02T13:53:33Z","title_canon_sha256":"a86897df71cfa3347b4f7334474b338628b1910357ead1b241f59702a8bb63cd"},"schema_version":"1.0","source":{"id":"1502.00479","kind":"arxiv","version":1}},"canonical_sha256":"694cbd372a314e927b37f7fe11966f117f7f2a2230ba29c780bd07c953cebda2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"694cbd372a314e927b37f7fe11966f117f7f2a2230ba29c780bd07c953cebda2","first_computed_at":"2026-05-18T02:28:05.943011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:05.943011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GaYuJxrs/wCNp41HAiGs+2jka59fR9AEK3lmwln+8XEh+OmoHNF32/P5xqJPxmVI91JpFwk6SVc0c8vVdeGxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:05.943360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dda33295b8ca9a8df6be33d2f98c7cc3245f4e750d93ef682145d5070890a0ef","sha256:d319dfd5e0f04cc090b8a6cdddb36eac87c624106fd91959a5f1f1d2e3dfa929"],"state_sha256":"78ba1dafbf1959307e020f5b72b815e010b9c0d3925e0fdca233c2f891ffeeb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEj63xO/ECWmZ3ds0yKcvLf8HVDkvNA2oEcF7tG2c61LYo1quO3Ym7UdGOrF/ryZMLBg/bi5ZVzMDeS3eWY5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:36:17.270629Z","bundle_sha256":"5d7647df129f2bb1c056d994c09d3ee2061cfbef738bb6e132f2e27437cd4664"}}