{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BZ6YUASOTLRO6FBCZI3IPTEWAT","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":"f25af7189de332ccfe5fa0ac52ca0a1ac3d021ad50c40f63b5917e17bf1ec622","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-02-06T09:03:58Z","title_canon_sha256":"e48c73bacc66507de3c03fd7f934da36970f373a074727e1015d2cfe8a38bace"},"schema_version":"1.0","source":{"id":"2502.03887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.03887","created_at":"2026-07-05T10:10:30Z"},{"alias_kind":"arxiv_version","alias_value":"2502.03887v1","created_at":"2026-07-05T10:10:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03887","created_at":"2026-07-05T10:10:30Z"},{"alias_kind":"pith_short_12","alias_value":"BZ6YUASOTLRO","created_at":"2026-07-05T10:10:30Z"},{"alias_kind":"pith_short_16","alias_value":"BZ6YUASOTLRO6FBC","created_at":"2026-07-05T10:10:30Z"},{"alias_kind":"pith_short_8","alias_value":"BZ6YUASO","created_at":"2026-07-05T10:10:30Z"}],"graph_snapshots":[{"event_id":"sha256:3d7c3152328e0c37490f85e3ab59a97bec4562c03bf24596e36912a361517d19","target":"graph","created_at":"2026-07-05T10:10:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.03887/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $( \\mathcal{A^{'}},\\mathcal{A},\\mathcal{A^{''}},i^\\ast,i_\\ast,i_!,j_!,j^\\ast,j_\\ast)$ be a recollement of abelian categories. We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in $\\mathcal{A^{'}}$ or $\\mathcal{A^{''}}$ can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in $\\mathcal{A}$, and the assignment $\\mathcal{C}\\mapsto j^*(\\mathcal{C})$ defines a bijection between certain ICE-closed subcategories in $\\mathcal{A}$ and those in $\\mathcal{A}''$. Moreover, the ICE-closed subcategory $\\mathcal{C}$ of $\\mathcal{A}$ containing $i_\\ast(\\mathcal{A","authors_text":"Jinrui Yang, Yongyun Qin","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-02-06T09:03:58Z","title":"ICE-closed subcategories and epibricks over recollements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03887","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":"sha256:0c5831cef38ccb6b66257bda294d501132c99660ce369d6c301f298aefecdb7a","target":"record","created_at":"2026-07-05T10:10:30Z","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":"f25af7189de332ccfe5fa0ac52ca0a1ac3d021ad50c40f63b5917e17bf1ec622","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-02-06T09:03:58Z","title_canon_sha256":"e48c73bacc66507de3c03fd7f934da36970f373a074727e1015d2cfe8a38bace"},"schema_version":"1.0","source":{"id":"2502.03887","kind":"arxiv","version":1}},"canonical_sha256":"0e7d8a024e9ae2ef1422ca3687cc9604d47f62c27adabb0fde9c4610de93f0c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e7d8a024e9ae2ef1422ca3687cc9604d47f62c27adabb0fde9c4610de93f0c8","first_computed_at":"2026-07-05T10:10:30.582898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:30.582898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lDz2Kie008hW8Z5gR+4TWlKsvdgmnSF6HwrDaNJlk2fftlhfZbjNYVDCTPkuNl8tpuRpZSlBL+4IkCk9L+IbAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:30.583332Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.03887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c5831cef38ccb6b66257bda294d501132c99660ce369d6c301f298aefecdb7a","sha256:3d7c3152328e0c37490f85e3ab59a97bec4562c03bf24596e36912a361517d19"],"state_sha256":"5ae6f4b022788c34677625a33dda583fa24224ad87719dc142760360565320a9"}