{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4KVJRDS35ASTXIS6YUTC24VIEI","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":"d89a5a048b55d96ea1403e51aa965acff727d35f75c22d051faa1d74185cad96","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-07T03:05:28Z","title_canon_sha256":"77fc12dbd459e84d55e3872ef041cb718e51ddfbad18c67d9195d9a9848fa40a"},"schema_version":"1.0","source":{"id":"1607.01867","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01867","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01867v3","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01867","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"4KVJRDS35AST","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4KVJRDS35ASTXIS6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4KVJRDS3","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:31f798586746d1dbecbfabaad7baec7cfb749de43752741b433d20f1beda0592","target":"graph","created_at":"2026-05-17T23:54:57Z","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 determine all values of the parameters for which the cell modules form a standard system, for a class of cellular diagram algebras including partition, Brauer, walled Brauer, Temperley-Lieb and Jones algebras. For this, we develop and apply a general theory of algebras with Borelic pairs. The theory is also applied to give new uniform proofs of the cellular and quasi-hereditary properties of the diagram algebras and to construct quasi-hereditary 1-covers, in the sense of Rouquier, with exact Borel subalgebras, in the sense of K\\\"onig. Another application of the theory leads to a proof that ","authors_text":"Kevin Coulembier, Ruibin Zhang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-07T03:05:28Z","title":"Borelic pairs for stratified algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01867","kind":"arxiv","version":3},"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":"sha256:0d191e823bd57ea79a74fce8768999640e6f7d8ce41f2cfcbbbccfe920eb5696","target":"record","created_at":"2026-05-17T23:54:57Z","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":"d89a5a048b55d96ea1403e51aa965acff727d35f75c22d051faa1d74185cad96","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-07T03:05:28Z","title_canon_sha256":"77fc12dbd459e84d55e3872ef041cb718e51ddfbad18c67d9195d9a9848fa40a"},"schema_version":"1.0","source":{"id":"1607.01867","kind":"arxiv","version":3}},"canonical_sha256":"e2aa988e5be8253ba25ec5262d72a8223289c591f969dcd1e717cffe3f58f848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2aa988e5be8253ba25ec5262d72a8223289c591f969dcd1e717cffe3f58f848","first_computed_at":"2026-05-17T23:54:57.087622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:57.087622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/6T8A596m8H0pOWuWUCqpjrUtYE/SebRcXyepydKb82BKqN3EGTG35n6of3Bafh2Bh46xoGeOexVZ5Dn58MDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:57.088253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01867","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d191e823bd57ea79a74fce8768999640e6f7d8ce41f2cfcbbbccfe920eb5696","sha256:31f798586746d1dbecbfabaad7baec7cfb749de43752741b433d20f1beda0592"],"state_sha256":"0b5cda9b41bb8bf78eae3d7fc59b58a839ccf7edb06d3be8233f94b1a4a81d83"}