{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GSPPHZ7ZFIWAZXCNCW2S2FAWCP","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":"af9b4e1636adb4c0300ebd3660db1d02923c89d09b383f1c018fabab4af97f59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-08-13T12:41:32Z","title_canon_sha256":"7152e94683eb3b5030b7d163a6483f04099ef177353f935c6257c2101c808343"},"schema_version":"1.0","source":{"id":"2608.13175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13175","created_at":"2026-08-14T01:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13175v1","created_at":"2026-08-14T01:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13175","created_at":"2026-08-14T01:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"GSPPHZ7ZFIWA","created_at":"2026-08-14T01:00:33Z"},{"alias_kind":"pith_short_16","alias_value":"GSPPHZ7ZFIWAZXCN","created_at":"2026-08-14T01:00:33Z"},{"alias_kind":"pith_short_8","alias_value":"GSPPHZ7Z","created_at":"2026-08-14T01:00:33Z"}],"graph_snapshots":[{"event_id":"sha256:4f1f642b0b94ce4ddb1addb361372001903ae4ba886a1dc1b6cbb85b998e9726","target":"graph","created_at":"2026-08-14T01:00:33Z","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/2608.13175/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the notion of $\\mathbf{g}$-vector fan so that it is defined for a Hom-finite Krull-Schmidt 0-Auslander $k$-linear extriangulated category $\\mathcal{C}$ with a projective silting object $T$. Moreover, we show that the $\\mathbf{g}$-vector fan admits an admissible partition, in the sense of the second-named author, which is induced by thick subcategories. One can thus define the picture category of $\\mathcal{C}$. We establish a bijection between thick subcategories of $\\mathcal{C}$ generated by presilting objects containing all projective-injective objects and $\\tau$-perpendicular subca","authors_text":"Erlend D. B{\\o}rve, Maximilian Kaipel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-08-13T12:41:32Z","title":"$g$-vector fans and picture categories for 0-Auslander extriangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13175","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":"sha256:332f00887a360ac3a4a085170bf58d251abd624c217b77249ab8672f8e42be70","target":"record","created_at":"2026-08-14T01:00:33Z","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":"af9b4e1636adb4c0300ebd3660db1d02923c89d09b383f1c018fabab4af97f59","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-08-13T12:41:32Z","title_canon_sha256":"7152e94683eb3b5030b7d163a6483f04099ef177353f935c6257c2101c808343"},"schema_version":"1.0","source":{"id":"2608.13175","kind":"arxiv","version":1}},"canonical_sha256":"349ef3e7f92a2c0cdc4d15b52d141613e46130998fbb8dbbc6bde7b8dc0a36af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"349ef3e7f92a2c0cdc4d15b52d141613e46130998fbb8dbbc6bde7b8dc0a36af","first_computed_at":"2026-08-14T01:00:33.716471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:00:33.716471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rN1num5ywBnAevcCNOFSyOGOcvkbmNyuX37GsnCx5loekG3IE6RSr9ndFyKPSXY+FZQv4+7cHEVpO68aKVw9AA==","signature_status":"signed_v1","signed_at":"2026-08-14T01:00:33.718476Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:332f00887a360ac3a4a085170bf58d251abd624c217b77249ab8672f8e42be70","sha256:4f1f642b0b94ce4ddb1addb361372001903ae4ba886a1dc1b6cbb85b998e9726"],"state_sha256":"9258387d2488674ca77a904f6379e0d13c99655d6910ab668c73c3e055bc97f2"}