{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PG5M3RWOCFSH6W4UMISHD3HTGN","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":"971ca7eea6d54656db1d3ba2b5cf406626c69bad6e0d2910982fd5c7e50434a0","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-09-04T16:24:31Z","title_canon_sha256":"6e1d91e87822ac709f60127d90f66215133daf7ed30b5d18b4b4164f8027ba18"},"schema_version":"1.0","source":{"id":"2509.04364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.04364","created_at":"2026-07-05T12:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"2509.04364v1","created_at":"2026-07-05T12:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.04364","created_at":"2026-07-05T12:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"PG5M3RWOCFSH","created_at":"2026-07-05T12:04:58Z"},{"alias_kind":"pith_short_16","alias_value":"PG5M3RWOCFSH6W4U","created_at":"2026-07-05T12:04:58Z"},{"alias_kind":"pith_short_8","alias_value":"PG5M3RWO","created_at":"2026-07-05T12:04:58Z"}],"graph_snapshots":[{"event_id":"sha256:71c9b87d80fe0ba58ce09157bd8aab3a790bd57b33e9f06c92efe2ff7fca88a6","target":"graph","created_at":"2026-07-05T12:04:58Z","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/2509.04364/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Frobenius splitting, pioneered by Hochster and Roberts in the 1970s and Mehta and Ramanathan in the 1980s, is a technique in characteristic $p$ commutative algebra and algebraic geometry used to control singularities. In the aughts, Knutson showed that Frobenius splittings of a certain type descend through Gr\\\"obner degeneration of a certain type, called geometric vertex decomposition. In the present paper, we give a partial converse to Knutson's result. We show that a Frobenius splitting that compatibly splits both link and deletion of a geometric vertex decomposition can, under an additional","authors_text":"Elisa Gorla, Emanuela De Negri, Jenna Rajchgot, Lisa Seccia, Patricia Klein","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-09-04T16:24:31Z","title":"Lifting Frobenius splittings through geometric vertex decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.04364","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:ff64c779a3912ee8fb14bb2d4f9332c107e373824add8c918bc6db9db3dc7ed4","target":"record","created_at":"2026-07-05T12:04:58Z","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":"971ca7eea6d54656db1d3ba2b5cf406626c69bad6e0d2910982fd5c7e50434a0","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-09-04T16:24:31Z","title_canon_sha256":"6e1d91e87822ac709f60127d90f66215133daf7ed30b5d18b4b4164f8027ba18"},"schema_version":"1.0","source":{"id":"2509.04364","kind":"arxiv","version":1}},"canonical_sha256":"79bacdc6ce11647f5b94622471ecf3334900cf39036ef8e5d1bd4f795b9b6dd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79bacdc6ce11647f5b94622471ecf3334900cf39036ef8e5d1bd4f795b9b6dd5","first_computed_at":"2026-07-05T12:04:58.320590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:58.320590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tx18oykewYlhAbrOCuhwjLZeHDUJ8Xr/aaMADYNPLB5khjaEyIYCQmGmUdVH5Wd2gsfCZsULvewYrwb3iJoYDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:58.321195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.04364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff64c779a3912ee8fb14bb2d4f9332c107e373824add8c918bc6db9db3dc7ed4","sha256:71c9b87d80fe0ba58ce09157bd8aab3a790bd57b33e9f06c92efe2ff7fca88a6"],"state_sha256":"20d817cda9f7485a61bbd4239629b1e656a0edcca2fb7dcbd4e809e8060fdba3"}