{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PN7QGQVFDCVLGHW3BLLYIZOV2L","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":"13e6778a1cde009a25f2eaaef2c647f2197af8951fcb2851ba0d258f87f8a677","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-24T08:49:23Z","title_canon_sha256":"f2353327c49a0c419fccc015059174df5a7abdea8488c158a0b2a365b56fcede"},"schema_version":"1.0","source":{"id":"2605.24948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24948","created_at":"2026-05-26T01:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24948v1","created_at":"2026-05-26T01:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24948","created_at":"2026-05-26T01:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"PN7QGQVFDCVL","created_at":"2026-05-26T01:04:07Z"},{"alias_kind":"pith_short_16","alias_value":"PN7QGQVFDCVLGHW3","created_at":"2026-05-26T01:04:07Z"},{"alias_kind":"pith_short_8","alias_value":"PN7QGQVF","created_at":"2026-05-26T01:04:07Z"}],"graph_snapshots":[{"event_id":"sha256:fc9a6e4a9f17cefe7e9df6953ec224b1193dd092ccddd40539af6ecb37d878cd","target":"graph","created_at":"2026-05-26T01:04:07Z","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/2605.24948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Brief proofs of classical results of Lie on finite dimensional subalgebras of vector fields in two and three variables are outlined. The results for algebras of maximal rank for vector fields in $\\mathbb{C}^N$ -- $N$ arbitrary -- are also given.","authors_text":"Hassan Azad, Indranil Biswas, Said Waqas Shah","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-24T08:49:23Z","title":"Lie's classification of finite dimensional algebras of Vector Fields in C^N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24948","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":"sha256:0deaf69c1479103ba638e3a0ad3f7d8e8b81831d38013ab5dca4fbc878a934d9","target":"record","created_at":"2026-05-26T01:04:07Z","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":"13e6778a1cde009a25f2eaaef2c647f2197af8951fcb2851ba0d258f87f8a677","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-24T08:49:23Z","title_canon_sha256":"f2353327c49a0c419fccc015059174df5a7abdea8488c158a0b2a365b56fcede"},"schema_version":"1.0","source":{"id":"2605.24948","kind":"arxiv","version":1}},"canonical_sha256":"7b7f0342a518aab31edb0ad78465d5d2e7b6d444e06b13e55b0adc012cb16aa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7f0342a518aab31edb0ad78465d5d2e7b6d444e06b13e55b0adc012cb16aa0","first_computed_at":"2026-05-26T01:04:07.165620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:04:07.165620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wwVHWD7p5PU63MZZhs0HpqQui5Uyw+uwQQLESYmrr5VVvaQ/Nb2vjojLQ+TYnXIwxxIMyNetS//Urslamdf8Cg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:04:07.166464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0deaf69c1479103ba638e3a0ad3f7d8e8b81831d38013ab5dca4fbc878a934d9","sha256:fc9a6e4a9f17cefe7e9df6953ec224b1193dd092ccddd40539af6ecb37d878cd"],"state_sha256":"9333a4fc62617372b058be69ab103217b77843a0434afb55161c6007380c2220"}