{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5V234BKMJGCNNKDI5WCBXAXHXF","short_pith_number":"pith:5V234BKM","canonical_record":{"source":{"id":"1102.3205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-15T23:21:06Z","cross_cats_sorted":[],"title_canon_sha256":"c1ded40a22fa23e0364b81c92e6cafb7107a8a6c497fbfadc9f3a8f7de9cb954","abstract_canon_sha256":"574b762cb0f4c66e762cd1188d7a85484a6302d1f2fd48a7fa5f5d5b7e45a8c2"},"schema_version":"1.0"},"canonical_sha256":"ed75be054c4984d6a868ed841b82e7b974ac4fa9b0a3c033b069263c5ba605b9","source":{"kind":"arxiv","id":"1102.3205","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3205","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3205v1","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3205","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"pith_short_12","alias_value":"5V234BKMJGCN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5V234BKMJGCNNKDI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5V234BKM","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5V234BKMJGCNNKDI5WCBXAXHXF","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-15T23:21:06Z","cross_cats_sorted":[],"title_canon_sha256":"c1ded40a22fa23e0364b81c92e6cafb7107a8a6c497fbfadc9f3a8f7de9cb954","abstract_canon_sha256":"574b762cb0f4c66e762cd1188d7a85484a6302d1f2fd48a7fa5f5d5b7e45a8c2"},"schema_version":"1.0"},"canonical_sha256":"ed75be054c4984d6a868ed841b82e7b974ac4fa9b0a3c033b069263c5ba605b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:36.854634Z","signature_b64":"0WijsPgf9Fnrb8+x9zBiRCaczpEAXya8FJPJ6t+2elQj475xiAXeXBcYCMN8lL2ch+TAGdilr2qcJIQ2UbF8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed75be054c4984d6a868ed841b82e7b974ac4fa9b0a3c033b069263c5ba605b9","last_reissued_at":"2026-05-18T04:28:36.854246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:36.854246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3205","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fnUirfiDEfRFNXGTz3TFKk9jI26L8pHWVGUmR7o+mgeTPwEPcFNks1gVn/dIFUKXjm8bzX+v1NqY248GxIp9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:10:36.688761Z"},"content_sha256":"56506a13d74634bfdbfd6642a4443d5c8fe5ed8225def38bf39f09beb3257612","schema_version":"1.0","event_id":"sha256:56506a13d74634bfdbfd6642a4443d5c8fe5ed8225def38bf39f09beb3257612"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5V234BKMJGCNNKDI5WCBXAXHXF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Picard-Vessiot Extensions For Unipotent Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"V. Ravi Srinivasan","submitted_at":"2011-02-15T23:21:06Z","abstract_excerpt":"Let F be a differential field of characteristic zero. In this article, we construct Picard-Vessiot extensions of F whose differential Galois group is isomorphic to the full unipotent subgroup of the upper triangular group defined over the field of constants of F. We will also give a procedure to compute linear differential operators for our Picard-Vessiot extensions. We do not require the condition that the field of constants be algebraically closed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3205","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2w8AS2vD+F7cB1kAj4sE5RG3eWTmBgvlEw0lYAyGqCFkfejhikSldVxj+xNd5yck2IBMbig0ORPaVyqBjUxcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:10:36.689496Z"},"content_sha256":"224173ea03b6a993cc94c77bf98355d10471bdd81c8821bca81b50cc7d0de3e5","schema_version":"1.0","event_id":"sha256:224173ea03b6a993cc94c77bf98355d10471bdd81c8821bca81b50cc7d0de3e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5V234BKMJGCNNKDI5WCBXAXHXF/bundle.json","state_url":"https://pith.science/pith/5V234BKMJGCNNKDI5WCBXAXHXF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5V234BKMJGCNNKDI5WCBXAXHXF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T06:10:36Z","links":{"resolver":"https://pith.science/pith/5V234BKMJGCNNKDI5WCBXAXHXF","bundle":"https://pith.science/pith/5V234BKMJGCNNKDI5WCBXAXHXF/bundle.json","state":"https://pith.science/pith/5V234BKMJGCNNKDI5WCBXAXHXF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5V234BKMJGCNNKDI5WCBXAXHXF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5V234BKMJGCNNKDI5WCBXAXHXF","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":"574b762cb0f4c66e762cd1188d7a85484a6302d1f2fd48a7fa5f5d5b7e45a8c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-15T23:21:06Z","title_canon_sha256":"c1ded40a22fa23e0364b81c92e6cafb7107a8a6c497fbfadc9f3a8f7de9cb954"},"schema_version":"1.0","source":{"id":"1102.3205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3205","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3205v1","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3205","created_at":"2026-05-18T04:28:36Z"},{"alias_kind":"pith_short_12","alias_value":"5V234BKMJGCN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5V234BKMJGCNNKDI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5V234BKM","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:224173ea03b6a993cc94c77bf98355d10471bdd81c8821bca81b50cc7d0de3e5","target":"graph","created_at":"2026-05-18T04:28:36Z","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":"Let F be a differential field of characteristic zero. In this article, we construct Picard-Vessiot extensions of F whose differential Galois group is isomorphic to the full unipotent subgroup of the upper triangular group defined over the field of constants of F. We will also give a procedure to compute linear differential operators for our Picard-Vessiot extensions. We do not require the condition that the field of constants be algebraically closed.","authors_text":"V. Ravi Srinivasan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-15T23:21:06Z","title":"Picard-Vessiot Extensions For Unipotent Algebraic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3205","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":"sha256:56506a13d74634bfdbfd6642a4443d5c8fe5ed8225def38bf39f09beb3257612","target":"record","created_at":"2026-05-18T04:28:36Z","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":"574b762cb0f4c66e762cd1188d7a85484a6302d1f2fd48a7fa5f5d5b7e45a8c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-02-15T23:21:06Z","title_canon_sha256":"c1ded40a22fa23e0364b81c92e6cafb7107a8a6c497fbfadc9f3a8f7de9cb954"},"schema_version":"1.0","source":{"id":"1102.3205","kind":"arxiv","version":1}},"canonical_sha256":"ed75be054c4984d6a868ed841b82e7b974ac4fa9b0a3c033b069263c5ba605b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed75be054c4984d6a868ed841b82e7b974ac4fa9b0a3c033b069263c5ba605b9","first_computed_at":"2026-05-18T04:28:36.854246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:36.854246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0WijsPgf9Fnrb8+x9zBiRCaczpEAXya8FJPJ6t+2elQj475xiAXeXBcYCMN8lL2ch+TAGdilr2qcJIQ2UbF8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:36.854634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56506a13d74634bfdbfd6642a4443d5c8fe5ed8225def38bf39f09beb3257612","sha256:224173ea03b6a993cc94c77bf98355d10471bdd81c8821bca81b50cc7d0de3e5"],"state_sha256":"5b8b95c9b603c2e2d80aa3097653aa0aeba581553c94881194831b1a3b58fa4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0z8JV5lPf+shJIL4peVUPjFm5P3A2C/kvrT9g1Ds0WsldqHjLC2AR5RE3W4iYTQ3zK4IMrxRgdhd6oZd164lBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:10:36.692960Z","bundle_sha256":"fb8d5e5d922e3d0799e32f7118ac24c29b21057d499254ce06fb48c541bcd93e"}}