{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RA3RZGLN3BJVTT5KI4JTX4FHU3","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":"37ccd27651544627717906da7ed4dcb90b16f560062693a2fdcb63208209e04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-01T14:03:34Z","title_canon_sha256":"35461a3e0f1f871f9dcca58eb3c068bfb9dcc7440896d820c17fd313cd86e7e0"},"schema_version":"1.0","source":{"id":"1103.0170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0170","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0170v1","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0170","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"RA3RZGLN3BJV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RA3RZGLN3BJVTT5K","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RA3RZGLN","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:c8d5eac22febb58e8f3261ebe1c9673cb5787f3d259cadbe7263aa830e6ad2e1","target":"graph","created_at":"2026-05-18T04:27:37Z","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":"In this article, we study the set of all solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of the set of all solutions. Moreover, we give explicit formulas that compute the group of differential automorphisms. We require neither that the underlying field be algebraically closed nor that the characteristic of the field be zero.","authors_text":"V. Ravi Srinivasan, William F. Keigher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-01T14:03:34Z","title":"Linear differential equations and Hurwitz series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0170","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":"sha256:77fe0fdf1226b08f3be2cc12332051d4829796686f2878d40b36a5ac9468a423","target":"record","created_at":"2026-05-18T04:27:37Z","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":"37ccd27651544627717906da7ed4dcb90b16f560062693a2fdcb63208209e04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-01T14:03:34Z","title_canon_sha256":"35461a3e0f1f871f9dcca58eb3c068bfb9dcc7440896d820c17fd313cd86e7e0"},"schema_version":"1.0","source":{"id":"1103.0170","kind":"arxiv","version":1}},"canonical_sha256":"88371c996dd85359cfaa47133bf0a7a6f74377fae1374490c21c3e1d88dbe83a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88371c996dd85359cfaa47133bf0a7a6f74377fae1374490c21c3e1d88dbe83a","first_computed_at":"2026-05-18T04:27:37.207648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:37.207648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BiB4dR4T92V1LvJGkecjaKYrXnCJeUKkAx/CdKoLMk3Cxw3oYHL/0YozU24BBB0rbUx6zSVh5VphED+ts3ntAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:37.208271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77fe0fdf1226b08f3be2cc12332051d4829796686f2878d40b36a5ac9468a423","sha256:c8d5eac22febb58e8f3261ebe1c9673cb5787f3d259cadbe7263aa830e6ad2e1"],"state_sha256":"2b65dcb4829852db75a0afd8a64dca8bae46c1da52f220d1aefcfd96b81314a1"}