{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:73TX2UB3ZJ2FV4PWJB37UVX2E6","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":"456a82e97f25c7135f88ee65c9620aceb08a98dac1f3d7d38d513d6bd2f7d716","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DS","submitted_at":"2026-01-31T22:50:32Z","title_canon_sha256":"13aa12300353e01587e656b37931d28565a23c97135b4b08e4b31ac2b984aeb1"},"schema_version":"1.0","source":{"id":"2602.00925","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00925","created_at":"2026-06-09T02:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00925v2","created_at":"2026-06-09T02:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00925","created_at":"2026-06-09T02:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"73TX2UB3ZJ2F","created_at":"2026-06-09T02:07:18Z"},{"alias_kind":"pith_short_16","alias_value":"73TX2UB3ZJ2FV4PW","created_at":"2026-06-09T02:07:18Z"},{"alias_kind":"pith_short_8","alias_value":"73TX2UB3","created_at":"2026-06-09T02:07:18Z"}],"graph_snapshots":[{"event_id":"sha256:79b777cc3482f9bbb42333795cd4c3b1c2690d0fdb699f4839be34b5d0a709d9","target":"graph","created_at":"2026-06-09T02:07:18Z","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/2602.00925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A structure of families of Laurent series solutions of a quasi-homogeneous vector field is studied, where a given vector field is assumed to have a commutable vector field. For an $m$ dimensional vector field, a family of Laurent series solutions is called principle if it includes $m$ arbitrary parameters, and called non-principle if the number is smaller than $m$. Starting from a principle Laurent series solutions, a systematic method to obtain a non-principle Laurent series solutions is given. In particular, from the Kovalevskaya exponents of the principle Laurent series solutions, which is ","authors_text":"Hayato Chiba","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DS","submitted_at":"2026-01-31T22:50:32Z","title":"On the degeneration of Kovalevskaya exponents of Laurent series solutions of quasi-homogeneous vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00925","kind":"arxiv","version":2},"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":"sha256:5ed4a56cb5d68c5ce7438ca2eec195bfd4e37b78bb51129becfb19aa6037e821","target":"record","created_at":"2026-06-09T02:07:18Z","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":"456a82e97f25c7135f88ee65c9620aceb08a98dac1f3d7d38d513d6bd2f7d716","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DS","submitted_at":"2026-01-31T22:50:32Z","title_canon_sha256":"13aa12300353e01587e656b37931d28565a23c97135b4b08e4b31ac2b984aeb1"},"schema_version":"1.0","source":{"id":"2602.00925","kind":"arxiv","version":2}},"canonical_sha256":"fee77d503bca745af1f64877fa56fa279b3f398030fcfb22eb122bf8b6115a51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fee77d503bca745af1f64877fa56fa279b3f398030fcfb22eb122bf8b6115a51","first_computed_at":"2026-06-09T02:07:18.861214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:18.861214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/V0Zrdqs+/K1zueM+0P8NZIcUPmcXgIB82I5vruBrkclkP6+vek7IzEZ9Up51ryf7rrH6ddpWV+2A6LEV0XKAA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:18.862133Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.00925","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ed4a56cb5d68c5ce7438ca2eec195bfd4e37b78bb51129becfb19aa6037e821","sha256:79b777cc3482f9bbb42333795cd4c3b1c2690d0fdb699f4839be34b5d0a709d9"],"state_sha256":"e95d366c36143cc922d14d119c83322bedd09507e99a9b6495cfe971e9fea0da"}