{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KUGS3SE7VO2RQVG6GKZAT23Y2U","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":"4e93cb166ee1b71c7cb824cb749e2f547e6509c4a60d2bad902dbcea891d1417","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-19T12:13:57Z","title_canon_sha256":"c9a9a8afb9765526729b5f985c1dd5bc9cc8b228ea99d76ec9a751354c0e832e"},"schema_version":"1.0","source":{"id":"1002.3725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3725","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3725v2","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3725","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"KUGS3SE7VO2R","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUGS3SE7VO2RQVG6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUGS3SE7","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9b804673557940ffe57ffbbcf4004d1e286c11cd9fe7d1183d29092c5ac3f871","target":"graph","created_at":"2026-05-18T04:24:54Z","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":"One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.","authors_text":"Tomasz Stachowiak","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-19T12:13:57Z","title":"On solvable Dirac equation with polynomial potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3725","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":"sha256:988be1226c4c82f78ec741f97e4b4cd63902e72f00dd2554c10b37ccdeb400b3","target":"record","created_at":"2026-05-18T04:24:54Z","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":"4e93cb166ee1b71c7cb824cb749e2f547e6509c4a60d2bad902dbcea891d1417","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-19T12:13:57Z","title_canon_sha256":"c9a9a8afb9765526729b5f985c1dd5bc9cc8b228ea99d76ec9a751354c0e832e"},"schema_version":"1.0","source":{"id":"1002.3725","kind":"arxiv","version":2}},"canonical_sha256":"550d2dc89fabb51854de32b209eb78d5121d3ce04de614796bbb5e4ca3d7d053","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"550d2dc89fabb51854de32b209eb78d5121d3ce04de614796bbb5e4ca3d7d053","first_computed_at":"2026-05-18T04:24:54.718695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:54.718695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bRwcShzKmg4wkaPzLnRn0Zvn95k86UNGCf95OoI6E3/G3U5hV2tSdzYUY+ave3v43Elm90RSiUp1Skuk9NmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:54.719186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:988be1226c4c82f78ec741f97e4b4cd63902e72f00dd2554c10b37ccdeb400b3","sha256:9b804673557940ffe57ffbbcf4004d1e286c11cd9fe7d1183d29092c5ac3f871"],"state_sha256":"6f6483862f2dd724f49ff1cd8843679c0b8e09ff9f3600eb4669e938582c7a57"}