{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:Y2PURBOSIIXRYYZ54CISA5FNO7","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":"4e6fa8eb52aab6378fdbaa099c1d167b2647cd7464b2091cd4a80ec03f2fc20f","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"1999-07-01T00:00:00Z","title_canon_sha256":"3e0e1930c930b29cce45a11931f0e0f3aa5e150e8d322b8d3e66ab47a5775563"},"schema_version":"1.0","source":{"id":"math/9907211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9907211","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9907211v1","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9907211","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"Y2PURBOSIIXR","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"Y2PURBOSIIXRYYZ5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"Y2PURBOS","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:4d690eb1c17116fcddb86656308c02d8d7558b10d017c93f669507526e58a3fa","target":"graph","created_at":"2026-05-18T01:38:22Z","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":"If we are given a smooth differential operator in the variable $x\\in {\\mathbb R}/2\\pi {\\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the $\\mbox{Diff}(S^1)$-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced $\\mbox{Diff}(S^1)$-actions endowed with centrally extended Lie-Poisson brackets. After constructing a gener","authors_text":"Anatoliy K. Prykarpatsky, Denis Blackmore","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"1999-07-01T00:00:00Z","title":"Versal deformations of a Dirac type differential operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9907211","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":"sha256:92646689338e8bde7ad4bdb67ebfecde65bd0ad87a30712027d6ec28eebba600","target":"record","created_at":"2026-05-18T01:38:22Z","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":"4e6fa8eb52aab6378fdbaa099c1d167b2647cd7464b2091cd4a80ec03f2fc20f","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"1999-07-01T00:00:00Z","title_canon_sha256":"3e0e1930c930b29cce45a11931f0e0f3aa5e150e8d322b8d3e66ab47a5775563"},"schema_version":"1.0","source":{"id":"math/9907211","kind":"arxiv","version":1}},"canonical_sha256":"c69f4885d2422f1c633de0912074ad77dc875c4fb4e257a8a9e4756c0719f52a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c69f4885d2422f1c633de0912074ad77dc875c4fb4e257a8a9e4756c0719f52a","first_computed_at":"2026-05-18T01:38:22.413540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.413540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BIb9xTsb4wmRh7nRLKoNewkiqYzRoM0fk25/b1XTNoc+6te1mb3owAizsD7IOW1AO7F08fGDqiTOTSlK5Q33Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.414253Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9907211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92646689338e8bde7ad4bdb67ebfecde65bd0ad87a30712027d6ec28eebba600","sha256:4d690eb1c17116fcddb86656308c02d8d7558b10d017c93f669507526e58a3fa"],"state_sha256":"14619e456cd8eb9286847d5fecfe9511a984756d44eb0fac48a3f3400715fc4f"}