{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:Y2PURBOSIIXRYYZ54CISA5FNO7","short_pith_number":"pith:Y2PURBOS","schema_version":"1.0","canonical_sha256":"c69f4885d2422f1c633de0912074ad77dc875c4fb4e257a8a9e4756c0719f52a","source":{"kind":"arxiv","id":"math/9907211","version":1},"attestation_state":"computed","paper":{"title":"Versal deformations of a Dirac type differential operator","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anatoliy K. Prykarpatsky, Denis Blackmore","submitted_at":"1999-07-01T00:00:00Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9907211","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"1999-07-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3e0e1930c930b29cce45a11931f0e0f3aa5e150e8d322b8d3e66ab47a5775563","abstract_canon_sha256":"4e6fa8eb52aab6378fdbaa099c1d167b2647cd7464b2091cd4a80ec03f2fc20f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:22.414253Z","signature_b64":"BIb9xTsb4wmRh7nRLKoNewkiqYzRoM0fk25/b1XTNoc+6te1mb3owAizsD7IOW1AO7F08fGDqiTOTSlK5Q33Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c69f4885d2422f1c633de0912074ad77dc875c4fb4e257a8a9e4756c0719f52a","last_reissued_at":"2026-05-18T01:38:22.413540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:22.413540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Versal deformations of a Dirac type differential operator","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anatoliy K. Prykarpatsky, Denis Blackmore","submitted_at":"1999-07-01T00:00:00Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9907211","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/9907211","created_at":"2026-05-18T01:38:22.413630+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9907211v1","created_at":"2026-05-18T01:38:22.413630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9907211","created_at":"2026-05-18T01:38:22.413630+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2PURBOSIIXR","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2PURBOSIIXRYYZ5","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2PURBOS","created_at":"2026-05-18T12:25:49.631198+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7","json":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7.json","graph_json":"https://pith.science/api/pith-number/Y2PURBOSIIXRYYZ54CISA5FNO7/graph.json","events_json":"https://pith.science/api/pith-number/Y2PURBOSIIXRYYZ54CISA5FNO7/events.json","paper":"https://pith.science/paper/Y2PURBOS"},"agent_actions":{"view_html":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7","download_json":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7.json","view_paper":"https://pith.science/paper/Y2PURBOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9907211&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2PURBOSIIXRYYZ54CISA5FNO7/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2PURBOSIIXRYYZ54CISA5FNO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7/action/storage_attestation","attest_author":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7/action/author_attestation","sign_citation":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7/action/citation_signature","submit_replication":"https://pith.science/pith/Y2PURBOSIIXRYYZ54CISA5FNO7/action/replication_record"}},"created_at":"2026-05-18T01:38:22.413630+00:00","updated_at":"2026-05-18T01:38:22.413630+00:00"}