{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P2U555BF344MRU4XSAUY32VTGF","short_pith_number":"pith:P2U555BF","schema_version":"1.0","canonical_sha256":"7ea9def425df38c8d39790298deab3315022727b42e839f01198210fb6a48352","source":{"kind":"arxiv","id":"1906.08005","version":2},"attestation_state":"computed","paper":{"title":"An analytic bifurcation principle for Fredholm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthias Stiefenhofer","submitted_at":"2019-06-19T10:01:03Z","abstract_excerpt":"Smooth Equations of the form G[z]=0 are investigated in Banach spaces with the aim of continuing the basic solution G[0]=0 to a solution curve of G[z]=0 with the implicit function theorem. If the linearization is surjective, then the transversality condition of the implicit function theorem can be satisfied in a straightforward way, yielding a regular solution curve, whereas otherwise the equation G[z]=0 has to be extended appropriately for reaching a surjective linearization accessible to the implicit function theorem. This extension process, implying in the first step the standard bifurcatio"},"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":"1906.08005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T10:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"a6ee84b5a1ae88328b5e12ba970cc7312245e8b3974ce429b0ce00363ce47706","abstract_canon_sha256":"17c1dac9f3643e45becbb210374d59940d2a1369f6a31971fd5e06053b4f2dab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:39.326249Z","signature_b64":"t3V7MB4dR4+hJFBqzyKeceqiX39hYoTqG32VtqdjTZBoJyre5RgYDTcQBdjLkE6P9cS/hLsjuHSH0x3xvekRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ea9def425df38c8d39790298deab3315022727b42e839f01198210fb6a48352","last_reissued_at":"2026-05-17T23:39:39.325695Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:39.325695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analytic bifurcation principle for Fredholm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthias Stiefenhofer","submitted_at":"2019-06-19T10:01:03Z","abstract_excerpt":"Smooth Equations of the form G[z]=0 are investigated in Banach spaces with the aim of continuing the basic solution G[0]=0 to a solution curve of G[z]=0 with the implicit function theorem. If the linearization is surjective, then the transversality condition of the implicit function theorem can be satisfied in a straightforward way, yielding a regular solution curve, whereas otherwise the equation G[z]=0 has to be extended appropriately for reaching a surjective linearization accessible to the implicit function theorem. This extension process, implying in the first step the standard bifurcatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08005","kind":"arxiv","version":2},"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":"1906.08005","created_at":"2026-05-17T23:39:39.325799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.08005v2","created_at":"2026-05-17T23:39:39.325799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08005","created_at":"2026-05-17T23:39:39.325799+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2U555BF344M","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2U555BF344MRU4X","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2U555BF","created_at":"2026-05-18T12:33:24.271573+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/P2U555BF344MRU4XSAUY32VTGF","json":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF.json","graph_json":"https://pith.science/api/pith-number/P2U555BF344MRU4XSAUY32VTGF/graph.json","events_json":"https://pith.science/api/pith-number/P2U555BF344MRU4XSAUY32VTGF/events.json","paper":"https://pith.science/paper/P2U555BF"},"agent_actions":{"view_html":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF","download_json":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF.json","view_paper":"https://pith.science/paper/P2U555BF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.08005&json=true","fetch_graph":"https://pith.science/api/pith-number/P2U555BF344MRU4XSAUY32VTGF/graph.json","fetch_events":"https://pith.science/api/pith-number/P2U555BF344MRU4XSAUY32VTGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF/action/storage_attestation","attest_author":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF/action/author_attestation","sign_citation":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF/action/citation_signature","submit_replication":"https://pith.science/pith/P2U555BF344MRU4XSAUY32VTGF/action/replication_record"}},"created_at":"2026-05-17T23:39:39.325799+00:00","updated_at":"2026-05-17T23:39:39.325799+00:00"}