{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TF75YEFIWJSNT73DSHCHPYDN47","short_pith_number":"pith:TF75YEFI","schema_version":"1.0","canonical_sha256":"997fdc10a8b264d9ff6391c477e06de7e611b51a36093889baf9c7e584d99a06","source":{"kind":"arxiv","id":"1504.00961","version":1},"attestation_state":"computed","paper":{"title":"Existence of Dirac Eigenvalues of higher Multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikolai Nowaczyk","submitted_at":"2015-04-04T00:12:47Z","abstract_excerpt":"In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by catching the desired metric in a subspace of Riemannian metrics with a loop that is not homotopically trivial. We show how this can be done on the sphere with a loop of metrics induced by a family of rotations. Finally, we transport this loop to an arbitrary manifold (of suitable dimension) by extending some known results about surgery theory on spin manifolds."},"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":"1504.00961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-04T00:12:47Z","cross_cats_sorted":[],"title_canon_sha256":"7a8abbf7bb7fb22f730f363fbb06f67828aee1ad24412e47e7fac0b98bd954c6","abstract_canon_sha256":"d3a192946e410fc9bd8af8d840b2777936ca30f085fe0e34670e49f99874f75b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.359161Z","signature_b64":"ig2nuwD27I+UWS7IjNpi1Z9qKeC9IFrJ4Znzvx76LgUFDfjAlMvpAon4p5wgGPp+8Wx/n0kkv8d5fXXzl6L9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"997fdc10a8b264d9ff6391c477e06de7e611b51a36093889baf9c7e584d99a06","last_reissued_at":"2026-05-18T01:00:10.358432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.358432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Dirac Eigenvalues of higher Multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikolai Nowaczyk","submitted_at":"2015-04-04T00:12:47Z","abstract_excerpt":"In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by catching the desired metric in a subspace of Riemannian metrics with a loop that is not homotopically trivial. We show how this can be done on the sphere with a loop of metrics induced by a family of rotations. Finally, we transport this loop to an arbitrary manifold (of suitable dimension) by extending some known results about surgery theory on spin manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00961","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":"1504.00961","created_at":"2026-05-18T01:00:10.358557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00961v1","created_at":"2026-05-18T01:00:10.358557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00961","created_at":"2026-05-18T01:00:10.358557+00:00"},{"alias_kind":"pith_short_12","alias_value":"TF75YEFIWJSN","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TF75YEFIWJSNT73D","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TF75YEFI","created_at":"2026-05-18T12:29:42.218222+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/TF75YEFIWJSNT73DSHCHPYDN47","json":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47.json","graph_json":"https://pith.science/api/pith-number/TF75YEFIWJSNT73DSHCHPYDN47/graph.json","events_json":"https://pith.science/api/pith-number/TF75YEFIWJSNT73DSHCHPYDN47/events.json","paper":"https://pith.science/paper/TF75YEFI"},"agent_actions":{"view_html":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47","download_json":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47.json","view_paper":"https://pith.science/paper/TF75YEFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00961&json=true","fetch_graph":"https://pith.science/api/pith-number/TF75YEFIWJSNT73DSHCHPYDN47/graph.json","fetch_events":"https://pith.science/api/pith-number/TF75YEFIWJSNT73DSHCHPYDN47/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47/action/storage_attestation","attest_author":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47/action/author_attestation","sign_citation":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47/action/citation_signature","submit_replication":"https://pith.science/pith/TF75YEFIWJSNT73DSHCHPYDN47/action/replication_record"}},"created_at":"2026-05-18T01:00:10.358557+00:00","updated_at":"2026-05-18T01:00:10.358557+00:00"}