{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:FZA3AOK7J6L27YOXWDLWMQ5N24","short_pith_number":"pith:FZA3AOK7","schema_version":"1.0","canonical_sha256":"2e41b0395f4f97afe1d7b0d76643add72c8f875131b73fae96bc9362176b2191","source":{"kind":"arxiv","id":"0705.3857","version":3},"attestation_state":"computed","paper":{"title":"Extremal metrics for spectral functions of Dirac operators in even and odd dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Niels Martin Moller","submitted_at":"2007-05-25T21:54:30Z","abstract_excerpt":"Let (M^n, g) be a closed smooth Riemannian spin manifold and denote by D its Atiyah-Singer-Dirac operator. We study the variation of Riemannian metrics for the zeta function and functional determinant of D^2, and prove finiteness of the Morse index at stationary metrics, and local extremality at such metrics under general, i.e. not only conformal, change of metrics.\n  In even dimensions, which is also a new case for the conformal Laplacian, the relevant stability operator is of log-polyhomogeneous pseudodifferential type, and we prove new results of independent interest, on the spectrum for su"},"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":"0705.3857","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-05-25T21:54:30Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6fc6b13da8c95f61b6382dcb075cfe20319ef0ef9abfe602ad41f9f41855c4b2","abstract_canon_sha256":"243e013e641066720e9a490094465d1e634f716a09dfedd7a6cbbae4d1df308c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:35.178069Z","signature_b64":"3CMDe1r2fIp6iz1TRdduDEXuV2jUt38h2cZfqQFdx+Mtp/Spg1jbrsFPtfdnnXeoSYVVvVCKfye7GzZ1AyxoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e41b0395f4f97afe1d7b0d76643add72c8f875131b73fae96bc9362176b2191","last_reissued_at":"2026-05-17T23:51:35.177270Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:35.177270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal metrics for spectral functions of Dirac operators in even and odd dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Niels Martin Moller","submitted_at":"2007-05-25T21:54:30Z","abstract_excerpt":"Let (M^n, g) be a closed smooth Riemannian spin manifold and denote by D its Atiyah-Singer-Dirac operator. We study the variation of Riemannian metrics for the zeta function and functional determinant of D^2, and prove finiteness of the Morse index at stationary metrics, and local extremality at such metrics under general, i.e. not only conformal, change of metrics.\n  In even dimensions, which is also a new case for the conformal Laplacian, the relevant stability operator is of log-polyhomogeneous pseudodifferential type, and we prove new results of independent interest, on the spectrum for su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3857","kind":"arxiv","version":3},"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":"0705.3857","created_at":"2026-05-17T23:51:35.177423+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.3857v3","created_at":"2026-05-17T23:51:35.177423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3857","created_at":"2026-05-17T23:51:35.177423+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZA3AOK7J6L2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZA3AOK7J6L27YOX","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZA3AOK7","created_at":"2026-05-18T12:25:55.427421+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/FZA3AOK7J6L27YOXWDLWMQ5N24","json":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24.json","graph_json":"https://pith.science/api/pith-number/FZA3AOK7J6L27YOXWDLWMQ5N24/graph.json","events_json":"https://pith.science/api/pith-number/FZA3AOK7J6L27YOXWDLWMQ5N24/events.json","paper":"https://pith.science/paper/FZA3AOK7"},"agent_actions":{"view_html":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24","download_json":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24.json","view_paper":"https://pith.science/paper/FZA3AOK7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.3857&json=true","fetch_graph":"https://pith.science/api/pith-number/FZA3AOK7J6L27YOXWDLWMQ5N24/graph.json","fetch_events":"https://pith.science/api/pith-number/FZA3AOK7J6L27YOXWDLWMQ5N24/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24/action/storage_attestation","attest_author":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24/action/author_attestation","sign_citation":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24/action/citation_signature","submit_replication":"https://pith.science/pith/FZA3AOK7J6L27YOXWDLWMQ5N24/action/replication_record"}},"created_at":"2026-05-17T23:51:35.177423+00:00","updated_at":"2026-05-17T23:51:35.177423+00:00"}