{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CJUG2G3IYMK2K66HR5WJZYTCOY","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":"a1b951a6b80186623af5112d4f5942cd0e98107fcb2a6e9f1b72d4316e51b42c","cross_cats_sorted":["math-ph","math.MP","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-11-11T11:26:43Z","title_canon_sha256":"442eb6804429a5571aaf92342e382fa3aec8790b59e62cbf4bb9733210c2abe5"},"schema_version":"1.0","source":{"id":"2011.05709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.05709","created_at":"2026-07-05T01:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"2011.05709v1","created_at":"2026-07-05T01:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.05709","created_at":"2026-07-05T01:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"CJUG2G3IYMK2","created_at":"2026-07-05T01:51:00Z"},{"alias_kind":"pith_short_16","alias_value":"CJUG2G3IYMK2K66H","created_at":"2026-07-05T01:51:00Z"},{"alias_kind":"pith_short_8","alias_value":"CJUG2G3I","created_at":"2026-07-05T01:51:00Z"}],"graph_snapshots":[{"event_id":"sha256:62eda0d2e6e9fb59c8ce9ab0e27bbaa7eebb66fdc4c58f3672c5218f81d02922","target":"graph","created_at":"2026-07-05T01:51:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.05709/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Spherical harmonic expansions (SHEs) play an important role in most of the physical sciences, especially in physical geodesy. Despite many decades of investigation, the large order behavior of the SHE coefficients, and the precise domain of convergence for these expansions, have remained open questions. These questions are settled in the present paper for generic planets, whose shape (topography) may include many local peaks, but just one globally highest peak. We show that regardless of the smoothness of the density and topography, short of outright analyticity, the spherical harmonic expansi","authors_text":"C. Ogle, M. Bevis, O. Costin, R. D. Costin","cross_cats":["math-ph","math.MP","physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-11-11T11:26:43Z","title":"On the domain of convergence of spherical harmonic expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.05709","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":"sha256:3d65ca7aa89d52be8760b9e7bb1cd977ab7578dd0ca13997380fe6f633267ff9","target":"record","created_at":"2026-07-05T01:51:00Z","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":"a1b951a6b80186623af5112d4f5942cd0e98107fcb2a6e9f1b72d4316e51b42c","cross_cats_sorted":["math-ph","math.MP","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-11-11T11:26:43Z","title_canon_sha256":"442eb6804429a5571aaf92342e382fa3aec8790b59e62cbf4bb9733210c2abe5"},"schema_version":"1.0","source":{"id":"2011.05709","kind":"arxiv","version":1}},"canonical_sha256":"12686d1b68c315a57bc78f6c9ce2627619ae64d5b01c750cdc1beb2aa3e0b750","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12686d1b68c315a57bc78f6c9ce2627619ae64d5b01c750cdc1beb2aa3e0b750","first_computed_at":"2026-07-05T01:51:00.859268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:00.859268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+4aivMHZhVB9FEv1mRpZ7Rq7zC4aDo275j5Ji20brr9nmd5cR2xY5v8GNZ0ISTi2TOxa5VVvTpfthcp5kXt1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:00.859638Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.05709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d65ca7aa89d52be8760b9e7bb1cd977ab7578dd0ca13997380fe6f633267ff9","sha256:62eda0d2e6e9fb59c8ce9ab0e27bbaa7eebb66fdc4c58f3672c5218f81d02922"],"state_sha256":"6a4d306c12d5198b8a8952a455b1d9a06b8e2a241d9bbecec54e64e86339e8b5"}