{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TKWJOK2SIMGE35LOC2R5PZDHII","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":"36dd8d05731b35ff056896246df9b3fb96fae541049dfc0877fe91d7799487e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-22T13:37:04Z","title_canon_sha256":"e0025e6bed815469012526dfb074b316beff63f12736289e86e8973eb1f9501a"},"schema_version":"1.0","source":{"id":"1610.07048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07048","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07048v1","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07048","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"TKWJOK2SIMGE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TKWJOK2SIMGE35LO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TKWJOK2S","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:ff5b2cfbdf3605a519dcaf8bc0982d3840a2555469973b81fc22a9e525c15af4","target":"graph","created_at":"2026-05-18T00:57:06Z","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"},"paper":{"abstract_excerpt":"We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions have the following features: (i) depend on the geodesic distance; (ii) are orthonormal with respect to the point-evaluation functionals; and (iii) have all derivatives equal zero up to a certain order at the interpolation points. Mo","authors_text":"Alessandra De Rossi, Giampietro Allasia, Roberto Cavoretto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-22T13:37:04Z","title":"Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07048","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":"sha256:8c0d48fc67d045acf66996bc0376e34e0216f99ab6364c832cecc7ca6ec3f23d","target":"record","created_at":"2026-05-18T00:57:06Z","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":"36dd8d05731b35ff056896246df9b3fb96fae541049dfc0877fe91d7799487e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-22T13:37:04Z","title_canon_sha256":"e0025e6bed815469012526dfb074b316beff63f12736289e86e8973eb1f9501a"},"schema_version":"1.0","source":{"id":"1610.07048","kind":"arxiv","version":1}},"canonical_sha256":"9aac972b52430c4df56e16a3d7e467420efc618fb02c26acabd2db4e10d2e6ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aac972b52430c4df56e16a3d7e467420efc618fb02c26acabd2db4e10d2e6ae","first_computed_at":"2026-05-18T00:57:06.840727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:06.840727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cTuB/BCNqIL4kTh3DgFikyBEyfGF5ve/TZkZNK2gE9q2qVN7KYJMnWtmZIAsr79z/B48yfH8+RTZq7urhK2cCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:06.841524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c0d48fc67d045acf66996bc0376e34e0216f99ab6364c832cecc7ca6ec3f23d","sha256:ff5b2cfbdf3605a519dcaf8bc0982d3840a2555469973b81fc22a9e525c15af4"],"state_sha256":"4eee4917889afab763b33eeca126502d103bfe0e86286bb4050e3aef9ab2a010"}