{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MTGE7YFUSFMDPJNSAEL7IMHB5R","short_pith_number":"pith:MTGE7YFU","canonical_record":{"source":{"id":"1812.00437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-02T17:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"d1b55cd8326d554bfb932bef489d21117eb56a89c8c2428401891c31adf0de84","abstract_canon_sha256":"4b90475428af9ef7f7768f8a0d4635be6a51d88e8977d6809f06e9cb5d7af7c5"},"schema_version":"1.0"},"canonical_sha256":"64cc4fe0b4915837a5b20117f430e1ec69613d2b2c3f76ba734ae31a676c67a6","source":{"kind":"arxiv","id":"1812.00437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00437","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00437v1","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00437","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"MTGE7YFUSFMD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MTGE7YFUSFMDPJNS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MTGE7YFU","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MTGE7YFUSFMDPJNSAEL7IMHB5R","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-02T17:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"d1b55cd8326d554bfb932bef489d21117eb56a89c8c2428401891c31adf0de84","abstract_canon_sha256":"4b90475428af9ef7f7768f8a0d4635be6a51d88e8977d6809f06e9cb5d7af7c5"},"schema_version":"1.0"},"canonical_sha256":"64cc4fe0b4915837a5b20117f430e1ec69613d2b2c3f76ba734ae31a676c67a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:21.348954Z","signature_b64":"llhPRtO1dk4JGbNG5Jtj+9k04Vx7if/BGyA0HAoDycC4i1oWv5pN2u2ifuz499EN4iR4NbdnCRgSfe4PSwpzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64cc4fe0b4915837a5b20117f430e1ec69613d2b2c3f76ba734ae31a676c67a6","last_reissued_at":"2026-05-17T23:59:21.348404Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:21.348404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00437","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VV4OIJ8Y8sHIZLlxepvosREAKVHnenzlXa2Sv76SetGHvvzhlyLC/GTN3onGdxCBJDA0aTwI/xgGrf4cixqQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:24:56.879689Z"},"content_sha256":"1644089ae455e833aaa77f46eba9f5b88786599586915d86d170ce8e5b2f5ec5","schema_version":"1.0","event_id":"sha256:1644089ae455e833aaa77f46eba9f5b88786599586915d86d170ce8e5b2f5ec5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MTGE7YFUSFMDPJNSAEL7IMHB5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Wolfgang Erb","submitted_at":"2018-12-02T17:57:52Z","abstract_excerpt":"Rhodonea curves are classical planar curves in the unit disk with the characteristic shape of a rose. In this work, we use point samples along such rose curves as node sets for a novel spectral interpolation scheme on the disk. By deriving a discrete orthogonality structure on these rhodonea nodes, we will show that the spectral interpolation problem is unisolvent. The underlying interpolation space is generated by a parity-modified Chebyshev-Fourier basis on the disk. This allows us to compute the spectral interpolant in an efficient way. Properties as continuity, convergence and numerical co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00437","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3KFrN7GHpHtXuCZauM9SkWPMef/we49aFfWwtfUgyBjM3SqV/T2OUoTtYcd1wHxCX2mWcUfi636DV833SONBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:24:56.880029Z"},"content_sha256":"b1f82c4432ca1d5d3e185cf21af644896a4a9b5c673c26f902c2742583c5abe4","schema_version":"1.0","event_id":"sha256:b1f82c4432ca1d5d3e185cf21af644896a4a9b5c673c26f902c2742583c5abe4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/bundle.json","state_url":"https://pith.science/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T00:24:56Z","links":{"resolver":"https://pith.science/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R","bundle":"https://pith.science/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/bundle.json","state":"https://pith.science/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTGE7YFUSFMDPJNSAEL7IMHB5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MTGE7YFUSFMDPJNSAEL7IMHB5R","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":"4b90475428af9ef7f7768f8a0d4635be6a51d88e8977d6809f06e9cb5d7af7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-02T17:57:52Z","title_canon_sha256":"d1b55cd8326d554bfb932bef489d21117eb56a89c8c2428401891c31adf0de84"},"schema_version":"1.0","source":{"id":"1812.00437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00437","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00437v1","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00437","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"MTGE7YFUSFMD","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MTGE7YFUSFMDPJNS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MTGE7YFU","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:b1f82c4432ca1d5d3e185cf21af644896a4a9b5c673c26f902c2742583c5abe4","target":"graph","created_at":"2026-05-17T23:59:21Z","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":"Rhodonea curves are classical planar curves in the unit disk with the characteristic shape of a rose. In this work, we use point samples along such rose curves as node sets for a novel spectral interpolation scheme on the disk. By deriving a discrete orthogonality structure on these rhodonea nodes, we will show that the spectral interpolation problem is unisolvent. The underlying interpolation space is generated by a parity-modified Chebyshev-Fourier basis on the disk. This allows us to compute the spectral interpolant in an efficient way. Properties as continuity, convergence and numerical co","authors_text":"Wolfgang Erb","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-02T17:57:52Z","title":"Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00437","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":"sha256:1644089ae455e833aaa77f46eba9f5b88786599586915d86d170ce8e5b2f5ec5","target":"record","created_at":"2026-05-17T23:59:21Z","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":"4b90475428af9ef7f7768f8a0d4635be6a51d88e8977d6809f06e9cb5d7af7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-02T17:57:52Z","title_canon_sha256":"d1b55cd8326d554bfb932bef489d21117eb56a89c8c2428401891c31adf0de84"},"schema_version":"1.0","source":{"id":"1812.00437","kind":"arxiv","version":1}},"canonical_sha256":"64cc4fe0b4915837a5b20117f430e1ec69613d2b2c3f76ba734ae31a676c67a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64cc4fe0b4915837a5b20117f430e1ec69613d2b2c3f76ba734ae31a676c67a6","first_computed_at":"2026-05-17T23:59:21.348404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:21.348404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llhPRtO1dk4JGbNG5Jtj+9k04Vx7if/BGyA0HAoDycC4i1oWv5pN2u2ifuz499EN4iR4NbdnCRgSfe4PSwpzCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:21.348954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1644089ae455e833aaa77f46eba9f5b88786599586915d86d170ce8e5b2f5ec5","sha256:b1f82c4432ca1d5d3e185cf21af644896a4a9b5c673c26f902c2742583c5abe4"],"state_sha256":"362c7a7fb4941f9bc9526e1916788aa6ea337f9c9bb72024a5f5bf054bc249bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dm2Gmd5m+qfuv3x9fywj5RDjVFGcWEzIWcKAP0UQFJQtr6I9DXQhPe/qFoCIeVZbGL8lhueCVpZb0o3yyO8eCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:24:56.881991Z","bundle_sha256":"d49bba00563f0db87582d9e2c7428a8961c06227083cfa66439a234381f53d56"}}