{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ZA3KL2P4UURFMW3THZWVYKYKZ2","short_pith_number":"pith:ZA3KL2P4","canonical_record":{"source":{"id":"math/0702019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-02-01T12:43:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0724e66ff00e2cb35ce0dd75899645acdc4ec9291430336ff26ec269f799ad5e","abstract_canon_sha256":"b241eebb25a51c8f4a237ff748bb049b65556fdd0decda9bcb99d0eb1d15df6c"},"schema_version":"1.0"},"canonical_sha256":"c836a5e9fca522565b733e6d5c2b0aceb3cafc98f331300a245f6df107304997","source":{"kind":"arxiv","id":"math/0702019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702019","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702019v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702019","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZA3KL2P4UURF","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"ZA3KL2P4UURFMW3T","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"ZA3KL2P4","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ZA3KL2P4UURFMW3THZWVYKYKZ2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0702019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-02-01T12:43:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0724e66ff00e2cb35ce0dd75899645acdc4ec9291430336ff26ec269f799ad5e","abstract_canon_sha256":"b241eebb25a51c8f4a237ff748bb049b65556fdd0decda9bcb99d0eb1d15df6c"},"schema_version":"1.0"},"canonical_sha256":"c836a5e9fca522565b733e6d5c2b0aceb3cafc98f331300a245f6df107304997","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.943295Z","signature_b64":"r/xrcqF0oQsHlH6qN/Dh/0FCw1IAuTb0O3xb4mzTzhL0LlSSyB+vXI7KifcDacS3sC/ZQ1q4Rmo4Gpn1I8aCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c836a5e9fca522565b733e6d5c2b0aceb3cafc98f331300a245f6df107304997","last_reissued_at":"2026-06-03T22:06:21.942885Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.942885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0702019","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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iI9dTlxleSVvEF5FAbTJ2qw0dnZiYkauegjvEuW1v/cP8pg0JN/uiEVDXX2S/QA+yIVkC26Krn07gyIV1EJACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:19:43.578361Z"},"content_sha256":"cc3e64aa4f14dcc984431ca36eb401d64ab1cbf2c041e1414b06374320223b37","schema_version":"1.0","event_id":"sha256:cc3e64aa4f14dcc984431ca36eb401d64ab1cbf2c041e1414b06374320223b37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ZA3KL2P4UURFMW3THZWVYKYKZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability Results for Scattered Data Interpolation by Trigonometric Polynomials","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Daniel Potts, Stefan Kunis","submitted_at":"2007-02-01T12:43:31Z","abstract_excerpt":"A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the fast Fourier transforms for nonequispaced nodes. The main result is that under mild assumptions the total complexity for solving the interpolation problem at M arbitrary nodes is of order O(M logM). This result is obtained by the use of localised trigonometric kernels where the localisation is chosen in accordance to the spatial dimension d. Numerical exampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702019","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0702019/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VB8aoeT17oN0RrNySzGX0Oxg+ISqRZfeqJQ3ttZ5VNuRrqXBtlbtOgoHhX/g50FFeA+DFlazRLUGDJNgzJLeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:19:43.578753Z"},"content_sha256":"a7d0110a9e69520078466dc0db2e5de0cd9df53780766fee680ab1bcbe40b699","schema_version":"1.0","event_id":"sha256:a7d0110a9e69520078466dc0db2e5de0cd9df53780766fee680ab1bcbe40b699"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/bundle.json","state_url":"https://pith.science/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/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":"2026-06-22T09:19:43Z","links":{"resolver":"https://pith.science/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2","bundle":"https://pith.science/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/bundle.json","state":"https://pith.science/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZA3KL2P4UURFMW3THZWVYKYKZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZA3KL2P4UURFMW3THZWVYKYKZ2","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":"b241eebb25a51c8f4a237ff748bb049b65556fdd0decda9bcb99d0eb1d15df6c","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-02-01T12:43:31Z","title_canon_sha256":"0724e66ff00e2cb35ce0dd75899645acdc4ec9291430336ff26ec269f799ad5e"},"schema_version":"1.0","source":{"id":"math/0702019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702019","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702019v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702019","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZA3KL2P4UURF","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"ZA3KL2P4UURFMW3T","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"ZA3KL2P4","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:a7d0110a9e69520078466dc0db2e5de0cd9df53780766fee680ab1bcbe40b699","target":"graph","created_at":"2026-06-03T22:06:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0702019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the fast Fourier transforms for nonequispaced nodes. The main result is that under mild assumptions the total complexity for solving the interpolation problem at M arbitrary nodes is of order O(M logM). This result is obtained by the use of localised trigonometric kernels where the localisation is chosen in accordance to the spatial dimension d. Numerical exampl","authors_text":"Daniel Potts, Stefan Kunis","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-02-01T12:43:31Z","title":"Stability Results for Scattered Data Interpolation by Trigonometric Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702019","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:cc3e64aa4f14dcc984431ca36eb401d64ab1cbf2c041e1414b06374320223b37","target":"record","created_at":"2026-06-03T22:06:21Z","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":"b241eebb25a51c8f4a237ff748bb049b65556fdd0decda9bcb99d0eb1d15df6c","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-02-01T12:43:31Z","title_canon_sha256":"0724e66ff00e2cb35ce0dd75899645acdc4ec9291430336ff26ec269f799ad5e"},"schema_version":"1.0","source":{"id":"math/0702019","kind":"arxiv","version":1}},"canonical_sha256":"c836a5e9fca522565b733e6d5c2b0aceb3cafc98f331300a245f6df107304997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c836a5e9fca522565b733e6d5c2b0aceb3cafc98f331300a245f6df107304997","first_computed_at":"2026-06-03T22:06:21.942885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.942885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/xrcqF0oQsHlH6qN/Dh/0FCw1IAuTb0O3xb4mzTzhL0LlSSyB+vXI7KifcDacS3sC/ZQ1q4Rmo4Gpn1I8aCBw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.943295Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc3e64aa4f14dcc984431ca36eb401d64ab1cbf2c041e1414b06374320223b37","sha256:a7d0110a9e69520078466dc0db2e5de0cd9df53780766fee680ab1bcbe40b699"],"state_sha256":"75ff2c5fad31b6978c9fe4d7ec9c3499ffa5d8574a25b0199a5c72c7ea486b67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H65jaDmWWIHXJZS+QNn3NzmyN3uF3mVwVhyFfb0N2bGpsdACUUjiI6BCVQdlENWjEKGHJn8LVxMJViIqLoj3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:19:43.581040Z","bundle_sha256":"cbaa87e954c0bcb5c492df3be1b3ecdc52c3577e96402cd7f539c466366b570b"}}