{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z6BCVRO3VQ2IMJWACRQPGIQ36I","short_pith_number":"pith:Z6BCVRO3","canonical_record":{"source":{"id":"1205.3255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-15T04:23:10Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c732d1210574ad4ca79016f7dbc7bd6042c8ba950db348f7f60379a9a2413f97","abstract_canon_sha256":"bb263f36a6486c6b6f702c22548bf280f45263e75236bb8ee8b7a282703b408c"},"schema_version":"1.0"},"canonical_sha256":"cf822ac5dbac348626c01460f3221bf229d4763325a6f81bb1ec5c7529c8528d","source":{"kind":"arxiv","id":"1205.3255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3255","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3255v1","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3255","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"Z6BCVRO3VQ2I","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z6BCVRO3VQ2IMJWA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z6BCVRO3","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z6BCVRO3VQ2IMJWACRQPGIQ36I","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-15T04:23:10Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c732d1210574ad4ca79016f7dbc7bd6042c8ba950db348f7f60379a9a2413f97","abstract_canon_sha256":"bb263f36a6486c6b6f702c22548bf280f45263e75236bb8ee8b7a282703b408c"},"schema_version":"1.0"},"canonical_sha256":"cf822ac5dbac348626c01460f3221bf229d4763325a6f81bb1ec5c7529c8528d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:46.504701Z","signature_b64":"aqxh9GtRxUQwpJoDkQ2L5cdXfJIGD4bFU+lY216/AZ9c3V7C9n4h9sFZ3aQi9fvwXij+2A/JWLJL1pX3J492BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf822ac5dbac348626c01460f3221bf229d4763325a6f81bb1ec5c7529c8528d","last_reissued_at":"2026-05-18T03:13:46.503950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:46.503950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3255","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":"2026-05-18T03:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIwugtsI96bKNh+SSEfSGYqylpFGHNqRSNys0+u2AUq3FD1MNwe0Uh3SU7eDyLine7EwCCnpaDFE6Kwc61i2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:31:42.476992Z"},"content_sha256":"c224aa73a3308cc329c338660ae725ddbf491f44f0e48aa2590bef7788168633","schema_version":"1.0","event_id":"sha256:c224aa73a3308cc329c338660ae725ddbf491f44f0e48aa2590bef7788168633"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z6BCVRO3VQ2IMJWACRQPGIQ36I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localized bases for kernel spaces on the unit sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NA","authors_text":"E. Fuselier, F.J. Narcowich, G.B. Wright, J.D. Ward, T. Hangelbroek","submitted_at":"2012-05-15T04:23:10Z","abstract_excerpt":"Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of $N$ scattered sites, the standard basis for such a space utilizes $N$ \\emph{globally} supported kernels; computing with it is prohibitively expensive for large $N$. Easily computable, well-localized bases, with \"small-footprint\" basis elements - i.e., elements using only a small number of kernels -- have been unavailable. Working on $\\sphere$, with focus on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3255","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":"2026-05-18T03:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exIUNnGXVBIUfMpiGOwzub4P1ALWsG8E0IRqlrVjBheg5YC6+wNRr+6jkCmYXi4p/RtoRm73IF9LVh2KbAitDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:31:42.477350Z"},"content_sha256":"e20b6ec4c9f144d05093a95480d4e117471b413a1e46cfe216782fb7a8864779","schema_version":"1.0","event_id":"sha256:e20b6ec4c9f144d05093a95480d4e117471b413a1e46cfe216782fb7a8864779"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/bundle.json","state_url":"https://pith.science/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/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":"2026-06-23T10:31:42Z","links":{"resolver":"https://pith.science/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I","bundle":"https://pith.science/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/bundle.json","state":"https://pith.science/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6BCVRO3VQ2IMJWACRQPGIQ36I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z6BCVRO3VQ2IMJWACRQPGIQ36I","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":"bb263f36a6486c6b6f702c22548bf280f45263e75236bb8ee8b7a282703b408c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-15T04:23:10Z","title_canon_sha256":"c732d1210574ad4ca79016f7dbc7bd6042c8ba950db348f7f60379a9a2413f97"},"schema_version":"1.0","source":{"id":"1205.3255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3255","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3255v1","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3255","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"Z6BCVRO3VQ2I","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z6BCVRO3VQ2IMJWA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z6BCVRO3","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e20b6ec4c9f144d05093a95480d4e117471b413a1e46cfe216782fb7a8864779","target":"graph","created_at":"2026-05-18T03:13:46Z","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":"Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of $N$ scattered sites, the standard basis for such a space utilizes $N$ \\emph{globally} supported kernels; computing with it is prohibitively expensive for large $N$. Easily computable, well-localized bases, with \"small-footprint\" basis elements - i.e., elements using only a small number of kernels -- have been unavailable. Working on $\\sphere$, with focus on ","authors_text":"E. Fuselier, F.J. Narcowich, G.B. Wright, J.D. Ward, T. Hangelbroek","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-15T04:23:10Z","title":"Localized bases for kernel spaces on the unit sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3255","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:c224aa73a3308cc329c338660ae725ddbf491f44f0e48aa2590bef7788168633","target":"record","created_at":"2026-05-18T03:13:46Z","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":"bb263f36a6486c6b6f702c22548bf280f45263e75236bb8ee8b7a282703b408c","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-15T04:23:10Z","title_canon_sha256":"c732d1210574ad4ca79016f7dbc7bd6042c8ba950db348f7f60379a9a2413f97"},"schema_version":"1.0","source":{"id":"1205.3255","kind":"arxiv","version":1}},"canonical_sha256":"cf822ac5dbac348626c01460f3221bf229d4763325a6f81bb1ec5c7529c8528d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf822ac5dbac348626c01460f3221bf229d4763325a6f81bb1ec5c7529c8528d","first_computed_at":"2026-05-18T03:13:46.503950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:46.503950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqxh9GtRxUQwpJoDkQ2L5cdXfJIGD4bFU+lY216/AZ9c3V7C9n4h9sFZ3aQi9fvwXij+2A/JWLJL1pX3J492BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:46.504701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c224aa73a3308cc329c338660ae725ddbf491f44f0e48aa2590bef7788168633","sha256:e20b6ec4c9f144d05093a95480d4e117471b413a1e46cfe216782fb7a8864779"],"state_sha256":"62e5c1de5bf700a24299c83bbcbbef826187003cdb839fb615246b002696943b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imCuFELb4aVdTJFe9Qi4j14aitT3rYiFjHPjksFRxS/aEvGT4GiUVkBeQiYWo3ZKaac9XgboOjXuMBKkEoojBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:31:42.479464Z","bundle_sha256":"37c29a1535a69ae0bd2f38c8bcd2eb9cf22a0bcb389dad79ac6561f7a9bca2d2"}}