{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZASF2RFY7PLXIDXBM6IVGWLGND","short_pith_number":"pith:ZASF2RFY","canonical_record":{"source":{"id":"1412.2323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-07T06:52:03Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"1af66cfbce7690cbb7e00f3c159a1b0ab36bf6eeb2b387215c37191b22d58404","abstract_canon_sha256":"a1006bc65be7edcb1bfe2a8ee076c0c0d6fd708d934f6077dba043891354d194"},"schema_version":"1.0"},"canonical_sha256":"c8245d44b8fbd7740ee1679153596668f34b37f4c4ed4bb0df3a6f4525bf1eba","source":{"kind":"arxiv","id":"1412.2323","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2323","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2323v1","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2323","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZASF2RFY7PLX","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZASF2RFY7PLXIDXB","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZASF2RFY","created_at":"2026-06-04T16:08:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZASF2RFY7PLXIDXBM6IVGWLGND","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-07T06:52:03Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"1af66cfbce7690cbb7e00f3c159a1b0ab36bf6eeb2b387215c37191b22d58404","abstract_canon_sha256":"a1006bc65be7edcb1bfe2a8ee076c0c0d6fd708d934f6077dba043891354d194"},"schema_version":"1.0"},"canonical_sha256":"c8245d44b8fbd7740ee1679153596668f34b37f4c4ed4bb0df3a6f4525bf1eba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T16:08:58.726461Z","signature_b64":"63ZS7R2vXxJBtnqsVQzfBBtJ9+dhmnM3o8gdSdQolu3ZwSnbgZzSlQdPVnK2l+H9QaX3euVjcuTkZGRXH/J4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8245d44b8fbd7740ee1679153596668f34b37f4c4ed4bb0df3a6f4525bf1eba","last_reissued_at":"2026-06-04T16:08:58.725952Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T16:08:58.725952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2323","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":"2026-06-04T16:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4wh2MRsqsG5q8c1Ok9aq93DCIo/jETHln30qbsjdIrYsCSO4zM/MiOEfT5jtX4QzAEZvdd86lO++oUAacDlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:49:32.063380Z"},"content_sha256":"8ecb4970770c48cacfb59bcd9ee3d1b242a31cd7699706d8b6b03108fb52c8bd","schema_version":"1.0","event_id":"sha256:8ecb4970770c48cacfb59bcd9ee3d1b242a31cd7699706d8b6b03108fb52c8bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZASF2RFY7PLXIDXBM6IVGWLGND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization theorem for best polynomial spline approximation with free knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Julien Ugon, Nadezda Sukhorukova","submitted_at":"2014-12-07T06:52:03Z","abstract_excerpt":"In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions. We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov-Rubinov. We start from identifying a special property of the knots. Then, using this property, we construct a characterization theorem for best free knots polynomial spline approximation, which is stronger than the existing characterisation results when only continuity is required."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2323","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/1412.2323/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":"2026-06-04T16:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOiHSJekucClmCDZxKMtnYkrgU0cFxJUp8SzWNl2hfETjhS+NrpE9MDNLeuYdu7MDOXg7Ha3oGIhVUnnK0/GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:49:32.063791Z"},"content_sha256":"b646a8587933201c6b9d52b97d30ec822bbbfb6bf83c267c6b620288ce5a32bf","schema_version":"1.0","event_id":"sha256:b646a8587933201c6b9d52b97d30ec822bbbfb6bf83c267c6b620288ce5a32bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/bundle.json","state_url":"https://pith.science/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/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":"2026-06-23T07:49:32Z","links":{"resolver":"https://pith.science/pith/ZASF2RFY7PLXIDXBM6IVGWLGND","bundle":"https://pith.science/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/bundle.json","state":"https://pith.science/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZASF2RFY7PLXIDXBM6IVGWLGND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZASF2RFY7PLXIDXBM6IVGWLGND","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":"a1006bc65be7edcb1bfe2a8ee076c0c0d6fd708d934f6077dba043891354d194","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-07T06:52:03Z","title_canon_sha256":"1af66cfbce7690cbb7e00f3c159a1b0ab36bf6eeb2b387215c37191b22d58404"},"schema_version":"1.0","source":{"id":"1412.2323","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2323","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2323v1","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2323","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZASF2RFY7PLX","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZASF2RFY7PLXIDXB","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZASF2RFY","created_at":"2026-06-04T16:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:b646a8587933201c6b9d52b97d30ec822bbbfb6bf83c267c6b620288ce5a32bf","target":"graph","created_at":"2026-06-04T16:08:58Z","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/1412.2323/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions. We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov-Rubinov. We start from identifying a special property of the knots. Then, using this property, we construct a characterization theorem for best free knots polynomial spline approximation, which is stronger than the existing characterisation results when only continuity is required.","authors_text":"Julien Ugon, Nadezda Sukhorukova","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-07T06:52:03Z","title":"Characterization theorem for best polynomial spline approximation with free knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2323","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":"sha256:8ecb4970770c48cacfb59bcd9ee3d1b242a31cd7699706d8b6b03108fb52c8bd","target":"record","created_at":"2026-06-04T16:08:58Z","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":"a1006bc65be7edcb1bfe2a8ee076c0c0d6fd708d934f6077dba043891354d194","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-07T06:52:03Z","title_canon_sha256":"1af66cfbce7690cbb7e00f3c159a1b0ab36bf6eeb2b387215c37191b22d58404"},"schema_version":"1.0","source":{"id":"1412.2323","kind":"arxiv","version":1}},"canonical_sha256":"c8245d44b8fbd7740ee1679153596668f34b37f4c4ed4bb0df3a6f4525bf1eba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8245d44b8fbd7740ee1679153596668f34b37f4c4ed4bb0df3a6f4525bf1eba","first_computed_at":"2026-06-04T16:08:58.725952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T16:08:58.725952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"63ZS7R2vXxJBtnqsVQzfBBtJ9+dhmnM3o8gdSdQolu3ZwSnbgZzSlQdPVnK2l+H9QaX3euVjcuTkZGRXH/J4DQ==","signature_status":"signed_v1","signed_at":"2026-06-04T16:08:58.726461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2323","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ecb4970770c48cacfb59bcd9ee3d1b242a31cd7699706d8b6b03108fb52c8bd","sha256:b646a8587933201c6b9d52b97d30ec822bbbfb6bf83c267c6b620288ce5a32bf"],"state_sha256":"93d4ba81b4a93fac25aa10b15db45385586847c49a867bdd3ec738662e8f5d8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1zAPu6RhAhkJWykMI7LKpAcghhGreKL573oTDVgUf8l0TMfJiw0QW/3bTsSTqUi7YKYOprrxH5ONKJwxTwIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:49:32.065863Z","bundle_sha256":"149d3925cb4d94fed879181cb801fb058f33b9b79e5f20297b5c70a5c6dea44c"}}