{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5KVJZXQIPPPYJGZW24URBY2DKE","short_pith_number":"pith:5KVJZXQI","canonical_record":{"source":{"id":"2203.12889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-03-24T07:23:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"284ff9669d28bd99f77340ab9c3ce6c5932c2f103731fe6081cd77318eb6f6b7","abstract_canon_sha256":"902c3821629054bafb7609efb9b3d51e94a7ada64fdcd1a71210c8c70ba539fa"},"schema_version":"1.0"},"canonical_sha256":"eaaa9cde087bdf849b36d72910e34351384878df6af04a035885c83408b8f277","source":{"kind":"arxiv","id":"2203.12889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.12889","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"2203.12889v1","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.12889","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"5KVJZXQIPPPY","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_16","alias_value":"5KVJZXQIPPPYJGZW","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_8","alias_value":"5KVJZXQI","created_at":"2026-07-05T04:08:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5KVJZXQIPPPYJGZW24URBY2DKE","target":"record","payload":{"canonical_record":{"source":{"id":"2203.12889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-03-24T07:23:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"284ff9669d28bd99f77340ab9c3ce6c5932c2f103731fe6081cd77318eb6f6b7","abstract_canon_sha256":"902c3821629054bafb7609efb9b3d51e94a7ada64fdcd1a71210c8c70ba539fa"},"schema_version":"1.0"},"canonical_sha256":"eaaa9cde087bdf849b36d72910e34351384878df6af04a035885c83408b8f277","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:08:18.489396Z","signature_b64":"ZGWeSvh0seRk2t5CnRV9g4Tcv7W8rn7Dlx0Q+wvypM/8+7bxiTuwIYhzCmgycWi7pSAEWmouhxm7aBa04WtCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaaa9cde087bdf849b36d72910e34351384878df6af04a035885c83408b8f277","last_reissued_at":"2026-07-05T04:08:18.489051Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:08:18.489051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.12889","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":"2026-07-05T04:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnNYhMg/fvieq2Lzqx6rk7eAPNUsV+eQplTxeRpDVbKJIpnt4gpdN97jQ3QYJ/BQUldWkJVBIL0SyxDUdUW9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T04:59:24.548988Z"},"content_sha256":"e149e19aa852595b7bf42013891a7f85f42ab34f8e5721eed56ba2db80a6d744","schema_version":"1.0","event_id":"sha256:e149e19aa852595b7bf42013891a7f85f42ab34f8e5721eed56ba2db80a6d744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5KVJZXQIPPPYJGZW24URBY2DKE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some suggestions concerning the conjecture in: 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel'","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CA","authors_text":"Mathias Oster, Reinhold Schneider","submitted_at":"2022-03-24T07:23:05Z","abstract_excerpt":"In 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel' Marx, Pauwels, Weisser, Henrion and Lasserre conjectured, that the approximation rate $\\mathcal O(\\frac 1 {\\sqrt(d)})$ of a Lipschitz functions by a semi-algebraic function induced by a Christoffel- Darboux kernel of degree $d$ in the $L^1$ norm can be improved for more regular functions. Here we will show, that for semi-algebraic and definable functions the results can be strengthened to a rational approximation rate in the $L^\\infty$ norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12889","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/2203.12889/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":"2026-07-05T04:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NtEBexe+uj7HmLwHW+yXXHkKRgn4RYg0Wi+o9HLwqL9wSQ+gBvMBXZ71SOuqyyClTZ16jqzFymnL6srP8IfJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T04:59:24.549517Z"},"content_sha256":"3d686f7a37543017fdaa63160b573440db382aeb1d71b8cb20c0e4fad19b116e","schema_version":"1.0","event_id":"sha256:3d686f7a37543017fdaa63160b573440db382aeb1d71b8cb20c0e4fad19b116e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KVJZXQIPPPYJGZW24URBY2DKE/bundle.json","state_url":"https://pith.science/pith/5KVJZXQIPPPYJGZW24URBY2DKE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KVJZXQIPPPYJGZW24URBY2DKE/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":"2026-08-23T04:59:24Z","links":{"resolver":"https://pith.science/pith/5KVJZXQIPPPYJGZW24URBY2DKE","bundle":"https://pith.science/pith/5KVJZXQIPPPYJGZW24URBY2DKE/bundle.json","state":"https://pith.science/pith/5KVJZXQIPPPYJGZW24URBY2DKE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KVJZXQIPPPYJGZW24URBY2DKE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5KVJZXQIPPPYJGZW24URBY2DKE","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":"902c3821629054bafb7609efb9b3d51e94a7ada64fdcd1a71210c8c70ba539fa","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-03-24T07:23:05Z","title_canon_sha256":"284ff9669d28bd99f77340ab9c3ce6c5932c2f103731fe6081cd77318eb6f6b7"},"schema_version":"1.0","source":{"id":"2203.12889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.12889","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"2203.12889v1","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.12889","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"5KVJZXQIPPPY","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_16","alias_value":"5KVJZXQIPPPYJGZW","created_at":"2026-07-05T04:08:18Z"},{"alias_kind":"pith_short_8","alias_value":"5KVJZXQI","created_at":"2026-07-05T04:08:18Z"}],"graph_snapshots":[{"event_id":"sha256:3d686f7a37543017fdaa63160b573440db382aeb1d71b8cb20c0e4fad19b116e","target":"graph","created_at":"2026-07-05T04:08:18Z","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/2203.12889/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel' Marx, Pauwels, Weisser, Henrion and Lasserre conjectured, that the approximation rate $\\mathcal O(\\frac 1 {\\sqrt(d)})$ of a Lipschitz functions by a semi-algebraic function induced by a Christoffel- Darboux kernel of degree $d$ in the $L^1$ norm can be improved for more regular functions. Here we will show, that for semi-algebraic and definable functions the results can be strengthened to a rational approximation rate in the $L^\\infty$ norm.","authors_text":"Mathias Oster, Reinhold Schneider","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-03-24T07:23:05Z","title":"Some suggestions concerning the conjecture in: 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel'"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12889","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:e149e19aa852595b7bf42013891a7f85f42ab34f8e5721eed56ba2db80a6d744","target":"record","created_at":"2026-07-05T04:08:18Z","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":"902c3821629054bafb7609efb9b3d51e94a7ada64fdcd1a71210c8c70ba539fa","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-03-24T07:23:05Z","title_canon_sha256":"284ff9669d28bd99f77340ab9c3ce6c5932c2f103731fe6081cd77318eb6f6b7"},"schema_version":"1.0","source":{"id":"2203.12889","kind":"arxiv","version":1}},"canonical_sha256":"eaaa9cde087bdf849b36d72910e34351384878df6af04a035885c83408b8f277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaaa9cde087bdf849b36d72910e34351384878df6af04a035885c83408b8f277","first_computed_at":"2026-07-05T04:08:18.489051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:18.489051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGWeSvh0seRk2t5CnRV9g4Tcv7W8rn7Dlx0Q+wvypM/8+7bxiTuwIYhzCmgycWi7pSAEWmouhxm7aBa04WtCAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:18.489396Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.12889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e149e19aa852595b7bf42013891a7f85f42ab34f8e5721eed56ba2db80a6d744","sha256:3d686f7a37543017fdaa63160b573440db382aeb1d71b8cb20c0e4fad19b116e"],"state_sha256":"50361fb25361bdf92bbae15dd15bc660b20d77e1404d46b0fc15eddf91038447"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3R0alRWbfIRTE/EGUNOVwH82iqPfCWOLVFfT1rzKSnQV9UzH3OTnybQupMzzM7TmNo1GSKpOZ3mCCM99hfa7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T04:59:24.554679Z","bundle_sha256":"25f5065d2e1f1761594ddb00573d61b670cee857e57fec73607f5efbaa0dd58e"}}