{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HTUHOIOPDJOEYED7D2YUI3U6QR","short_pith_number":"pith:HTUHOIOP","canonical_record":{"source":{"id":"1510.01842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-07T06:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"ff22e46b73ab24aa477c6ce2b187fd9e49c1cf48ac654cfbe8f45706a947cf71","abstract_canon_sha256":"efb328540944012041e58c3a44b3df0018dab6398ae38535ab51cb225a1388ff"},"schema_version":"1.0"},"canonical_sha256":"3ce87721cf1a5c4c107f1eb1446e9e8468fdf71f52fcc9c14c14a9bb96f8fde1","source":{"kind":"arxiv","id":"1510.01842","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01842","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01842v2","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01842","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"HTUHOIOPDJOE","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HTUHOIOPDJOEYED7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HTUHOIOP","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HTUHOIOPDJOEYED7D2YUI3U6QR","target":"record","payload":{"canonical_record":{"source":{"id":"1510.01842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-07T06:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"ff22e46b73ab24aa477c6ce2b187fd9e49c1cf48ac654cfbe8f45706a947cf71","abstract_canon_sha256":"efb328540944012041e58c3a44b3df0018dab6398ae38535ab51cb225a1388ff"},"schema_version":"1.0"},"canonical_sha256":"3ce87721cf1a5c4c107f1eb1446e9e8468fdf71f52fcc9c14c14a9bb96f8fde1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:00.785338Z","signature_b64":"6ltmpIHeJuUbD/SNHAIt5Mr/Zzp4/WklBvCVzLuq9oR6wTGUa3nBu5pTzdf6jQVQrvCyxD6RGwNd+LWRw5mTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ce87721cf1a5c4c107f1eb1446e9e8468fdf71f52fcc9c14c14a9bb96f8fde1","last_reissued_at":"2026-05-18T01:22:00.784937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:00.784937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.01842","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rem/jIWfPN5kynbMZ06cvBnWbqZ8aAozX6UJauhLCg9hZNfZkTBjPxy0NQXko8+ytcCtRPu7gbceomQ/MQBBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:31:51.732487Z"},"content_sha256":"e7f5ba7c9ceb325d64f3effc8fcf661539b8bce5813a26878b10a17648b8dacb","schema_version":"1.0","event_id":"sha256:e7f5ba7c9ceb325d64f3effc8fcf661539b8bce5813a26878b10a17648b8dacb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HTUHOIOPDJOEYED7D2YUI3U6QR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lebesgue decomposition in action via semidefinite relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Bernard Lasserre (LAAS-MAC)","submitted_at":"2015-10-07T06:56:36Z","abstract_excerpt":"Given all (finite) moments of two measures $\\mu$ and $\\lambda$ on $\\R^n$, we provide a numerical scheme to obtain the Lebesgue decomposition $\\mu=\\nu+\\psi$ with $\\nu\\ll\\lambda$ and $\\psi\\perp\\lambda$. When$\\nu$ has a density in $L\\_\\infty(\\lambda)$ then we obtain two sequences of finite moments vectorsof increasing size (the number of moments) which converge to the moments of $\\nu$ and $\\psi$ respectively, as the number of moments increases. Importantly, {\\it no} \\`a priori knowledge on the supports of $\\mu, \\nu$ and $\\psi$ is required."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01842","kind":"arxiv","version":2},"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":"2026-05-18T01:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdZaKAXV/L0PwpY+O36B/Tc6/PJ8CkjSJNtun/a/r62tNR6Xf+cf09ENJlDhO6sj8erdXBiJdNu+B5AcqpSoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:31:51.733153Z"},"content_sha256":"fd964a2c758d7edd10ed03e8ab68dc190ea1ef8e8b8fe145349d32bc5be513fe","schema_version":"1.0","event_id":"sha256:fd964a2c758d7edd10ed03e8ab68dc190ea1ef8e8b8fe145349d32bc5be513fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/bundle.json","state_url":"https://pith.science/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/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":"2026-05-27T03:31:51Z","links":{"resolver":"https://pith.science/pith/HTUHOIOPDJOEYED7D2YUI3U6QR","bundle":"https://pith.science/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/bundle.json","state":"https://pith.science/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTUHOIOPDJOEYED7D2YUI3U6QR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HTUHOIOPDJOEYED7D2YUI3U6QR","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":"efb328540944012041e58c3a44b3df0018dab6398ae38535ab51cb225a1388ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-07T06:56:36Z","title_canon_sha256":"ff22e46b73ab24aa477c6ce2b187fd9e49c1cf48ac654cfbe8f45706a947cf71"},"schema_version":"1.0","source":{"id":"1510.01842","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01842","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01842v2","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01842","created_at":"2026-05-18T01:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"HTUHOIOPDJOE","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HTUHOIOPDJOEYED7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HTUHOIOP","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fd964a2c758d7edd10ed03e8ab68dc190ea1ef8e8b8fe145349d32bc5be513fe","target":"graph","created_at":"2026-05-18T01:22:00Z","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":"Given all (finite) moments of two measures $\\mu$ and $\\lambda$ on $\\R^n$, we provide a numerical scheme to obtain the Lebesgue decomposition $\\mu=\\nu+\\psi$ with $\\nu\\ll\\lambda$ and $\\psi\\perp\\lambda$. When$\\nu$ has a density in $L\\_\\infty(\\lambda)$ then we obtain two sequences of finite moments vectorsof increasing size (the number of moments) which converge to the moments of $\\nu$ and $\\psi$ respectively, as the number of moments increases. Importantly, {\\it no} \\`a priori knowledge on the supports of $\\mu, \\nu$ and $\\psi$ is required.","authors_text":"Jean-Bernard Lasserre (LAAS-MAC)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-07T06:56:36Z","title":"Lebesgue decomposition in action via semidefinite relaxations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01842","kind":"arxiv","version":2},"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:e7f5ba7c9ceb325d64f3effc8fcf661539b8bce5813a26878b10a17648b8dacb","target":"record","created_at":"2026-05-18T01:22:00Z","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":"efb328540944012041e58c3a44b3df0018dab6398ae38535ab51cb225a1388ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-07T06:56:36Z","title_canon_sha256":"ff22e46b73ab24aa477c6ce2b187fd9e49c1cf48ac654cfbe8f45706a947cf71"},"schema_version":"1.0","source":{"id":"1510.01842","kind":"arxiv","version":2}},"canonical_sha256":"3ce87721cf1a5c4c107f1eb1446e9e8468fdf71f52fcc9c14c14a9bb96f8fde1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ce87721cf1a5c4c107f1eb1446e9e8468fdf71f52fcc9c14c14a9bb96f8fde1","first_computed_at":"2026-05-18T01:22:00.784937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:00.784937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ltmpIHeJuUbD/SNHAIt5Mr/Zzp4/WklBvCVzLuq9oR6wTGUa3nBu5pTzdf6jQVQrvCyxD6RGwNd+LWRw5mTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:00.785338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01842","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7f5ba7c9ceb325d64f3effc8fcf661539b8bce5813a26878b10a17648b8dacb","sha256:fd964a2c758d7edd10ed03e8ab68dc190ea1ef8e8b8fe145349d32bc5be513fe"],"state_sha256":"cb9963d33dcc8152120b9f96e30c42207ca4e3adbd779447028834c6a21249f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctucTEztO2pi81wFKZT4wSUMSNJYtLqHYRzAt5Tjck0NofXBoLS/GME+A4jF1d2tPhlPLgIPDzBvwMYx7VFqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:31:51.736435Z","bundle_sha256":"335f8f4baf9814af343563526b2d9e12338a5922bf0e705c62bf767b4a0efa0f"}}