{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4KV5BMNDZFWGHNSIIDTSREXUVU","short_pith_number":"pith:4KV5BMND","canonical_record":{"source":{"id":"1902.02976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-08T08:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"88f658e615e92fc3db85c5c9ab78cde66d1b0332d49de6094a405f7aff725e57","abstract_canon_sha256":"60127001ff922d229fa21f1ff8105485451c79ef307aaf6bbd2acf4062b2f53c"},"schema_version":"1.0"},"canonical_sha256":"e2abd0b1a3c96c63b64840e72892f4ad0f39b1e1c8afbb2389520e29c528cf26","source":{"kind":"arxiv","id":"1902.02976","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02976","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02976v2","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02976","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"4KV5BMNDZFWG","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"4KV5BMNDZFWGHNSI","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"4KV5BMND","created_at":"2026-07-05T01:22:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4KV5BMNDZFWGHNSIIDTSREXUVU","target":"record","payload":{"canonical_record":{"source":{"id":"1902.02976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-08T08:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"88f658e615e92fc3db85c5c9ab78cde66d1b0332d49de6094a405f7aff725e57","abstract_canon_sha256":"60127001ff922d229fa21f1ff8105485451c79ef307aaf6bbd2acf4062b2f53c"},"schema_version":"1.0"},"canonical_sha256":"e2abd0b1a3c96c63b64840e72892f4ad0f39b1e1c8afbb2389520e29c528cf26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:13.563719Z","signature_b64":"kJhApposWmffcJHDOvU37NdlkjtoSjORpkPoEDZ/wwTdfMH7hpBSja4uz1SahzFOb8EoVddct2165O5lROACDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2abd0b1a3c96c63b64840e72892f4ad0f39b1e1c8afbb2389520e29c528cf26","last_reissued_at":"2026-07-05T01:22:13.563249Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:13.563249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.02976","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":"2026-07-05T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wr3nA64bShMmqyqRbleQPfHKUvt0INNvqErtxj76l4Udi7BE0py0kutBXzLyBZgjb/jNir6uFajvuqdUdtRnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:15:19.030811Z"},"content_sha256":"514c77f54a398038925cd1bccfa00d0c6307f08090a6b16b06c28c38eb8515c9","schema_version":"1.0","event_id":"sha256:514c77f54a398038925cd1bccfa00d0c6307f08090a6b16b06c28c38eb8515c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4KV5BMNDZFWGHNSIIDTSREXUVU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploiting Sparsity for Semi-Algebraic Set Volume Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Didier Henrion (LAAS-MAC), Jean-Bernard Lasserre (IMT, LAAS-MAC), Matteo Tacchi (LAAS-MAC), Tillmann Weisser (LANL)","submitted_at":"2019-02-08T08:40:57Z","abstract_excerpt":"We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying strategy is to consider an infinite-dimensional linear program on measures whose optimal value is the volume of the set. This is a particular instance of a generalized moment problem which in turn can be approximated as closely as desired by solving a hierarchy of semidefinite relaxations of increasing size. The novelty with respect to previous work is that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02976","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.02976/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":"2026-07-05T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y8YohWpH+PTbMu/aP6cXszHMjpwAbKzG9IVWWssqjefwja5suDj8WHq4uP5w6TL/B1nYXfpvFkyYS7tSvRCzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:15:19.031406Z"},"content_sha256":"c03a483d740c23d11f158e8f79073ece9d6333a03214a3e41e5b219fb95a8541","schema_version":"1.0","event_id":"sha256:c03a483d740c23d11f158e8f79073ece9d6333a03214a3e41e5b219fb95a8541"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/bundle.json","state_url":"https://pith.science/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/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":"2026-08-23T19:15:19Z","links":{"resolver":"https://pith.science/pith/4KV5BMNDZFWGHNSIIDTSREXUVU","bundle":"https://pith.science/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/bundle.json","state":"https://pith.science/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KV5BMNDZFWGHNSIIDTSREXUVU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4KV5BMNDZFWGHNSIIDTSREXUVU","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":"60127001ff922d229fa21f1ff8105485451c79ef307aaf6bbd2acf4062b2f53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-08T08:40:57Z","title_canon_sha256":"88f658e615e92fc3db85c5c9ab78cde66d1b0332d49de6094a405f7aff725e57"},"schema_version":"1.0","source":{"id":"1902.02976","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02976","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02976v2","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02976","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"4KV5BMNDZFWG","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"4KV5BMNDZFWGHNSI","created_at":"2026-07-05T01:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"4KV5BMND","created_at":"2026-07-05T01:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:c03a483d740c23d11f158e8f79073ece9d6333a03214a3e41e5b219fb95a8541","target":"graph","created_at":"2026-07-05T01:22:13Z","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/1902.02976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying strategy is to consider an infinite-dimensional linear program on measures whose optimal value is the volume of the set. This is a particular instance of a generalized moment problem which in turn can be approximated as closely as desired by solving a hierarchy of semidefinite relaxations of increasing size. The novelty with respect to previous work is that","authors_text":"Didier Henrion (LAAS-MAC), Jean-Bernard Lasserre (IMT, LAAS-MAC), Matteo Tacchi (LAAS-MAC), Tillmann Weisser (LANL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-08T08:40:57Z","title":"Exploiting Sparsity for Semi-Algebraic Set Volume Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02976","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":"sha256:514c77f54a398038925cd1bccfa00d0c6307f08090a6b16b06c28c38eb8515c9","target":"record","created_at":"2026-07-05T01:22:13Z","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":"60127001ff922d229fa21f1ff8105485451c79ef307aaf6bbd2acf4062b2f53c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-08T08:40:57Z","title_canon_sha256":"88f658e615e92fc3db85c5c9ab78cde66d1b0332d49de6094a405f7aff725e57"},"schema_version":"1.0","source":{"id":"1902.02976","kind":"arxiv","version":2}},"canonical_sha256":"e2abd0b1a3c96c63b64840e72892f4ad0f39b1e1c8afbb2389520e29c528cf26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2abd0b1a3c96c63b64840e72892f4ad0f39b1e1c8afbb2389520e29c528cf26","first_computed_at":"2026-07-05T01:22:13.563249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:22:13.563249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJhApposWmffcJHDOvU37NdlkjtoSjORpkPoEDZ/wwTdfMH7hpBSja4uz1SahzFOb8EoVddct2165O5lROACDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:22:13.563719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02976","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:514c77f54a398038925cd1bccfa00d0c6307f08090a6b16b06c28c38eb8515c9","sha256:c03a483d740c23d11f158e8f79073ece9d6333a03214a3e41e5b219fb95a8541"],"state_sha256":"baf12cc64c33eb307f0cb593eaf89ff21320292e536bf6478b472ef3e5581161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLD4858pQShHfgHbZlLHWcWDOgeQqelmpFjQk9LsMkNRH8CbYu4flbZP5i5DZTiv8HAFBGH34pzzyLC/oooODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T19:15:19.036110Z","bundle_sha256":"4bd2901c60fb2e1684a10c467367240c3658d948cb9705784245514e60ab99a1"}}