{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TERJLUTHFIPD3EPIPPU2PRVLB3","short_pith_number":"pith:TERJLUTH","canonical_record":{"source":{"id":"2305.16122","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T14:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"6a58b58b2b3859a92b57f4f4fa6b267b91132a4aff900cf1975ea4676becacd0","abstract_canon_sha256":"78d636749d81595aedaddecacf6b2f3504a625b11028d6add13be0b14a256ef7"},"schema_version":"1.0"},"canonical_sha256":"992295d2672a1e3d91e87be9a7c6ab0eda78738b6f8f63ba621ca0cb32074482","source":{"kind":"arxiv","id":"2305.16122","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16122","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16122v3","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16122","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"TERJLUTHFIPD","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_16","alias_value":"TERJLUTHFIPD3EPI","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_8","alias_value":"TERJLUTH","created_at":"2026-07-05T06:50:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TERJLUTHFIPD3EPIPPU2PRVLB3","target":"record","payload":{"canonical_record":{"source":{"id":"2305.16122","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T14:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"6a58b58b2b3859a92b57f4f4fa6b267b91132a4aff900cf1975ea4676becacd0","abstract_canon_sha256":"78d636749d81595aedaddecacf6b2f3504a625b11028d6add13be0b14a256ef7"},"schema_version":"1.0"},"canonical_sha256":"992295d2672a1e3d91e87be9a7c6ab0eda78738b6f8f63ba621ca0cb32074482","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:00.296914Z","signature_b64":"BW+ntG++ljZUDRa6P3pv3OEttvreXQCijXESmsfkpCkVxIWtrVxtSsk2pjQz6K7ap7oaJlRdiEbcBKr0bdPRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"992295d2672a1e3d91e87be9a7c6ab0eda78738b6f8f63ba621ca0cb32074482","last_reissued_at":"2026-07-05T06:50:00.296418Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:00.296418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.16122","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDLW0XzCKMM8czq+MF/ShrFM5DzH6dUwLW5SiAVNztVO7e9mgyHet6yZxoIb2WPrqwsneL6QIgQ+O/EdF344CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:56:44.410770Z"},"content_sha256":"97d1b35d07be06a0123df28e21fdb6a2bf4bd3620f78c8440b97647b2f9384de","schema_version":"1.0","event_id":"sha256:97d1b35d07be06a0123df28e21fdb6a2bf4bd3620f78c8440b97647b2f9384de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TERJLUTHFIPD3EPIPPU2PRVLB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hybrid Methods in Polynomial Optimisation","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gilles Bareilles, Jakub Marecek, Johannes Aspman, Martin Tak\\'a\\v{c}, Vyacheslav Kungurtsev","submitted_at":"2023-05-25T14:55:36Z","abstract_excerpt":"The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly large semidefinite programs (SDPs). We consider large-scale POPs, for which interior-point methods are no longer able to solve the resulting SDPs. We propose an algorithm that combines a first-order method for solving the SDP relaxation, and a second-order method on a non-convex problem obtained from the POP. The switch from the first to the second-order method is based on a quantitative criterion, whose satisfaction en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16122","kind":"arxiv","version":3},"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/2305.16122/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":"2026-07-05T06:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFzozL6s/EYGpA2tx+cCEwRuhIC8gaErG0QjwplI/sTUJLLVAsOzC5DYwy7z2WfkeQxQtCFf9W01U0cIyQVRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:56:44.411784Z"},"content_sha256":"b3d468dc41a6246a34e4e2721014c99d9873dea56c5774135f8ab6bfe038023f","schema_version":"1.0","event_id":"sha256:b3d468dc41a6246a34e4e2721014c99d9873dea56c5774135f8ab6bfe038023f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/bundle.json","state_url":"https://pith.science/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/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":"2026-08-04T05:56:44Z","links":{"resolver":"https://pith.science/pith/TERJLUTHFIPD3EPIPPU2PRVLB3","bundle":"https://pith.science/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/bundle.json","state":"https://pith.science/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TERJLUTHFIPD3EPIPPU2PRVLB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TERJLUTHFIPD3EPIPPU2PRVLB3","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":"78d636749d81595aedaddecacf6b2f3504a625b11028d6add13be0b14a256ef7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T14:55:36Z","title_canon_sha256":"6a58b58b2b3859a92b57f4f4fa6b267b91132a4aff900cf1975ea4676becacd0"},"schema_version":"1.0","source":{"id":"2305.16122","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16122","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16122v3","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16122","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"TERJLUTHFIPD","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_16","alias_value":"TERJLUTHFIPD3EPI","created_at":"2026-07-05T06:50:00Z"},{"alias_kind":"pith_short_8","alias_value":"TERJLUTH","created_at":"2026-07-05T06:50:00Z"}],"graph_snapshots":[{"event_id":"sha256:b3d468dc41a6246a34e4e2721014c99d9873dea56c5774135f8ab6bfe038023f","target":"graph","created_at":"2026-07-05T06:50:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.16122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly large semidefinite programs (SDPs). We consider large-scale POPs, for which interior-point methods are no longer able to solve the resulting SDPs. We propose an algorithm that combines a first-order method for solving the SDP relaxation, and a second-order method on a non-convex problem obtained from the POP. The switch from the first to the second-order method is based on a quantitative criterion, whose satisfaction en","authors_text":"Gilles Bareilles, Jakub Marecek, Johannes Aspman, Martin Tak\\'a\\v{c}, Vyacheslav Kungurtsev","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T14:55:36Z","title":"Hybrid Methods in Polynomial Optimisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16122","kind":"arxiv","version":3},"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":"sha256:97d1b35d07be06a0123df28e21fdb6a2bf4bd3620f78c8440b97647b2f9384de","target":"record","created_at":"2026-07-05T06:50:00Z","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":"78d636749d81595aedaddecacf6b2f3504a625b11028d6add13be0b14a256ef7","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T14:55:36Z","title_canon_sha256":"6a58b58b2b3859a92b57f4f4fa6b267b91132a4aff900cf1975ea4676becacd0"},"schema_version":"1.0","source":{"id":"2305.16122","kind":"arxiv","version":3}},"canonical_sha256":"992295d2672a1e3d91e87be9a7c6ab0eda78738b6f8f63ba621ca0cb32074482","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"992295d2672a1e3d91e87be9a7c6ab0eda78738b6f8f63ba621ca0cb32074482","first_computed_at":"2026-07-05T06:50:00.296418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:50:00.296418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BW+ntG++ljZUDRa6P3pv3OEttvreXQCijXESmsfkpCkVxIWtrVxtSsk2pjQz6K7ap7oaJlRdiEbcBKr0bdPRDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:50:00.296914Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.16122","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97d1b35d07be06a0123df28e21fdb6a2bf4bd3620f78c8440b97647b2f9384de","sha256:b3d468dc41a6246a34e4e2721014c99d9873dea56c5774135f8ab6bfe038023f"],"state_sha256":"753aa1332cec25bb365ccedd217935c756e525b1d6937d9d8b8668d602a503b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nioF4w+Ciyszf4L1MVqPTA5EpZxV/2YNw9KR9fefeS4esAnlfpGrTCuJr+TKCeYqHkMS7c4mZQAiHJR5XJ/SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:56:44.418473Z","bundle_sha256":"777a221fa4a2085f355fb4eb78f81b684a0ee2d784df8d641b14ce1933f58316"}}