{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EXNQG3ARSN6PXZFE5ERQF4MLUC","short_pith_number":"pith:EXNQG3AR","canonical_record":{"source":{"id":"1903.04996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-12T15:29:15Z","cross_cats_sorted":["cs.CC","math.AG","math.OC"],"title_canon_sha256":"2af4f7242f3ca3244803bf3a9252b2d5158cbb99a71b9837259c5565dbf253d0","abstract_canon_sha256":"e3f1c042adec229ca20b16d2bd7fd0ad1ccc4758a17d566cf48dc731324de408"},"schema_version":"1.0"},"canonical_sha256":"25db036c11937cfbe4a4e92302f18ba0aa97d9eb56e07115cd88ae6919e4f784","source":{"kind":"arxiv","id":"1903.04996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04996","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04996v1","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04996","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"EXNQG3ARSN6P","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXNQG3ARSN6PXZFE","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXNQG3AR","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EXNQG3ARSN6PXZFE5ERQF4MLUC","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-12T15:29:15Z","cross_cats_sorted":["cs.CC","math.AG","math.OC"],"title_canon_sha256":"2af4f7242f3ca3244803bf3a9252b2d5158cbb99a71b9837259c5565dbf253d0","abstract_canon_sha256":"e3f1c042adec229ca20b16d2bd7fd0ad1ccc4758a17d566cf48dc731324de408"},"schema_version":"1.0"},"canonical_sha256":"25db036c11937cfbe4a4e92302f18ba0aa97d9eb56e07115cd88ae6919e4f784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:26.563975Z","signature_b64":"RQAN5defpjDUlhpNj1wZuFbZ6C16MFSVaiCGiJc8mCzUUaR/yLedyC6ACuip+d+zOS3W1+1deCw8OHnLSgI7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25db036c11937cfbe4a4e92302f18ba0aa97d9eb56e07115cd88ae6919e4f784","last_reissued_at":"2026-05-17T23:51:26.563433Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:26.563433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04996","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":"2026-05-17T23:51:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhr1NVWhtO/JbijZ1fKWjvpHGIvBiEnX0JsreVMW2EFdA1JhA+ZVPNdXCSepE/P3G5ttQ7rBHZGRkhT4TMqTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:04.961761Z"},"content_sha256":"2869bdf9b35a832cc9070e7aa7dc943d1c807e2e69dff767f4995c4ebac7b0e7","schema_version":"1.0","event_id":"sha256:2869bdf9b35a832cc9070e7aa7dc943d1c807e2e69dff767f4995c4ebac7b0e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EXNQG3ARSN6PXZFE5ERQF4MLUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Dependencies of Hierarchies in Polynomial Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AG","math.OC"],"primary_cat":"cs.DS","authors_text":"Adam Kurpisz, Timo de Wolff","submitted_at":"2019-03-12T15:29:15Z","abstract_excerpt":"We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04996","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":""},"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":"2026-05-17T23:51:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eF5Yb/m3IhlMueRRmUdSVHVL9VtbJ246oqZKYTHy/Ry08tyMyQ+aY7g1j94vHLX1BmPYqRqQacOndlv4DgiwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:04.962120Z"},"content_sha256":"6c110f88829abb138d453112ea3827b9fd929f301289c7c35493496c6f63eba3","schema_version":"1.0","event_id":"sha256:6c110f88829abb138d453112ea3827b9fd929f301289c7c35493496c6f63eba3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/bundle.json","state_url":"https://pith.science/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/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":"2026-06-26T14:32:04Z","links":{"resolver":"https://pith.science/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC","bundle":"https://pith.science/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/bundle.json","state":"https://pith.science/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXNQG3ARSN6PXZFE5ERQF4MLUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EXNQG3ARSN6PXZFE5ERQF4MLUC","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":"e3f1c042adec229ca20b16d2bd7fd0ad1ccc4758a17d566cf48dc731324de408","cross_cats_sorted":["cs.CC","math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-12T15:29:15Z","title_canon_sha256":"2af4f7242f3ca3244803bf3a9252b2d5158cbb99a71b9837259c5565dbf253d0"},"schema_version":"1.0","source":{"id":"1903.04996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04996","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04996v1","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04996","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"EXNQG3ARSN6P","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXNQG3ARSN6PXZFE","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXNQG3AR","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:6c110f88829abb138d453112ea3827b9fd929f301289c7c35493496c6f63eba3","target":"graph","created_at":"2026-05-17T23:51:26Z","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":"We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz","authors_text":"Adam Kurpisz, Timo de Wolff","cross_cats":["cs.CC","math.AG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-12T15:29:15Z","title":"New Dependencies of Hierarchies in Polynomial Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04996","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":"sha256:2869bdf9b35a832cc9070e7aa7dc943d1c807e2e69dff767f4995c4ebac7b0e7","target":"record","created_at":"2026-05-17T23:51:26Z","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":"e3f1c042adec229ca20b16d2bd7fd0ad1ccc4758a17d566cf48dc731324de408","cross_cats_sorted":["cs.CC","math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-12T15:29:15Z","title_canon_sha256":"2af4f7242f3ca3244803bf3a9252b2d5158cbb99a71b9837259c5565dbf253d0"},"schema_version":"1.0","source":{"id":"1903.04996","kind":"arxiv","version":1}},"canonical_sha256":"25db036c11937cfbe4a4e92302f18ba0aa97d9eb56e07115cd88ae6919e4f784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25db036c11937cfbe4a4e92302f18ba0aa97d9eb56e07115cd88ae6919e4f784","first_computed_at":"2026-05-17T23:51:26.563433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:26.563433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQAN5defpjDUlhpNj1wZuFbZ6C16MFSVaiCGiJc8mCzUUaR/yLedyC6ACuip+d+zOS3W1+1deCw8OHnLSgI7Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:26.563975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2869bdf9b35a832cc9070e7aa7dc943d1c807e2e69dff767f4995c4ebac7b0e7","sha256:6c110f88829abb138d453112ea3827b9fd929f301289c7c35493496c6f63eba3"],"state_sha256":"1b74a92cdc6bccf821527a0e54ef052cf8d6afd7f2de96a5e44838d3395ef7ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yes3fh6+OiXXYQYF+EIfH0RrpGLftw/DZMExVf8IF7umS4CRl0sI+0kIPk+VmFUvtHH5KMozxumxjua7RoE3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:32:04.964238Z","bundle_sha256":"961a22123900783e80a91c8c60c226e3b2ee39cc73dad54559b4226384465906"}}