{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NZQVF4PKTSIYWL2SOVSR6PMX7S","short_pith_number":"pith:NZQVF4PK","canonical_record":{"source":{"id":"1308.6562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-29T19:11:37Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f7821275e98c6df089d518dfd73c740b2d38fdc5731bda05aa08186669afbda3","abstract_canon_sha256":"d3bb9bd72c1ce409c54bc36062c544c6bf08284913f1b42457209f4bde20016d"},"schema_version":"1.0"},"canonical_sha256":"6e6152f1ea9c918b2f5275651f3d97fcbe60ad4dfec0e792ce5fcac1791824d1","source":{"kind":"arxiv","id":"1308.6562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6562","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6562v2","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6562","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"pith_short_12","alias_value":"NZQVF4PKTSIY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"NZQVF4PKTSIYWL2S","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"NZQVF4PK","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NZQVF4PKTSIYWL2SOVSR6PMX7S","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-29T19:11:37Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f7821275e98c6df089d518dfd73c740b2d38fdc5731bda05aa08186669afbda3","abstract_canon_sha256":"d3bb9bd72c1ce409c54bc36062c544c6bf08284913f1b42457209f4bde20016d"},"schema_version":"1.0"},"canonical_sha256":"6e6152f1ea9c918b2f5275651f3d97fcbe60ad4dfec0e792ce5fcac1791824d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:51.802113Z","signature_b64":"L20V2mjeKnAMbCWPdM+9LJ7y0SkQoozBLxWmmq85FNrj1kpGTYzgPlVtrEtKpB4owgyioFN/hUeCt9snDWpJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e6152f1ea9c918b2f5275651f3d97fcbe60ad4dfec0e792ce5fcac1791824d1","last_reissued_at":"2026-05-18T02:50:51.801674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:51.801674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6562","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":"2026-05-18T02:50:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNDGN9iA+VNBepBnp1poyyCokI/eiy8Au6Xl6+n0ULAHtKf3TKcuRiaVMTvMvOQM5SgKPi6QUR4ePqxUv1MSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:52:48.583889Z"},"content_sha256":"fddd0c8b86235536628af0c02368d3c8f363f7dc40d39395dc337bfe52cdc80f","schema_version":"1.0","event_id":"sha256:fddd0c8b86235536628af0c02368d3c8f363f7dc40d39395dc337bfe52cdc80f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NZQVF4PKTSIYWL2SOVSR6PMX7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semidefinite Relaxations for Best Rank-1 Tensor Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Jiawang Nie, Li Wang","submitted_at":"2013-08-29T19:11:37Z","abstract_excerpt":"This paper studies the problem of finding best rank-1 approximations for both symmetric and nonsymmetric tensors. For symmetric tensors, this is equivalent to optimizing homogeneous polynomials over unit spheres; for nonsymmetric tensors, this is equivalent to optimizing multi-quadratic forms over multi-spheres. We propose semidefinite relaxations, based on sum of squares representations, to solve these polynomial optimization problems. Their properties and structures are studied. In applications, the resulting semidefinite programs are often large scale. The recent Newton-CG augmented Lagrang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6562","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":"2026-05-18T02:50:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/n32OeR+1CgdfBwr0JHhSAcxr7NG7Jr1KaMKxwOus0LZfUZoUq8Z80UEYS2xED3eTeXNRVKTzrn653TpRaiGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:52:48.584231Z"},"content_sha256":"d67358c7e072eb97ab2b4a4cdc9920c86e2b2e20fa196856d29431c8034ee2ce","schema_version":"1.0","event_id":"sha256:d67358c7e072eb97ab2b4a4cdc9920c86e2b2e20fa196856d29431c8034ee2ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/bundle.json","state_url":"https://pith.science/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/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":"2026-06-01T21:52:48Z","links":{"resolver":"https://pith.science/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S","bundle":"https://pith.science/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/bundle.json","state":"https://pith.science/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZQVF4PKTSIYWL2SOVSR6PMX7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NZQVF4PKTSIYWL2SOVSR6PMX7S","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":"d3bb9bd72c1ce409c54bc36062c544c6bf08284913f1b42457209f4bde20016d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-29T19:11:37Z","title_canon_sha256":"f7821275e98c6df089d518dfd73c740b2d38fdc5731bda05aa08186669afbda3"},"schema_version":"1.0","source":{"id":"1308.6562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6562","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6562v2","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6562","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"pith_short_12","alias_value":"NZQVF4PKTSIY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"NZQVF4PKTSIYWL2S","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"NZQVF4PK","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d67358c7e072eb97ab2b4a4cdc9920c86e2b2e20fa196856d29431c8034ee2ce","target":"graph","created_at":"2026-05-18T02:50:51Z","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":"This paper studies the problem of finding best rank-1 approximations for both symmetric and nonsymmetric tensors. For symmetric tensors, this is equivalent to optimizing homogeneous polynomials over unit spheres; for nonsymmetric tensors, this is equivalent to optimizing multi-quadratic forms over multi-spheres. We propose semidefinite relaxations, based on sum of squares representations, to solve these polynomial optimization problems. Their properties and structures are studied. In applications, the resulting semidefinite programs are often large scale. The recent Newton-CG augmented Lagrang","authors_text":"Jiawang Nie, Li Wang","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-29T19:11:37Z","title":"Semidefinite Relaxations for Best Rank-1 Tensor Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6562","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:fddd0c8b86235536628af0c02368d3c8f363f7dc40d39395dc337bfe52cdc80f","target":"record","created_at":"2026-05-18T02:50:51Z","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":"d3bb9bd72c1ce409c54bc36062c544c6bf08284913f1b42457209f4bde20016d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-29T19:11:37Z","title_canon_sha256":"f7821275e98c6df089d518dfd73c740b2d38fdc5731bda05aa08186669afbda3"},"schema_version":"1.0","source":{"id":"1308.6562","kind":"arxiv","version":2}},"canonical_sha256":"6e6152f1ea9c918b2f5275651f3d97fcbe60ad4dfec0e792ce5fcac1791824d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6152f1ea9c918b2f5275651f3d97fcbe60ad4dfec0e792ce5fcac1791824d1","first_computed_at":"2026-05-18T02:50:51.801674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:51.801674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L20V2mjeKnAMbCWPdM+9LJ7y0SkQoozBLxWmmq85FNrj1kpGTYzgPlVtrEtKpB4owgyioFN/hUeCt9snDWpJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:51.802113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fddd0c8b86235536628af0c02368d3c8f363f7dc40d39395dc337bfe52cdc80f","sha256:d67358c7e072eb97ab2b4a4cdc9920c86e2b2e20fa196856d29431c8034ee2ce"],"state_sha256":"394a9b306436fd23c8f4603bddacb051aa426d5153d9958fd71a5d63ea3af1b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OcEtzAPRWYelD5G9AxWKzsqzv7RwsHqLnMYjWiMxUqdW9C+UeMX6VqpHNYhuOVfTI1V5CT0LwJIuBRtNxIhkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:52:48.586186Z","bundle_sha256":"256ec193a3547b0c4fa4b5660b3184a13f382dd7bbefd4936b7deb0f472b23b7"}}