{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BJM7N42BA4PLLHY5663IHGC4CQ","short_pith_number":"pith:BJM7N42B","canonical_record":{"source":{"id":"1308.5207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-23T18:53:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"53d488a5d1599bcccdeb79782c33af1ec2c9ad24ad2ba5bda4051b5cb1470e2a","abstract_canon_sha256":"a6de8926cfdc2fda10baa7f32e393950618ad06ce8a0b883b97c34d9fa516050"},"schema_version":"1.0"},"canonical_sha256":"0a59f6f341071eb59f1df7b683985c14325564ef7424e3a0366c4118d9febdcb","source":{"kind":"arxiv","id":"1308.5207","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5207","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5207v4","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5207","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"BJM7N42BA4PL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJM7N42BA4PLLHY5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJM7N42B","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BJM7N42BA4PLLHY5663IHGC4CQ","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-23T18:53:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"53d488a5d1599bcccdeb79782c33af1ec2c9ad24ad2ba5bda4051b5cb1470e2a","abstract_canon_sha256":"a6de8926cfdc2fda10baa7f32e393950618ad06ce8a0b883b97c34d9fa516050"},"schema_version":"1.0"},"canonical_sha256":"0a59f6f341071eb59f1df7b683985c14325564ef7424e3a0366c4118d9febdcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:55.646085Z","signature_b64":"1+TgjhgFWJ1w/+Bk7egWY+qJvGzK+C27uvbJFTeDW0RyA2SfrVTgowjy8A98Ixa3KUh8MyejFV2AuAv1hb6UDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a59f6f341071eb59f1df7b683985c14325564ef7424e3a0366c4118d9febdcb","last_reissued_at":"2026-05-18T01:30:55.645562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:55.645562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5207","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5dgVzubeCmC3mbMw8LZRPzLW7hncfKDwd9Zo83D7ftxyXQHclj5J4jAPHj/Ni794G4M73iy9oCd1cAqwyqImCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:58.709471Z"},"content_sha256":"4414da9937a45a7e044d9cef6d8fb113274a1e683c0ec98b5bf02a9b8e0cfbb4","schema_version":"1.0","event_id":"sha256:4414da9937a45a7e044d9cef6d8fb113274a1e683c0ec98b5bf02a9b8e0cfbb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BJM7N42BA4PLLHY5663IHGC4CQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Afonso S. Bandeira, Amit Singer, Christopher Kennedy","submitted_at":"2013-08-23T18:53:30Z","abstract_excerpt":"The little Grothendieck problem consists of maximizing $\\sum_{ij}C_{ij}x_ix_j$ over binary variables $x_i\\in\\{\\pm1\\}$, where C is a positive semidefinite matrix. In this paper we focus on a natural generalization of this problem, the little Grothendieck problem over the orthogonal group. Given C a dn x dn positive semidefinite matrix, the objective is to maximize $\\sum_{ij}Tr (C_{ij}^TO_iO_j^T)$ restricting $O_i$ to take values in the group of orthogonal matrices, where $C_{ij}$ denotes the (ij)-th d x d block of C. We propose an approximation algorithm, which we refer to as Orthogonal-Cut, to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5207","kind":"arxiv","version":4},"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":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP+O7sJOZT8TEw1xofDzaGBS8mcy1DG0qeJ/YR87FegepLZOmd/i/J0korc0prbUJa1Dw089m9Bj7IFcyVgBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:58.709828Z"},"content_sha256":"6054c6b37f247c55c30da4112347f370d963a81bff45fd84bf48678c88dd9724","schema_version":"1.0","event_id":"sha256:6054c6b37f247c55c30da4112347f370d963a81bff45fd84bf48678c88dd9724"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJM7N42BA4PLLHY5663IHGC4CQ/bundle.json","state_url":"https://pith.science/pith/BJM7N42BA4PLLHY5663IHGC4CQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJM7N42BA4PLLHY5663IHGC4CQ/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":"2026-05-28T23:38:58Z","links":{"resolver":"https://pith.science/pith/BJM7N42BA4PLLHY5663IHGC4CQ","bundle":"https://pith.science/pith/BJM7N42BA4PLLHY5663IHGC4CQ/bundle.json","state":"https://pith.science/pith/BJM7N42BA4PLLHY5663IHGC4CQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJM7N42BA4PLLHY5663IHGC4CQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BJM7N42BA4PLLHY5663IHGC4CQ","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":"a6de8926cfdc2fda10baa7f32e393950618ad06ce8a0b883b97c34d9fa516050","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-23T18:53:30Z","title_canon_sha256":"53d488a5d1599bcccdeb79782c33af1ec2c9ad24ad2ba5bda4051b5cb1470e2a"},"schema_version":"1.0","source":{"id":"1308.5207","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5207","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5207v4","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5207","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"BJM7N42BA4PL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJM7N42BA4PLLHY5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJM7N42B","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:6054c6b37f247c55c30da4112347f370d963a81bff45fd84bf48678c88dd9724","target":"graph","created_at":"2026-05-18T01:30:55Z","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":"The little Grothendieck problem consists of maximizing $\\sum_{ij}C_{ij}x_ix_j$ over binary variables $x_i\\in\\{\\pm1\\}$, where C is a positive semidefinite matrix. In this paper we focus on a natural generalization of this problem, the little Grothendieck problem over the orthogonal group. Given C a dn x dn positive semidefinite matrix, the objective is to maximize $\\sum_{ij}Tr (C_{ij}^TO_iO_j^T)$ restricting $O_i$ to take values in the group of orthogonal matrices, where $C_{ij}$ denotes the (ij)-th d x d block of C. We propose an approximation algorithm, which we refer to as Orthogonal-Cut, to","authors_text":"Afonso S. Bandeira, Amit Singer, Christopher Kennedy","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-23T18:53:30Z","title":"Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5207","kind":"arxiv","version":4},"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":"sha256:4414da9937a45a7e044d9cef6d8fb113274a1e683c0ec98b5bf02a9b8e0cfbb4","target":"record","created_at":"2026-05-18T01:30:55Z","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":"a6de8926cfdc2fda10baa7f32e393950618ad06ce8a0b883b97c34d9fa516050","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-23T18:53:30Z","title_canon_sha256":"53d488a5d1599bcccdeb79782c33af1ec2c9ad24ad2ba5bda4051b5cb1470e2a"},"schema_version":"1.0","source":{"id":"1308.5207","kind":"arxiv","version":4}},"canonical_sha256":"0a59f6f341071eb59f1df7b683985c14325564ef7424e3a0366c4118d9febdcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a59f6f341071eb59f1df7b683985c14325564ef7424e3a0366c4118d9febdcb","first_computed_at":"2026-05-18T01:30:55.645562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:55.645562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1+TgjhgFWJ1w/+Bk7egWY+qJvGzK+C27uvbJFTeDW0RyA2SfrVTgowjy8A98Ixa3KUh8MyejFV2AuAv1hb6UDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:55.646085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5207","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4414da9937a45a7e044d9cef6d8fb113274a1e683c0ec98b5bf02a9b8e0cfbb4","sha256:6054c6b37f247c55c30da4112347f370d963a81bff45fd84bf48678c88dd9724"],"state_sha256":"8b1c257b49dec4c9ad3c0349ce43aa50da49d55ec2a6661cdda36c5e81b6128d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1h8PmzxMGw4ZSBA+SZntJIUhhoiMe4gbyeyRnXQJNSlFvzsNZNWkVMwHFaq549divTsS7lf8yzr3fRCCkdZLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:38:58.712125Z","bundle_sha256":"b635a8fcc918143a10ae84c1a8e62b4c2afcbc2779fc557210732387011176eb"}}