{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EWEVXFOBKHDU6OMU7IH3RV44SL","short_pith_number":"pith:EWEVXFOB","canonical_record":{"source":{"id":"1107.0088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-01T00:36:03Z","cross_cats_sorted":["cs.DS","cs.NA","math.CO"],"title_canon_sha256":"97d04080e8cc0c68318fa3a7a7eeea1ba12759f278321457dcc5bab4d897efff","abstract_canon_sha256":"fae59238f2697dfee114a0448caed05590a4d58a98522ab7681a4f4fa1f5d41b"},"schema_version":"1.0"},"canonical_sha256":"25895b95c151c74f3994fa0fb8d79c92d0459259bf63eb861b66536e7f5bf7c6","source":{"kind":"arxiv","id":"1107.0088","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0088","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0088v2","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0088","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"EWEVXFOBKHDU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EWEVXFOBKHDU6OMU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EWEVXFOB","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EWEVXFOBKHDU6OMU7IH3RV44SL","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-01T00:36:03Z","cross_cats_sorted":["cs.DS","cs.NA","math.CO"],"title_canon_sha256":"97d04080e8cc0c68318fa3a7a7eeea1ba12759f278321457dcc5bab4d897efff","abstract_canon_sha256":"fae59238f2697dfee114a0448caed05590a4d58a98522ab7681a4f4fa1f5d41b"},"schema_version":"1.0"},"canonical_sha256":"25895b95c151c74f3994fa0fb8d79c92d0459259bf63eb861b66536e7f5bf7c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:02.584519Z","signature_b64":"x3RRugT+JWIFX6q0LAlC7+ARQXH7YcL3Z6CGwnIsusW/Sj23dU9W1PCsmvFNuj71mw6HDlMJexqOJuWOp6N6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25895b95c151c74f3994fa0fb8d79c92d0459259bf63eb861b66536e7f5bf7c6","last_reissued_at":"2026-05-18T00:25:02.583862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:02.583862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0088","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":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbRLu6yrZo71FCodTdXbdATfM+77pVBHT5YjkFlB0Ze5e2GWzN4XPy/qEKH/v9mIfu3J58yj+RKsYSoLPWPQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:00:41.998969Z"},"content_sha256":"9595d34b043be09176c44557a9d4f226aac2fe2cd355d47b1233c4a7386379c7","schema_version":"1.0","event_id":"sha256:9595d34b043be09176c44557a9d4f226aac2fe2cd355d47b1233c4a7386379c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EWEVXFOBKHDU6OMU7IH3RV44SL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Sums of Positive Semidefinite Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NA","math.CO"],"primary_cat":"cs.DM","authors_text":"Cristiane M. Sato, Marcel K. de Carli Silva, Nicholas J. A. Harvey","submitted_at":"2011-07-01T00:36:03Z","abstract_excerpt":"Recently there has been much interest in \"sparsifying\" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that results from the sum. Results of this sort have found applications in many different areas, including sparsifying graphs. In this paper we consider the more general problem of sparsifying sums of positive semidefinite matrices that have arbitrary rank.\n  We give several algorithms for solving this problem. The first algorithm is based on the method of Batson, Spielman and Srivastava (2009). The second algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0088","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":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efC34RzyLjK9f6/H0oGymjzpHzxRM4wQoVYQ6p/jd8mSj6MnylIsKyxF3URVnsvIpMs6x7nZp08XjACt4/P0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:00:41.999339Z"},"content_sha256":"13e44b0ba9a3882dbe7bd30ba3820828a6e206ba7071b0f9fada4efa784e7069","schema_version":"1.0","event_id":"sha256:13e44b0ba9a3882dbe7bd30ba3820828a6e206ba7071b0f9fada4efa784e7069"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/bundle.json","state_url":"https://pith.science/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/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":"2026-06-01T17:00:42Z","links":{"resolver":"https://pith.science/pith/EWEVXFOBKHDU6OMU7IH3RV44SL","bundle":"https://pith.science/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/bundle.json","state":"https://pith.science/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWEVXFOBKHDU6OMU7IH3RV44SL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EWEVXFOBKHDU6OMU7IH3RV44SL","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":"fae59238f2697dfee114a0448caed05590a4d58a98522ab7681a4f4fa1f5d41b","cross_cats_sorted":["cs.DS","cs.NA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-01T00:36:03Z","title_canon_sha256":"97d04080e8cc0c68318fa3a7a7eeea1ba12759f278321457dcc5bab4d897efff"},"schema_version":"1.0","source":{"id":"1107.0088","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0088","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0088v2","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0088","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"EWEVXFOBKHDU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EWEVXFOBKHDU6OMU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EWEVXFOB","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:13e44b0ba9a3882dbe7bd30ba3820828a6e206ba7071b0f9fada4efa784e7069","target":"graph","created_at":"2026-05-18T00:25:02Z","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":"Recently there has been much interest in \"sparsifying\" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that results from the sum. Results of this sort have found applications in many different areas, including sparsifying graphs. In this paper we consider the more general problem of sparsifying sums of positive semidefinite matrices that have arbitrary rank.\n  We give several algorithms for solving this problem. The first algorithm is based on the method of Batson, Spielman and Srivastava (2009). The second algor","authors_text":"Cristiane M. Sato, Marcel K. de Carli Silva, Nicholas J. A. Harvey","cross_cats":["cs.DS","cs.NA","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-01T00:36:03Z","title":"Sparse Sums of Positive Semidefinite Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0088","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":"sha256:9595d34b043be09176c44557a9d4f226aac2fe2cd355d47b1233c4a7386379c7","target":"record","created_at":"2026-05-18T00:25:02Z","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":"fae59238f2697dfee114a0448caed05590a4d58a98522ab7681a4f4fa1f5d41b","cross_cats_sorted":["cs.DS","cs.NA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-01T00:36:03Z","title_canon_sha256":"97d04080e8cc0c68318fa3a7a7eeea1ba12759f278321457dcc5bab4d897efff"},"schema_version":"1.0","source":{"id":"1107.0088","kind":"arxiv","version":2}},"canonical_sha256":"25895b95c151c74f3994fa0fb8d79c92d0459259bf63eb861b66536e7f5bf7c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25895b95c151c74f3994fa0fb8d79c92d0459259bf63eb861b66536e7f5bf7c6","first_computed_at":"2026-05-18T00:25:02.583862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:02.583862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x3RRugT+JWIFX6q0LAlC7+ARQXH7YcL3Z6CGwnIsusW/Sj23dU9W1PCsmvFNuj71mw6HDlMJexqOJuWOp6N6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:02.584519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0088","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9595d34b043be09176c44557a9d4f226aac2fe2cd355d47b1233c4a7386379c7","sha256:13e44b0ba9a3882dbe7bd30ba3820828a6e206ba7071b0f9fada4efa784e7069"],"state_sha256":"058076455a82af5854aaa2ad2378f62ea0af2144424bc79fe07fe3b7b1cff216"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGI4YLU/P4URi9skULHlmScV9eY2vVM8nXxhXI3pAZGnpgFk7BVE2KfeKfYk6wSeWg+uMdVx7tHLpGk3B5J9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:00:42.001331Z","bundle_sha256":"1294904365b40338523a0566b73ea0c60b51cc8a343014da0e37810b8e7be49d"}}