{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:PNVD37GUZTWD4HHXJQURGEISU4","short_pith_number":"pith:PNVD37GU","canonical_record":{"source":{"id":"2009.07735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-16T15:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"e72a967b15efcc56dd85e52c112e5946c6ff236e1a17f8f1125438365fe6dd65","abstract_canon_sha256":"c85c70964254c2b3932bd183af558e7eb5f052de7b53499bf197dc88ec11a418"},"schema_version":"1.0"},"canonical_sha256":"7b6a3dfcd4ccec3e1cf74c29131112a733de85cad3b179f70824b7236db120b8","source":{"kind":"arxiv","id":"2009.07735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07735","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07735v1","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07735","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"PNVD37GUZTWD","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"PNVD37GUZTWD4HHX","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"PNVD37GU","created_at":"2026-07-05T01:35:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:PNVD37GUZTWD4HHXJQURGEISU4","target":"record","payload":{"canonical_record":{"source":{"id":"2009.07735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-16T15:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"e72a967b15efcc56dd85e52c112e5946c6ff236e1a17f8f1125438365fe6dd65","abstract_canon_sha256":"c85c70964254c2b3932bd183af558e7eb5f052de7b53499bf197dc88ec11a418"},"schema_version":"1.0"},"canonical_sha256":"7b6a3dfcd4ccec3e1cf74c29131112a733de85cad3b179f70824b7236db120b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:35:55.464102Z","signature_b64":"nO5JrdFgB4oklQVoh4HrNpmVrS7d0vGy6NO4jhqARzXY5lJRUV4BqgNZjbxLJNfBhhvjfM2psjROaNaoQ7vJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b6a3dfcd4ccec3e1cf74c29131112a733de85cad3b179f70824b7236db120b8","last_reissued_at":"2026-07-05T01:35:55.463718Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:35:55.463718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.07735","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":"2026-07-05T01:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdfrf678NlXdw6GxIS0Bu01wcCyW57pVTXYOtq8LO60luZ3aKpY13TeWDT8rUCFhqb0+/AQdbLbn4r2lwK+FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:58:29.216594Z"},"content_sha256":"4d45c777ac816a1d279d6f9057c8e1e81d14a9fef07c5abbbb97bf7bd178e5f2","schema_version":"1.0","event_id":"sha256:4d45c777ac816a1d279d6f9057c8e1e81d14a9fef07c5abbbb97bf7bd178e5f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:PNVD37GUZTWD4HHXJQURGEISU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Symmetric Rectilinear Matrix Partitioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abdurrahman Ya\\c{s}ar, Kaan Sancak, Muhammed Fat\\.ih Balin, \\\"Umit V. \\c{C}ataly\\\"urek, Xiaojing An","submitted_at":"2020-09-16T15:10:14Z","abstract_excerpt":"Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized block distribution) of sparse matrices. More specifically, in this work, we address the problem of symmetric rectilinear partitioning of a square matrix. By symmetric, we mean the rows and columns of the matrix are identically partitioned yielding a tiling where the diagonal tiles (blocks) will be squares. We first show that the optimal solution to this pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07735","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.07735/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":"2026-07-05T01:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwRchxfrpJTgxUsIPO1J4HXesHq6VAhEEPmD7p/fXs0gomImWX5kmUmYXonDxjP45fS3vZXJ97ckGoSQ/CKoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:58:29.217167Z"},"content_sha256":"583104721f0a4d4613365633b643f5559e1146f7e9601d1436b3a7ecbb86d635","schema_version":"1.0","event_id":"sha256:583104721f0a4d4613365633b643f5559e1146f7e9601d1436b3a7ecbb86d635"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNVD37GUZTWD4HHXJQURGEISU4/bundle.json","state_url":"https://pith.science/pith/PNVD37GUZTWD4HHXJQURGEISU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNVD37GUZTWD4HHXJQURGEISU4/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":"2026-08-03T17:58:29Z","links":{"resolver":"https://pith.science/pith/PNVD37GUZTWD4HHXJQURGEISU4","bundle":"https://pith.science/pith/PNVD37GUZTWD4HHXJQURGEISU4/bundle.json","state":"https://pith.science/pith/PNVD37GUZTWD4HHXJQURGEISU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNVD37GUZTWD4HHXJQURGEISU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:PNVD37GUZTWD4HHXJQURGEISU4","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":"c85c70964254c2b3932bd183af558e7eb5f052de7b53499bf197dc88ec11a418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-16T15:10:14Z","title_canon_sha256":"e72a967b15efcc56dd85e52c112e5946c6ff236e1a17f8f1125438365fe6dd65"},"schema_version":"1.0","source":{"id":"2009.07735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07735","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07735v1","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07735","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"PNVD37GUZTWD","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"PNVD37GUZTWD4HHX","created_at":"2026-07-05T01:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"PNVD37GU","created_at":"2026-07-05T01:35:55Z"}],"graph_snapshots":[{"event_id":"sha256:583104721f0a4d4613365633b643f5559e1146f7e9601d1436b3a7ecbb86d635","target":"graph","created_at":"2026-07-05T01:35:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.07735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized block distribution) of sparse matrices. More specifically, in this work, we address the problem of symmetric rectilinear partitioning of a square matrix. By symmetric, we mean the rows and columns of the matrix are identically partitioned yielding a tiling where the diagonal tiles (blocks) will be squares. We first show that the optimal solution to this pro","authors_text":"Abdurrahman Ya\\c{s}ar, Kaan Sancak, Muhammed Fat\\.ih Balin, \\\"Umit V. \\c{C}ataly\\\"urek, Xiaojing An","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-16T15:10:14Z","title":"On Symmetric Rectilinear Matrix Partitioning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07735","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":"sha256:4d45c777ac816a1d279d6f9057c8e1e81d14a9fef07c5abbbb97bf7bd178e5f2","target":"record","created_at":"2026-07-05T01:35:55Z","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":"c85c70964254c2b3932bd183af558e7eb5f052de7b53499bf197dc88ec11a418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-16T15:10:14Z","title_canon_sha256":"e72a967b15efcc56dd85e52c112e5946c6ff236e1a17f8f1125438365fe6dd65"},"schema_version":"1.0","source":{"id":"2009.07735","kind":"arxiv","version":1}},"canonical_sha256":"7b6a3dfcd4ccec3e1cf74c29131112a733de85cad3b179f70824b7236db120b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b6a3dfcd4ccec3e1cf74c29131112a733de85cad3b179f70824b7236db120b8","first_computed_at":"2026-07-05T01:35:55.463718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:35:55.463718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nO5JrdFgB4oklQVoh4HrNpmVrS7d0vGy6NO4jhqARzXY5lJRUV4BqgNZjbxLJNfBhhvjfM2psjROaNaoQ7vJAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:35:55.464102Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d45c777ac816a1d279d6f9057c8e1e81d14a9fef07c5abbbb97bf7bd178e5f2","sha256:583104721f0a4d4613365633b643f5559e1146f7e9601d1436b3a7ecbb86d635"],"state_sha256":"d269dd05ef71e55274084eb0e61094b87b2f1ea61cadaee3c3d51f64ac000d50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pY9XeKKfv8PNkoIhYumeIBLi8z1EEBT5TedNeeTokkoFfRNpEgw+zIEsSENUQlVLoXzZQgSxzrafDoFlESnoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:58:29.222293Z","bundle_sha256":"14aa1572c9c2342a9c6a84baec4d6e878fda8936c5e9eac6aaf6951df5dc5adc"}}