{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KAUHDLT3PTPXKPD2GBZZWI2IY4","short_pith_number":"pith:KAUHDLT3","canonical_record":{"source":{"id":"1510.00844","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-03T16:32:43Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d0c62799ab109c90f72f25fb01bb1f77e880c0b7418099dcd99517b61c86653c","abstract_canon_sha256":"4d04bbf6bc02e60d8fc0622579c9f554a08c7589a34e6a82fb4cca2fc4229f2b"},"schema_version":"1.0"},"canonical_sha256":"502871ae7b7cdf753c7a30739b2348c71b1076c075aae65a660fd7454772b90b","source":{"kind":"arxiv","id":"1510.00844","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00844","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00844v3","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00844","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"pith_short_12","alias_value":"KAUHDLT3PTPX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KAUHDLT3PTPXKPD2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KAUHDLT3","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KAUHDLT3PTPXKPD2GBZZWI2IY4","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00844","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-03T16:32:43Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d0c62799ab109c90f72f25fb01bb1f77e880c0b7418099dcd99517b61c86653c","abstract_canon_sha256":"4d04bbf6bc02e60d8fc0622579c9f554a08c7589a34e6a82fb4cca2fc4229f2b"},"schema_version":"1.0"},"canonical_sha256":"502871ae7b7cdf753c7a30739b2348c71b1076c075aae65a660fd7454772b90b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:04.410340Z","signature_b64":"NW1Acxm0UNpPOw9q7Ypfzb4tFfIYS49V0s7h6Og0irZLbRyHgBmtSffxuc6Ur1/Ew9Xy3oG+QdBhTnT279tUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"502871ae7b7cdf753c7a30739b2348c71b1076c075aae65a660fd7454772b90b","last_reissued_at":"2026-05-18T00:58:04.409934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:04.409934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00844","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+KPVpT7Av/8DOOduar/mI3lGheZRkK710h42KEsOcbKIQmk5K1DplP1acMSBo2qBfxBV26dqIoeJCGIeT83Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:59:17.528839Z"},"content_sha256":"de205fe6f72a4e6fbf49bfc3609bb126ee9837522e24b363813319c36eeafe27","schema_version":"1.0","event_id":"sha256:de205fe6f72a4e6fbf49bfc3609bb126ee9837522e24b363813319c36eeafe27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KAUHDLT3PTPXKPD2GBZZWI2IY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DC","authors_text":"Ariful Azad, Aydin Buluc, Grey Ballard, James Demmel, Laura Grigori, Oded Schwartz, Samuel Williams, Sivan Toledo","submitted_at":"2015-10-03T16:32:43Z","abstract_excerpt":"Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00844","kind":"arxiv","version":3},"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":"2026-05-18T00:58:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nb55QJ65sT68ri46WmANO9cDn7MCu+YOapOq/0Dg72AiIRJzjN5XnhXBo8GT1CcddkRn6ClljM3FIJRADTGBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:59:17.529185Z"},"content_sha256":"5f4ee7f5501c79fe7cfe06f964607de084bd50a3ae6456f2f6d89d53d7fddb32","schema_version":"1.0","event_id":"sha256:5f4ee7f5501c79fe7cfe06f964607de084bd50a3ae6456f2f6d89d53d7fddb32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/bundle.json","state_url":"https://pith.science/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/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":"2026-06-02T20:59:17Z","links":{"resolver":"https://pith.science/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4","bundle":"https://pith.science/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/bundle.json","state":"https://pith.science/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAUHDLT3PTPXKPD2GBZZWI2IY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KAUHDLT3PTPXKPD2GBZZWI2IY4","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":"4d04bbf6bc02e60d8fc0622579c9f554a08c7589a34e6a82fb4cca2fc4229f2b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-03T16:32:43Z","title_canon_sha256":"d0c62799ab109c90f72f25fb01bb1f77e880c0b7418099dcd99517b61c86653c"},"schema_version":"1.0","source":{"id":"1510.00844","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00844","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00844v3","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00844","created_at":"2026-05-18T00:58:04Z"},{"alias_kind":"pith_short_12","alias_value":"KAUHDLT3PTPX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KAUHDLT3PTPXKPD2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KAUHDLT3","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:5f4ee7f5501c79fe7cfe06f964607de084bd50a3ae6456f2f6d89d53d7fddb32","target":"graph","created_at":"2026-05-18T00:58:04Z","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":"Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulati","authors_text":"Ariful Azad, Aydin Buluc, Grey Ballard, James Demmel, Laura Grigori, Oded Schwartz, Samuel Williams, Sivan Toledo","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-03T16:32:43Z","title":"Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00844","kind":"arxiv","version":3},"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:de205fe6f72a4e6fbf49bfc3609bb126ee9837522e24b363813319c36eeafe27","target":"record","created_at":"2026-05-18T00:58:04Z","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":"4d04bbf6bc02e60d8fc0622579c9f554a08c7589a34e6a82fb4cca2fc4229f2b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-03T16:32:43Z","title_canon_sha256":"d0c62799ab109c90f72f25fb01bb1f77e880c0b7418099dcd99517b61c86653c"},"schema_version":"1.0","source":{"id":"1510.00844","kind":"arxiv","version":3}},"canonical_sha256":"502871ae7b7cdf753c7a30739b2348c71b1076c075aae65a660fd7454772b90b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"502871ae7b7cdf753c7a30739b2348c71b1076c075aae65a660fd7454772b90b","first_computed_at":"2026-05-18T00:58:04.409934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:04.409934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NW1Acxm0UNpPOw9q7Ypfzb4tFfIYS49V0s7h6Og0irZLbRyHgBmtSffxuc6Ur1/Ew9Xy3oG+QdBhTnT279tUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:04.410340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00844","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de205fe6f72a4e6fbf49bfc3609bb126ee9837522e24b363813319c36eeafe27","sha256:5f4ee7f5501c79fe7cfe06f964607de084bd50a3ae6456f2f6d89d53d7fddb32"],"state_sha256":"99f79ad6cf5214ae25353cf5dfd6a73d9142268649831f7fdee46a4055a72a55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsW5KPy8/LnLVlVmiOdHoEkY1B0FIUVS4yA34KW3m/TrROiWVulyzh7x0AguiSSLe7QF6MnGvYVAM01u2QGcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:59:17.531059Z","bundle_sha256":"786c551cb6f1fb01727bb991b23edddfd09d709a6f5f16660c8b5a6fd1a0b6d1"}}