{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YAOSM4DOILAGUNW2FYPRITQU6B","short_pith_number":"pith:YAOSM4DO","canonical_record":{"source":{"id":"1202.3173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-02-14T23:12:23Z","cross_cats_sorted":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"title_canon_sha256":"9a146f2e183adf6d00132e47d1da42ece76fd6b394a389f0810be4b73f78e9c3","abstract_canon_sha256":"0eab787a0b574f540d09483773dcafee9a1a32ed764eed2c386e87d513218e4a"},"schema_version":"1.0"},"canonical_sha256":"c01d26706e42c06a36da2e1f144e14f04164ba6f00e6635ad692fadee2d01a61","source":{"kind":"arxiv","id":"1202.3173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3173","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3173v1","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3173","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"YAOSM4DOILAG","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YAOSM4DOILAGUNW2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YAOSM4DO","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YAOSM4DOILAGUNW2FYPRITQU6B","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-02-14T23:12:23Z","cross_cats_sorted":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"title_canon_sha256":"9a146f2e183adf6d00132e47d1da42ece76fd6b394a389f0810be4b73f78e9c3","abstract_canon_sha256":"0eab787a0b574f540d09483773dcafee9a1a32ed764eed2c386e87d513218e4a"},"schema_version":"1.0"},"canonical_sha256":"c01d26706e42c06a36da2e1f144e14f04164ba6f00e6635ad692fadee2d01a61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:14.512394Z","signature_b64":"8cXAQhPjYhV0x7y2VJG9Gx/BaouWM87E3isLpQiBsnGhLfUMOVRQA6voDnwHqEJMK1oHlC9+9vXCmVwHckEeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01d26706e42c06a36da2e1f144e14f04164ba6f00e6635ad692fadee2d01a61","last_reissued_at":"2026-05-18T04:02:14.511629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:14.511629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3173","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":"2026-05-18T04:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMG1yVmLRqMKNxaq9dVYES8+v1cg17A3UANS8m4zT2lu2gyPl3hjkii+t5K7F0uK5G8tfdoee2HScm8FywGDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:35:16.829678Z"},"content_sha256":"62ed6c79273b12b8381c67e79ff9773e850dc37c791cbc4e353edfacc8280698","schema_version":"1.0","event_id":"sha256:62ed6c79273b12b8381c67e79ff9773e850dc37c791cbc4e353edfacc8280698"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YAOSM4DOILAGUNW2FYPRITQU6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Communication-Optimal Parallel Algorithm for Strassen's Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"primary_cat":"cs.DS","authors_text":"Benjamin Lipshitz, Grey Ballard, James Demmel, Oded Schwartz, Olga Holtz","submitted_at":"2012-02-14T23:12:23Z","abstract_excerpt":"Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication. The algorithm outperforms all known parallel matrix multiplication algorithms, classical and Strassen-based, both asymptotically and in practice.\n  A critical bottleneck in parallelizing Strassen's algorithm is the communication between the processors. Ballard, Demmel, Holtz, and Schwartz (SPAA'11) prove lower bounds on these communication costs, using "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3173","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":""},"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":"2026-05-18T04:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZvsdX6qKcC0AdA3axKaUwa6uOXvWqawfVFTjLkwtMK4FvQho5KWNrolHE8vsicuH7TnSZFh4u6gI4HiyV4tAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:35:16.830242Z"},"content_sha256":"a302de0a83cf00dc511511ac4001c5dbc50e8c54a9ac86da3bfe8fa792e06333","schema_version":"1.0","event_id":"sha256:a302de0a83cf00dc511511ac4001c5dbc50e8c54a9ac86da3bfe8fa792e06333"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAOSM4DOILAGUNW2FYPRITQU6B/bundle.json","state_url":"https://pith.science/pith/YAOSM4DOILAGUNW2FYPRITQU6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAOSM4DOILAGUNW2FYPRITQU6B/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":"2026-05-31T06:35:16Z","links":{"resolver":"https://pith.science/pith/YAOSM4DOILAGUNW2FYPRITQU6B","bundle":"https://pith.science/pith/YAOSM4DOILAGUNW2FYPRITQU6B/bundle.json","state":"https://pith.science/pith/YAOSM4DOILAGUNW2FYPRITQU6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAOSM4DOILAGUNW2FYPRITQU6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YAOSM4DOILAGUNW2FYPRITQU6B","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":"0eab787a0b574f540d09483773dcafee9a1a32ed764eed2c386e87d513218e4a","cross_cats_sorted":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-02-14T23:12:23Z","title_canon_sha256":"9a146f2e183adf6d00132e47d1da42ece76fd6b394a389f0810be4b73f78e9c3"},"schema_version":"1.0","source":{"id":"1202.3173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3173","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3173v1","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3173","created_at":"2026-05-18T04:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"YAOSM4DOILAG","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YAOSM4DOILAGUNW2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YAOSM4DO","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:a302de0a83cf00dc511511ac4001c5dbc50e8c54a9ac86da3bfe8fa792e06333","target":"graph","created_at":"2026-05-18T04:02:14Z","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":"Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication. The algorithm outperforms all known parallel matrix multiplication algorithms, classical and Strassen-based, both asymptotically and in practice.\n  A critical bottleneck in parallelizing Strassen's algorithm is the communication between the processors. Ballard, Demmel, Holtz, and Schwartz (SPAA'11) prove lower bounds on these communication costs, using ","authors_text":"Benjamin Lipshitz, Grey Ballard, James Demmel, Oded Schwartz, Olga Holtz","cross_cats":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-02-14T23:12:23Z","title":"Communication-Optimal Parallel Algorithm for Strassen's Matrix Multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3173","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":"sha256:62ed6c79273b12b8381c67e79ff9773e850dc37c791cbc4e353edfacc8280698","target":"record","created_at":"2026-05-18T04:02:14Z","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":"0eab787a0b574f540d09483773dcafee9a1a32ed764eed2c386e87d513218e4a","cross_cats_sorted":["cs.CC","cs.DC","cs.NA","math.CO","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-02-14T23:12:23Z","title_canon_sha256":"9a146f2e183adf6d00132e47d1da42ece76fd6b394a389f0810be4b73f78e9c3"},"schema_version":"1.0","source":{"id":"1202.3173","kind":"arxiv","version":1}},"canonical_sha256":"c01d26706e42c06a36da2e1f144e14f04164ba6f00e6635ad692fadee2d01a61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c01d26706e42c06a36da2e1f144e14f04164ba6f00e6635ad692fadee2d01a61","first_computed_at":"2026-05-18T04:02:14.511629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:14.511629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8cXAQhPjYhV0x7y2VJG9Gx/BaouWM87E3isLpQiBsnGhLfUMOVRQA6voDnwHqEJMK1oHlC9+9vXCmVwHckEeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:14.512394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62ed6c79273b12b8381c67e79ff9773e850dc37c791cbc4e353edfacc8280698","sha256:a302de0a83cf00dc511511ac4001c5dbc50e8c54a9ac86da3bfe8fa792e06333"],"state_sha256":"4113983e026459748e3a5460a84987ef53a31feea038bb10c74487e1571bb14c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kK3bdO/IxReGhTz1YHtycBQY2Q3lamcbyb7g6E6psx4wcAMExZbLujvUtPttk0CMy9hlL1zdnLQyT/v0JzYcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:35:16.833061Z","bundle_sha256":"1a22a80ac75e9e6098a740c1a4de01972ee0b0f18dbd28301cf212f9d018e5e6"}}