{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q377OX7I3EM3IWUBFGFJDNXKDF","short_pith_number":"pith:Q377OX7I","canonical_record":{"source":{"id":"1512.00066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-11-30T22:08:23Z","cross_cats_sorted":[],"title_canon_sha256":"d01157b5a5ac7bfb2ee64fb5064e0178bc2081678af414eb4c81968457991a0f","abstract_canon_sha256":"8443a0ed5a03302d474fe8544a3f0265a124978f601c6f37eb8467b5087bf0b1"},"schema_version":"1.0"},"canonical_sha256":"86fff75fe8d919b45a81298a91b6ea195e56a47c8e5f8650b4b64412a0a65290","source":{"kind":"arxiv","id":"1512.00066","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00066","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00066v1","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00066","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"pith_short_12","alias_value":"Q377OX7I3EM3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q377OX7I3EM3IWUB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q377OX7I","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q377OX7I3EM3IWUBFGFJDNXKDF","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-11-30T22:08:23Z","cross_cats_sorted":[],"title_canon_sha256":"d01157b5a5ac7bfb2ee64fb5064e0178bc2081678af414eb4c81968457991a0f","abstract_canon_sha256":"8443a0ed5a03302d474fe8544a3f0265a124978f601c6f37eb8467b5087bf0b1"},"schema_version":"1.0"},"canonical_sha256":"86fff75fe8d919b45a81298a91b6ea195e56a47c8e5f8650b4b64412a0a65290","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:32.861664Z","signature_b64":"uoa07lfCsGHtxLF5hw88R68/E6H22qLaKq6YrQFGtSPh549i5xr250K5FzRMXPFSVOEmMqk2dfM90WlSChOnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86fff75fe8d919b45a81298a91b6ea195e56a47c8e5f8650b4b64412a0a65290","last_reissued_at":"2026-05-18T01:25:32.861218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:32.861218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00066","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":"2026-05-18T01:25:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yyAi2ipf/WsGK9e+tzvya5KiQJhROqlJDNzs3Jwk0WpLWYmsx1TCai37f6gq/kr+AFHVjOtfbg3P29Std0ubCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:20:16.382784Z"},"content_sha256":"e8b0993cf9e33ab47d12c293261232231db05242b3ee2ba4a874ac188c5e7e3c","schema_version":"1.0","event_id":"sha256:e8b0993cf9e33ab47d12c293261232231db05242b3ee2ba4a874ac188c5e7e3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q377OX7I3EM3IWUBFGFJDNXKDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Tensor Algebra as a Parallel Programming Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Edgar Solomonik, Torsten Hoefler","submitted_at":"2015-11-30T22:08:23Z","abstract_excerpt":"Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially those which are parallelizable. Tensor computations are a natural generalization of matrix and graph computations. We extend the usual basic operations of tensor summation and contraction to arbitrary functions, and further operations such as reductions and mapping. The expression of these transformations in a high-level sparse linear algebra domain specific "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00066","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":"2026-05-18T01:25:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4we4sT0FqXLfL3sHUTKgXg8JNMkOJ8362auyh+TjASte9FN8oeO+//O22SDVPHHAKC0qBU8r+1v0EQ9PqQF0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:20:16.383863Z"},"content_sha256":"a11c9c3fcf4083089bd8f776c78e818f86b2050e1478d2c7b327bb414bf365d3","schema_version":"1.0","event_id":"sha256:a11c9c3fcf4083089bd8f776c78e818f86b2050e1478d2c7b327bb414bf365d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/bundle.json","state_url":"https://pith.science/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/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":"2026-06-01T06:20:16Z","links":{"resolver":"https://pith.science/pith/Q377OX7I3EM3IWUBFGFJDNXKDF","bundle":"https://pith.science/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/bundle.json","state":"https://pith.science/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q377OX7I3EM3IWUBFGFJDNXKDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q377OX7I3EM3IWUBFGFJDNXKDF","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":"8443a0ed5a03302d474fe8544a3f0265a124978f601c6f37eb8467b5087bf0b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-11-30T22:08:23Z","title_canon_sha256":"d01157b5a5ac7bfb2ee64fb5064e0178bc2081678af414eb4c81968457991a0f"},"schema_version":"1.0","source":{"id":"1512.00066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00066","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00066v1","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00066","created_at":"2026-05-18T01:25:32Z"},{"alias_kind":"pith_short_12","alias_value":"Q377OX7I3EM3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q377OX7I3EM3IWUB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q377OX7I","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:a11c9c3fcf4083089bd8f776c78e818f86b2050e1478d2c7b327bb414bf365d3","target":"graph","created_at":"2026-05-18T01:25:32Z","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":"Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially those which are parallelizable. Tensor computations are a natural generalization of matrix and graph computations. We extend the usual basic operations of tensor summation and contraction to arbitrary functions, and further operations such as reductions and mapping. The expression of these transformations in a high-level sparse linear algebra domain specific ","authors_text":"Edgar Solomonik, Torsten Hoefler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-11-30T22:08:23Z","title":"Sparse Tensor Algebra as a Parallel Programming Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00066","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:e8b0993cf9e33ab47d12c293261232231db05242b3ee2ba4a874ac188c5e7e3c","target":"record","created_at":"2026-05-18T01:25:32Z","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":"8443a0ed5a03302d474fe8544a3f0265a124978f601c6f37eb8467b5087bf0b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-11-30T22:08:23Z","title_canon_sha256":"d01157b5a5ac7bfb2ee64fb5064e0178bc2081678af414eb4c81968457991a0f"},"schema_version":"1.0","source":{"id":"1512.00066","kind":"arxiv","version":1}},"canonical_sha256":"86fff75fe8d919b45a81298a91b6ea195e56a47c8e5f8650b4b64412a0a65290","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86fff75fe8d919b45a81298a91b6ea195e56a47c8e5f8650b4b64412a0a65290","first_computed_at":"2026-05-18T01:25:32.861218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:32.861218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uoa07lfCsGHtxLF5hw88R68/E6H22qLaKq6YrQFGtSPh549i5xr250K5FzRMXPFSVOEmMqk2dfM90WlSChOnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:32.861664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8b0993cf9e33ab47d12c293261232231db05242b3ee2ba4a874ac188c5e7e3c","sha256:a11c9c3fcf4083089bd8f776c78e818f86b2050e1478d2c7b327bb414bf365d3"],"state_sha256":"fd046ca29acb343d3fa2d00f7f5df1ea4061aa22c629830305ace2d145d60075"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKPSqXzo5vnPwVpmH5RtoEh4tY2lXS14d4P69uGzjWh5EGztckIii16jHLe1holdldk+rxCQ/biYMIEgKbjjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:20:16.387038Z","bundle_sha256":"a4d4c67eb6cc16b558a5332e03f19b9f8589265596dd452fcebcdbc4bc1c6595"}}