{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HSOQN64TRPI2MSILRILHUJLEKT","short_pith_number":"pith:HSOQN64T","canonical_record":{"source":{"id":"1006.4173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-06-21T20:47:46Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"8c233f92fd0463754e60712bf4a87dfb65410cf3d649e01f8b75b92181afaf2d","abstract_canon_sha256":"dea19a8834e75c7ee9c0a2ba2b9542fd148c594ce6470f21057f87466eb50af3"},"schema_version":"1.0"},"canonical_sha256":"3c9d06fb938bd1a6490b8a167a256454c291c7eb16a4a5baf30645490f3903ce","source":{"kind":"arxiv","id":"1006.4173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4173","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4173v2","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4173","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"HSOQN64TRPI2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HSOQN64TRPI2MSIL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HSOQN64T","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HSOQN64TRPI2MSILRILHUJLEKT","target":"record","payload":{"canonical_record":{"source":{"id":"1006.4173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-06-21T20:47:46Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"8c233f92fd0463754e60712bf4a87dfb65410cf3d649e01f8b75b92181afaf2d","abstract_canon_sha256":"dea19a8834e75c7ee9c0a2ba2b9542fd148c594ce6470f21057f87466eb50af3"},"schema_version":"1.0"},"canonical_sha256":"3c9d06fb938bd1a6490b8a167a256454c291c7eb16a4a5baf30645490f3903ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:09.716385Z","signature_b64":"uD7cF+KWo3Krw+sYZllsxkk7U+ksemPqxcAIJlL3O+jzKVxLNP3ZZxsjtUcszUkZRv9l6ndj1KoIMjSs5a/mBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c9d06fb938bd1a6490b8a167a256454c291c7eb16a4a5baf30645490f3903ce","last_reissued_at":"2026-05-18T04:28:09.715840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:09.715840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.4173","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":"2026-05-18T04:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KnRgKfcWmFP5PzOHnQhEncoaVY5riC7coajEylwct85dYL5NIWptY7QDKMnuZab6CQV4VYDtVprXaRVyaDzIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:20:30.360267Z"},"content_sha256":"af668cbf3fc1c4596a1ad0f9446e0ad01445c6b32f790f4acc579b6801a8eccb","schema_version":"1.0","event_id":"sha256:af668cbf3fc1c4596a1ad0f9446e0ad01445c6b32f790f4acc579b6801a8eccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HSOQN64TRPI2MSILRILHUJLEKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Better size estimation for sparse matrix products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Andrea Campagna, Rasmus Pagh, Rasmus Resen Amossen","submitted_at":"2010-06-21T20:47:46Z","abstract_excerpt":"We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse boolean matrix product. This problem has applications in databases and computer algebra. Let n denote the total number of non-zero entries in the input matrices. We show how to compute a 1 +- epsilon approximation (with small probability of error) in expected time O(n) for any epsilon > 4/\\sqrt[4]{z}. The previously best estimation algorithm, due to Cohen (JCSS 1997), uses time O(n/epsilon^2). We also present a variant using O(sort(n)) I/Os in expectation in the cache-oblivious model. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4173","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":"2026-05-18T04:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUpX+NpjS2I82QfjPCiKztymgbWaNYvhIrov6TRCOH2WaMSPhJ+sDR4qufqWFSDSpcQisIL6blzYOmnXOaZNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:20:30.360936Z"},"content_sha256":"85148e08f69d29634247af5a639e116660a541e3f3e539ff77fab4ac7015141b","schema_version":"1.0","event_id":"sha256:85148e08f69d29634247af5a639e116660a541e3f3e539ff77fab4ac7015141b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSOQN64TRPI2MSILRILHUJLEKT/bundle.json","state_url":"https://pith.science/pith/HSOQN64TRPI2MSILRILHUJLEKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSOQN64TRPI2MSILRILHUJLEKT/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":"2026-06-06T12:20:30Z","links":{"resolver":"https://pith.science/pith/HSOQN64TRPI2MSILRILHUJLEKT","bundle":"https://pith.science/pith/HSOQN64TRPI2MSILRILHUJLEKT/bundle.json","state":"https://pith.science/pith/HSOQN64TRPI2MSILRILHUJLEKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSOQN64TRPI2MSILRILHUJLEKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HSOQN64TRPI2MSILRILHUJLEKT","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":"dea19a8834e75c7ee9c0a2ba2b9542fd148c594ce6470f21057f87466eb50af3","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-06-21T20:47:46Z","title_canon_sha256":"8c233f92fd0463754e60712bf4a87dfb65410cf3d649e01f8b75b92181afaf2d"},"schema_version":"1.0","source":{"id":"1006.4173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4173","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4173v2","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4173","created_at":"2026-05-18T04:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"HSOQN64TRPI2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HSOQN64TRPI2MSIL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HSOQN64T","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:85148e08f69d29634247af5a639e116660a541e3f3e539ff77fab4ac7015141b","target":"graph","created_at":"2026-05-18T04:28:09Z","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":"We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse boolean matrix product. This problem has applications in databases and computer algebra. Let n denote the total number of non-zero entries in the input matrices. We show how to compute a 1 +- epsilon approximation (with small probability of error) in expected time O(n) for any epsilon > 4/\\sqrt[4]{z}. The previously best estimation algorithm, due to Cohen (JCSS 1997), uses time O(n/epsilon^2). We also present a variant using O(sort(n)) I/Os in expectation in the cache-oblivious model. In","authors_text":"Andrea Campagna, Rasmus Pagh, Rasmus Resen Amossen","cross_cats":["cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-06-21T20:47:46Z","title":"Better size estimation for sparse matrix products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4173","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:af668cbf3fc1c4596a1ad0f9446e0ad01445c6b32f790f4acc579b6801a8eccb","target":"record","created_at":"2026-05-18T04:28:09Z","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":"dea19a8834e75c7ee9c0a2ba2b9542fd148c594ce6470f21057f87466eb50af3","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-06-21T20:47:46Z","title_canon_sha256":"8c233f92fd0463754e60712bf4a87dfb65410cf3d649e01f8b75b92181afaf2d"},"schema_version":"1.0","source":{"id":"1006.4173","kind":"arxiv","version":2}},"canonical_sha256":"3c9d06fb938bd1a6490b8a167a256454c291c7eb16a4a5baf30645490f3903ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c9d06fb938bd1a6490b8a167a256454c291c7eb16a4a5baf30645490f3903ce","first_computed_at":"2026-05-18T04:28:09.715840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:09.715840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uD7cF+KWo3Krw+sYZllsxkk7U+ksemPqxcAIJlL3O+jzKVxLNP3ZZxsjtUcszUkZRv9l6ndj1KoIMjSs5a/mBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:09.716385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af668cbf3fc1c4596a1ad0f9446e0ad01445c6b32f790f4acc579b6801a8eccb","sha256:85148e08f69d29634247af5a639e116660a541e3f3e539ff77fab4ac7015141b"],"state_sha256":"e41ca1dbf73e71d01f2bd3e26a674513f07a60518a2002c7f41d2d4cb6b17d6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHJsi6dncMrfSHUh0MBuQQTw0g9ATx77XwIFTO9HnUu17xX0gbm8wEixYbkIUFWIPpAnCsLjAQlx/kA+qfdHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:20:30.364537Z","bundle_sha256":"ef870a1764180c0212420fcfe402646e81b30c583117d3907155d63aa43b6c3a"}}