{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3H7S7HMUO6CJZRF455LFACONK3","short_pith_number":"pith:3H7S7HMU","canonical_record":{"source":{"id":"1404.0703","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-04-02T20:50:22Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"f4afb924d9a3e9a97ddf579a8a5acee871f85e5c34a2882465d1e96a779a2f12","abstract_canon_sha256":"b6bb9e4126c56828c9683ced6726ee3dbf644adc9e2f3b3f55db039e08b4450b"},"schema_version":"1.0"},"canonical_sha256":"d9ff2f9d9477849cc4bcef565009cd56cf1918aa92b8062cabf9a2ff45bb1aa7","source":{"kind":"arxiv","id":"1404.0703","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0703","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0703v7","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0703","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"3H7S7HMUO6CJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3H7S7HMUO6CJZRF4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3H7S7HMU","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3H7S7HMUO6CJZRF455LFACONK3","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0703","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-04-02T20:50:22Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"f4afb924d9a3e9a97ddf579a8a5acee871f85e5c34a2882465d1e96a779a2f12","abstract_canon_sha256":"b6bb9e4126c56828c9683ced6726ee3dbf644adc9e2f3b3f55db039e08b4450b"},"schema_version":"1.0"},"canonical_sha256":"d9ff2f9d9477849cc4bcef565009cd56cf1918aa92b8062cabf9a2ff45bb1aa7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:09.167986Z","signature_b64":"g8moQT/qUOj+vfRo5Crh+GWh8emOe1c7UxeIjZvlMsiq+V7crptAjdxz8uv1Mha6ySEiUIgNf9hmTwlBsrMYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9ff2f9d9477849cc4bcef565009cd56cf1918aa92b8062cabf9a2ff45bb1aa7","last_reissued_at":"2026-05-18T00:54:09.167427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:09.167427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0703","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GoqiMQegfgUGa95RNoiRI72cIT5kBUqiV1cuG9mAx0knu6u2WV3Tz9G8wQ1j/83POI9pNplzLsfOgJIpEKUZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:39:36.539490Z"},"content_sha256":"0dfb0f838c780f938ef321475a895adf6fd0d862e6cec0a24418141c3bc33b66","schema_version":"1.0","event_id":"sha256:0dfb0f838c780f938ef321475a895adf6fd0d862e6cec0a24418141c3bc33b66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3H7S7HMUO6CJZRF455LFACONK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joins via Geometric Resolutions: Worst-case and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DB","authors_text":"Atri Rudra, Christopher R\\'e, Hung Q. Ngo, Mahmoud Abo Khamis","submitted_at":"2014-04-02T20:50:22Z","abstract_excerpt":"We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as beyond worst-case results. The framework allows us to prove results for data stored in Btrees, multidimensional data structures, and even multiple indices per table. A key idea in our framework is formalizing the inference one does with an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0703","kind":"arxiv","version":7},"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":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/zS23jHxIVon6DnmXsN2pp46EmJinGz2a2f0efBdnRyBBPZBOBC60/vmsx71Ai88wvRZhIALy+tsRr4k7QGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:39:36.540082Z"},"content_sha256":"87c8207648a0662f57216615daf44558829fb7559d23546f828759f4ee495895","schema_version":"1.0","event_id":"sha256:87c8207648a0662f57216615daf44558829fb7559d23546f828759f4ee495895"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3H7S7HMUO6CJZRF455LFACONK3/bundle.json","state_url":"https://pith.science/pith/3H7S7HMUO6CJZRF455LFACONK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3H7S7HMUO6CJZRF455LFACONK3/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":"2026-05-27T22:39:36Z","links":{"resolver":"https://pith.science/pith/3H7S7HMUO6CJZRF455LFACONK3","bundle":"https://pith.science/pith/3H7S7HMUO6CJZRF455LFACONK3/bundle.json","state":"https://pith.science/pith/3H7S7HMUO6CJZRF455LFACONK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3H7S7HMUO6CJZRF455LFACONK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3H7S7HMUO6CJZRF455LFACONK3","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":"b6bb9e4126c56828c9683ced6726ee3dbf644adc9e2f3b3f55db039e08b4450b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-04-02T20:50:22Z","title_canon_sha256":"f4afb924d9a3e9a97ddf579a8a5acee871f85e5c34a2882465d1e96a779a2f12"},"schema_version":"1.0","source":{"id":"1404.0703","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0703","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0703v7","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0703","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"3H7S7HMUO6CJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3H7S7HMUO6CJZRF4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3H7S7HMU","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:87c8207648a0662f57216615daf44558829fb7559d23546f828759f4ee495895","target":"graph","created_at":"2026-05-18T00:54:09Z","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 present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as beyond worst-case results. The framework allows us to prove results for data stored in Btrees, multidimensional data structures, and even multiple indices per table. A key idea in our framework is formalizing the inference one does with an ","authors_text":"Atri Rudra, Christopher R\\'e, Hung Q. Ngo, Mahmoud Abo Khamis","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-04-02T20:50:22Z","title":"Joins via Geometric Resolutions: Worst-case and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0703","kind":"arxiv","version":7},"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":"sha256:0dfb0f838c780f938ef321475a895adf6fd0d862e6cec0a24418141c3bc33b66","target":"record","created_at":"2026-05-18T00:54:09Z","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":"b6bb9e4126c56828c9683ced6726ee3dbf644adc9e2f3b3f55db039e08b4450b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-04-02T20:50:22Z","title_canon_sha256":"f4afb924d9a3e9a97ddf579a8a5acee871f85e5c34a2882465d1e96a779a2f12"},"schema_version":"1.0","source":{"id":"1404.0703","kind":"arxiv","version":7}},"canonical_sha256":"d9ff2f9d9477849cc4bcef565009cd56cf1918aa92b8062cabf9a2ff45bb1aa7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9ff2f9d9477849cc4bcef565009cd56cf1918aa92b8062cabf9a2ff45bb1aa7","first_computed_at":"2026-05-18T00:54:09.167427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:09.167427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g8moQT/qUOj+vfRo5Crh+GWh8emOe1c7UxeIjZvlMsiq+V7crptAjdxz8uv1Mha6ySEiUIgNf9hmTwlBsrMYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:09.167986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0703","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dfb0f838c780f938ef321475a895adf6fd0d862e6cec0a24418141c3bc33b66","sha256:87c8207648a0662f57216615daf44558829fb7559d23546f828759f4ee495895"],"state_sha256":"248159a43885bff592b8f7732261fce963b11acdd340ac350d4a1a2f7b995659"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yBgaUBpa2odtbcfB0UcHRmrHRNCBNg4iN9WHindZ3XisxMjOujRD2GIl2JTY35pSIbhcMN0mzobbnOCtWEGfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:39:36.543096Z","bundle_sha256":"bb92fc5633cf0dbfbae8a664f7886359bf5b78b5885777edb7257ec11fd95a24"}}