{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TN2FCZKXK4IBP4ACL3ESDNZWJI","short_pith_number":"pith:TN2FCZKX","canonical_record":{"source":{"id":"1609.08723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"97b4583aef747376c653ea8b156deae80e4941fe0c90de6f7597756f504ffd52","abstract_canon_sha256":"fd67ba2069b3572c4a3468da19f24a7be40a7bde886f92568c83127169208621"},"schema_version":"1.0"},"canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","source":{"kind":"arxiv","id":"1609.08723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08723","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08723v1","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08723","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"TN2FCZKXK4IB","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TN2FCZKXK4IBP4AC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TN2FCZKX","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TN2FCZKXK4IBP4ACL3ESDNZWJI","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"97b4583aef747376c653ea8b156deae80e4941fe0c90de6f7597756f504ffd52","abstract_canon_sha256":"fd67ba2069b3572c4a3468da19f24a7be40a7bde886f92568c83127169208621"},"schema_version":"1.0"},"canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:42.095718Z","signature_b64":"YqRy7+MV1bJtX0I2OeaKeJoCH5eH6KqnHC+XX4DDVRWgspHXpzF/O1m8VOjOfRUZ/rL4HgmF2U1QPHUH+apVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","last_reissued_at":"2026-05-18T01:03:42.095261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:42.095261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08723","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":"2026-05-18T01:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAe11FO/xgjl5E0X3o/UyM0xr5ru8lLfhmHgll7dTbwrKL60upvTH/mpSHkNHm6037ernOhNVQdtdDeKcq94CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:15:03.744299Z"},"content_sha256":"0a4da27b2bb26e95491ab91b8688d24478d1cb58185291868b96d3ffbcafe9ac","schema_version":"1.0","event_id":"sha256:0a4da27b2bb26e95491ab91b8688d24478d1cb58185291868b96d3ffbcafe9ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TN2FCZKXK4IBP4ACL3ESDNZWJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cut Tree Construction from Massive Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.DS","authors_text":"Naoto Mizuno, Takuya Akiba, Yoichi Iwata, Yosuke Sameshima, Yosuke Yano","submitted_at":"2016-09-28T01:49:46Z","abstract_excerpt":"The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08723","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":"2026-05-18T01:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfhttutz4CW2ABVOG7vkeCf0oF8hdiEIrkGi0EG7b1yEN2kmcbm+aH7CiBTyT918AbgvRF12OPVp4Tb6/bELCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:15:03.744708Z"},"content_sha256":"91f74e425c24ae4432fa25b8f9b600d25559c6ceb67bf81ba29593a11575699c","schema_version":"1.0","event_id":"sha256:91f74e425c24ae4432fa25b8f9b600d25559c6ceb67bf81ba29593a11575699c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/bundle.json","state_url":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/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":"2026-05-30T07:15:03Z","links":{"resolver":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI","bundle":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/bundle.json","state":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TN2FCZKXK4IBP4ACL3ESDNZWJI","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":"fd67ba2069b3572c4a3468da19f24a7be40a7bde886f92568c83127169208621","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","title_canon_sha256":"97b4583aef747376c653ea8b156deae80e4941fe0c90de6f7597756f504ffd52"},"schema_version":"1.0","source":{"id":"1609.08723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08723","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08723v1","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08723","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"TN2FCZKXK4IB","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TN2FCZKXK4IBP4AC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TN2FCZKX","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:91f74e425c24ae4432fa25b8f9b600d25559c6ceb67bf81ba29593a11575699c","target":"graph","created_at":"2026-05-18T01:03:42Z","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":"The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach re","authors_text":"Naoto Mizuno, Takuya Akiba, Yoichi Iwata, Yosuke Sameshima, Yosuke Yano","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","title":"Cut Tree Construction from Massive Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08723","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":"sha256:0a4da27b2bb26e95491ab91b8688d24478d1cb58185291868b96d3ffbcafe9ac","target":"record","created_at":"2026-05-18T01:03:42Z","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":"fd67ba2069b3572c4a3468da19f24a7be40a7bde886f92568c83127169208621","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","title_canon_sha256":"97b4583aef747376c653ea8b156deae80e4941fe0c90de6f7597756f504ffd52"},"schema_version":"1.0","source":{"id":"1609.08723","kind":"arxiv","version":1}},"canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","first_computed_at":"2026-05-18T01:03:42.095261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:42.095261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YqRy7+MV1bJtX0I2OeaKeJoCH5eH6KqnHC+XX4DDVRWgspHXpzF/O1m8VOjOfRUZ/rL4HgmF2U1QPHUH+apVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:42.095718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a4da27b2bb26e95491ab91b8688d24478d1cb58185291868b96d3ffbcafe9ac","sha256:91f74e425c24ae4432fa25b8f9b600d25559c6ceb67bf81ba29593a11575699c"],"state_sha256":"deeb79c3ad3b4de1bee560de6775b74a27034dec25ae525128c847d899b0cdb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IeFP4aAbBlbQLx/8XLUa49d6GcT9m6mQJG2HiIlb1PeZq/S1vTjMJDs7/2M7mbRLRpeYi788PqUFb8d5OlqTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:15:03.746948Z","bundle_sha256":"838324d7133916d76dc393a33e42f6201f3177ba117238422bafb521a0671625"}}