{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M2ZYUWQUSTLHR64Q7Y4WHWOX4R","short_pith_number":"pith:M2ZYUWQU","canonical_record":{"source":{"id":"1411.7631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-27T15:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"3154b0bcd35dcd56625fa90839c0d6570428917f25ed4a4df2f861aea08dceb8","abstract_canon_sha256":"c847bfde1f22f7a50a086a299a7a6df040d19cfe415720febc74e97bea3ef8c1"},"schema_version":"1.0"},"canonical_sha256":"66b38a5a1494d678fb90fe3963d9d7e47fe15f19a5fa4751893b89c1972f1be3","source":{"kind":"arxiv","id":"1411.7631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7631","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7631v2","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7631","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"pith_short_12","alias_value":"M2ZYUWQUSTLH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M2ZYUWQUSTLHR64Q","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M2ZYUWQU","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M2ZYUWQUSTLHR64Q7Y4WHWOX4R","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-27T15:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"3154b0bcd35dcd56625fa90839c0d6570428917f25ed4a4df2f861aea08dceb8","abstract_canon_sha256":"c847bfde1f22f7a50a086a299a7a6df040d19cfe415720febc74e97bea3ef8c1"},"schema_version":"1.0"},"canonical_sha256":"66b38a5a1494d678fb90fe3963d9d7e47fe15f19a5fa4751893b89c1972f1be3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:50.441813Z","signature_b64":"5Atp6WWINidiBDibGzSU9jHqOK+hNNGLDYMOs7cHR9ir483hOd9WQD+MaCZDbRUeL1c8vp+mD2ekIlJjGWDSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66b38a5a1494d678fb90fe3963d9d7e47fe15f19a5fa4751893b89c1972f1be3","last_reissued_at":"2026-05-18T01:26:50.441162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:50.441162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7631","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":"2026-05-18T01:26:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zG6lgTfRHKHP889Qd98GcedmeMOlHJssT3x+EL08b2J7/t7+/QJ31j1lhD42QUMW9N/UAXorrJ9gRQHlf7oMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:11:45.240879Z"},"content_sha256":"b629ec6525fe4fc38d7bd603d012ff3a8df08c683be8734eac20ba9911a68360","schema_version":"1.0","event_id":"sha256:b629ec6525fe4fc38d7bd603d012ff3a8df08c683be8734eac20ba9911a68360"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M2ZYUWQUSTLHR64Q7Y4WHWOX4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Undirected Maximum Flows in O(m polylog(n)) Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Richard Peng","submitted_at":"2014-11-27T15:48:55Z","abstract_excerpt":"We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for these two problems recursively while gradually incorporating size reductions. These size reductions are in turn obtained via ultra-sparsifiers, which are key tools in solvers for symmetric diagonally dominant (SDD) linear systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7631","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":"2026-05-18T01:26:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OiGNXECkTUAYRZ1SToDErL4x3787hyyYxTqMRjfhZJJhT3ZlLWmqm8756ZR2FOvjTDZea0DB3E56MmufeoTwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:11:45.241556Z"},"content_sha256":"50057c6014cd6db7652677a6f9b9969991949461346cfcae65e52bb776d790ef","schema_version":"1.0","event_id":"sha256:50057c6014cd6db7652677a6f9b9969991949461346cfcae65e52bb776d790ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/bundle.json","state_url":"https://pith.science/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/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":"2026-05-27T13:11:45Z","links":{"resolver":"https://pith.science/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R","bundle":"https://pith.science/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/bundle.json","state":"https://pith.science/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2ZYUWQUSTLHR64Q7Y4WHWOX4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M2ZYUWQUSTLHR64Q7Y4WHWOX4R","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":"c847bfde1f22f7a50a086a299a7a6df040d19cfe415720febc74e97bea3ef8c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-27T15:48:55Z","title_canon_sha256":"3154b0bcd35dcd56625fa90839c0d6570428917f25ed4a4df2f861aea08dceb8"},"schema_version":"1.0","source":{"id":"1411.7631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7631","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7631v2","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7631","created_at":"2026-05-18T01:26:50Z"},{"alias_kind":"pith_short_12","alias_value":"M2ZYUWQUSTLH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M2ZYUWQUSTLHR64Q","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M2ZYUWQU","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:50057c6014cd6db7652677a6f9b9969991949461346cfcae65e52bb776d790ef","target":"graph","created_at":"2026-05-18T01:26:50Z","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 give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for these two problems recursively while gradually incorporating size reductions. These size reductions are in turn obtained via ultra-sparsifiers, which are key tools in solvers for symmetric diagonally dominant (SDD) linear systems.","authors_text":"Richard Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-27T15:48:55Z","title":"Approximate Undirected Maximum Flows in O(m polylog(n)) Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7631","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:b629ec6525fe4fc38d7bd603d012ff3a8df08c683be8734eac20ba9911a68360","target":"record","created_at":"2026-05-18T01:26:50Z","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":"c847bfde1f22f7a50a086a299a7a6df040d19cfe415720febc74e97bea3ef8c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-27T15:48:55Z","title_canon_sha256":"3154b0bcd35dcd56625fa90839c0d6570428917f25ed4a4df2f861aea08dceb8"},"schema_version":"1.0","source":{"id":"1411.7631","kind":"arxiv","version":2}},"canonical_sha256":"66b38a5a1494d678fb90fe3963d9d7e47fe15f19a5fa4751893b89c1972f1be3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66b38a5a1494d678fb90fe3963d9d7e47fe15f19a5fa4751893b89c1972f1be3","first_computed_at":"2026-05-18T01:26:50.441162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:50.441162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Atp6WWINidiBDibGzSU9jHqOK+hNNGLDYMOs7cHR9ir483hOd9WQD+MaCZDbRUeL1c8vp+mD2ekIlJjGWDSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:50.441813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b629ec6525fe4fc38d7bd603d012ff3a8df08c683be8734eac20ba9911a68360","sha256:50057c6014cd6db7652677a6f9b9969991949461346cfcae65e52bb776d790ef"],"state_sha256":"11aa643479c34145fa5663a8341a618d86706eeb7aee8b085283f4799e570bce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"smqAaN1w2BiNo9IQA9k2JYj+piKKWVY+Gs+Kw6Ai0ufqHXLGZ+ws6nTCTAiFzLGFVWxqjKeHdpuB2B5M6f4hBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:11:45.245283Z","bundle_sha256":"05f5dbc1c12c41714f0a2dd1d3e316b930a74ea5571c97b9a426da5ade55c7f2"}}