{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PIYPBTBCOKKGUK5XGI5NLDN6GM","short_pith_number":"pith:PIYPBTBC","canonical_record":{"source":{"id":"1708.01632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-04T18:26:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"df22d6ab0420b0ce5886384a0e004200889936102325d358d8602e4c6642a126","abstract_canon_sha256":"bb3b57a2c70b097fb84b8d1a4f94d828f1db6e19b41aab07bdb416116b716a64"},"schema_version":"1.0"},"canonical_sha256":"7a30f0cc2272946a2bb7323ad58dbe330c7e1893040cac616e8febfca7aae227","source":{"kind":"arxiv","id":"1708.01632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01632","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01632v1","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01632","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"PIYPBTBCOKKG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PIYPBTBCOKKGUK5X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PIYPBTBC","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PIYPBTBCOKKGUK5XGI5NLDN6GM","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-04T18:26:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"df22d6ab0420b0ce5886384a0e004200889936102325d358d8602e4c6642a126","abstract_canon_sha256":"bb3b57a2c70b097fb84b8d1a4f94d828f1db6e19b41aab07bdb416116b716a64"},"schema_version":"1.0"},"canonical_sha256":"7a30f0cc2272946a2bb7323ad58dbe330c7e1893040cac616e8febfca7aae227","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:35.369394Z","signature_b64":"GneejWzPTCE6I7HPJo8D992XvTasYMR3FnzEUjAyx9f/Z4Ej5ojZyMScUcktA7zgF29VuNtjN42Nnk55eEtGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a30f0cc2272946a2bb7323ad58dbe330c7e1893040cac616e8febfca7aae227","last_reissued_at":"2026-05-18T00:38:35.368907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:35.368907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01632","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":"2026-05-18T00:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3rjJ+8lZNV4LIdl7wQPzZjQ0iSZgEwZRVwuQ4JSXKiAq/NEKfvVxAP+4pHv9r43be4+VQbFGcDxfKar8HemAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T04:26:33.473448Z"},"content_sha256":"4ba656dcf77b2ffccb9405ebf39793c5e48ef17365a667b75dd6546d208224df","schema_version":"1.0","event_id":"sha256:4ba656dcf77b2ffccb9405ebf39793c5e48ef17365a667b75dd6546d208224df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PIYPBTBCOKKGUK5XGI5NLDN6GM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization of Electrical Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Aaron Schild, Nikhil Srivastava, Satish Rao","submitted_at":"2017-08-04T18:26:03Z","abstract_excerpt":"We show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a random edge is $O(\\log^2 n)$. This is a consequence of a more general result which shows that the spectral norm of the entrywise absolute value of the transfer impedance matrix of a graph is $O(\\log^2 n)$. This result implies a simple oblivious routing scheme based on electrical flows in the case of transitive graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01632","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":"2026-05-18T00:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"saD94YkovnIIrqUZqI80iCxbqRK0sW9caN5K5ktNmoKV5BmB8jHeEMvnq2Kjbrq5m24T5aqw51KBmsm8pWi4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T04:26:33.474087Z"},"content_sha256":"39c6e0bd5d7d9b8cf5d112e4b00f9d37d763df61739e8b343b78c8b2c4cbb0e5","schema_version":"1.0","event_id":"sha256:39c6e0bd5d7d9b8cf5d112e4b00f9d37d763df61739e8b343b78c8b2c4cbb0e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/bundle.json","state_url":"https://pith.science/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/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":"2026-05-19T04:26:33Z","links":{"resolver":"https://pith.science/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM","bundle":"https://pith.science/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/bundle.json","state":"https://pith.science/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PIYPBTBCOKKGUK5XGI5NLDN6GM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PIYPBTBCOKKGUK5XGI5NLDN6GM","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":"bb3b57a2c70b097fb84b8d1a4f94d828f1db6e19b41aab07bdb416116b716a64","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-04T18:26:03Z","title_canon_sha256":"df22d6ab0420b0ce5886384a0e004200889936102325d358d8602e4c6642a126"},"schema_version":"1.0","source":{"id":"1708.01632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01632","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01632v1","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01632","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"PIYPBTBCOKKG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PIYPBTBCOKKGUK5X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PIYPBTBC","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:39c6e0bd5d7d9b8cf5d112e4b00f9d37d763df61739e8b343b78c8b2c4cbb0e5","target":"graph","created_at":"2026-05-18T00:38:35Z","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 show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a random edge is $O(\\log^2 n)$. This is a consequence of a more general result which shows that the spectral norm of the entrywise absolute value of the transfer impedance matrix of a graph is $O(\\log^2 n)$. This result implies a simple oblivious routing scheme based on electrical flows in the case of transitive graphs.","authors_text":"Aaron Schild, Nikhil Srivastava, Satish Rao","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-04T18:26:03Z","title":"Localization of Electrical Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01632","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":"sha256:4ba656dcf77b2ffccb9405ebf39793c5e48ef17365a667b75dd6546d208224df","target":"record","created_at":"2026-05-18T00:38:35Z","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":"bb3b57a2c70b097fb84b8d1a4f94d828f1db6e19b41aab07bdb416116b716a64","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-04T18:26:03Z","title_canon_sha256":"df22d6ab0420b0ce5886384a0e004200889936102325d358d8602e4c6642a126"},"schema_version":"1.0","source":{"id":"1708.01632","kind":"arxiv","version":1}},"canonical_sha256":"7a30f0cc2272946a2bb7323ad58dbe330c7e1893040cac616e8febfca7aae227","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a30f0cc2272946a2bb7323ad58dbe330c7e1893040cac616e8febfca7aae227","first_computed_at":"2026-05-18T00:38:35.368907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:35.368907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GneejWzPTCE6I7HPJo8D992XvTasYMR3FnzEUjAyx9f/Z4Ej5ojZyMScUcktA7zgF29VuNtjN42Nnk55eEtGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:35.369394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ba656dcf77b2ffccb9405ebf39793c5e48ef17365a667b75dd6546d208224df","sha256:39c6e0bd5d7d9b8cf5d112e4b00f9d37d763df61739e8b343b78c8b2c4cbb0e5"],"state_sha256":"efedb4d2e7458e38986d4d3cc243c1823134751c4d80b4843edbc4398c51cf8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sv5uwwBKB80YijRPuH+jp7xg1dNpnBmv4BkG6WQtOA1YBusI54XjAMxoab4kkf38E6joe0T0cuUmBbK99F18Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T04:26:33.476112Z","bundle_sha256":"a5cec8490ffe98c122f2f1a7dce405184f71fc101d5794f937dc0c1414c24125"}}