{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6NCQHHLXND6AWWOEPSSVMNR2R6","short_pith_number":"pith:6NCQHHLX","canonical_record":{"source":{"id":"1608.06545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T15:26:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"92ff877bf51076289f516d10f8c85f0b8e908c86b3acc1efd3da3c9a2703777a","abstract_canon_sha256":"97e7f9eaa1c068ff63b441110663a7b8e4c5f54fc3a94fee7f35b9520aee9da6"},"schema_version":"1.0"},"canonical_sha256":"f345039d7768fc0b59c47ca556363a8f960c2876852a9e59535f9877ddcbe835","source":{"kind":"arxiv","id":"1608.06545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06545","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06545v1","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06545","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"6NCQHHLXND6A","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6NCQHHLXND6AWWOE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6NCQHHLX","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6NCQHHLXND6AWWOEPSSVMNR2R6","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T15:26:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"92ff877bf51076289f516d10f8c85f0b8e908c86b3acc1efd3da3c9a2703777a","abstract_canon_sha256":"97e7f9eaa1c068ff63b441110663a7b8e4c5f54fc3a94fee7f35b9520aee9da6"},"schema_version":"1.0"},"canonical_sha256":"f345039d7768fc0b59c47ca556363a8f960c2876852a9e59535f9877ddcbe835","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:13.814402Z","signature_b64":"WF8BUy3qUxhOdbfDfxm9xinTi0ulFnxy8wtDipDB82PVrXFIfY7e24HvFg/gAS/Igs9hTktS7SmGg3UACW+oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f345039d7768fc0b59c47ca556363a8f960c2876852a9e59535f9877ddcbe835","last_reissued_at":"2026-05-18T01:08:13.813955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:13.813955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06545","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":"2026-05-18T01:08:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6dy8wIKqqKrmeQJQL19T+YY0APcUBKtj53D15/llyLSCOwQ/ICOGpZDBsDcT9nf8nc3SH+9UnvHKYNnKaczAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:04:55.060788Z"},"content_sha256":"99c09575de646916cccd4181b358a6dc913f30dc6a5a71f03474d1e73593aab3","schema_version":"1.0","event_id":"sha256:99c09575de646916cccd4181b358a6dc913f30dc6a5a71f03474d1e73593aab3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6NCQHHLXND6AWWOEPSSVMNR2R6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Network coding in undirected graphs is either very helpful or not helpful at all","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ariel Schvartzman, Mark Braverman, Sumegha Garg","submitted_at":"2016-08-23T15:26:34Z","abstract_excerpt":"While it is known that using network coding can significantly improve the throughput of directed networks, it is a notorious open problem whether coding yields any advantage over the multicommodity flow (MCF) rate in undirected networks. It was conjectured by Li and Li (2004) that the answer is \"no\". In this paper we show that even a small advantage over MCF can be amplified to yield a near-maximum possible gap.\n  We prove that any undirected network with $k$ source-sink pairs that exhibits a $(1+\\varepsilon)$ gap between its MCF rate and its network coding rate can be used to construct a fami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06545","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":"2026-05-18T01:08:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mkDwiZU8GgIDkhwd4vkM/Xt14byh5+f9ptXx9qcB83IzkCDMMkkkIC6B4RITOhSwKKXF6Gq0G+a8KPIl84cBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:04:55.061455Z"},"content_sha256":"5721a6edd7299bdae2557e72934ad270f467236d2c7adb6e794665e1ae0d3297","schema_version":"1.0","event_id":"sha256:5721a6edd7299bdae2557e72934ad270f467236d2c7adb6e794665e1ae0d3297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/bundle.json","state_url":"https://pith.science/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/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":"2026-06-11T23:04:55Z","links":{"resolver":"https://pith.science/pith/6NCQHHLXND6AWWOEPSSVMNR2R6","bundle":"https://pith.science/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/bundle.json","state":"https://pith.science/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NCQHHLXND6AWWOEPSSVMNR2R6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6NCQHHLXND6AWWOEPSSVMNR2R6","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":"97e7f9eaa1c068ff63b441110663a7b8e4c5f54fc3a94fee7f35b9520aee9da6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T15:26:34Z","title_canon_sha256":"92ff877bf51076289f516d10f8c85f0b8e908c86b3acc1efd3da3c9a2703777a"},"schema_version":"1.0","source":{"id":"1608.06545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06545","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06545v1","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06545","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"6NCQHHLXND6A","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6NCQHHLXND6AWWOE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6NCQHHLX","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:5721a6edd7299bdae2557e72934ad270f467236d2c7adb6e794665e1ae0d3297","target":"graph","created_at":"2026-05-18T01:08:13Z","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":"While it is known that using network coding can significantly improve the throughput of directed networks, it is a notorious open problem whether coding yields any advantage over the multicommodity flow (MCF) rate in undirected networks. It was conjectured by Li and Li (2004) that the answer is \"no\". In this paper we show that even a small advantage over MCF can be amplified to yield a near-maximum possible gap.\n  We prove that any undirected network with $k$ source-sink pairs that exhibits a $(1+\\varepsilon)$ gap between its MCF rate and its network coding rate can be used to construct a fami","authors_text":"Ariel Schvartzman, Mark Braverman, Sumegha Garg","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T15:26:34Z","title":"Network coding in undirected graphs is either very helpful or not helpful at all"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06545","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":"sha256:99c09575de646916cccd4181b358a6dc913f30dc6a5a71f03474d1e73593aab3","target":"record","created_at":"2026-05-18T01:08:13Z","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":"97e7f9eaa1c068ff63b441110663a7b8e4c5f54fc3a94fee7f35b9520aee9da6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-23T15:26:34Z","title_canon_sha256":"92ff877bf51076289f516d10f8c85f0b8e908c86b3acc1efd3da3c9a2703777a"},"schema_version":"1.0","source":{"id":"1608.06545","kind":"arxiv","version":1}},"canonical_sha256":"f345039d7768fc0b59c47ca556363a8f960c2876852a9e59535f9877ddcbe835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f345039d7768fc0b59c47ca556363a8f960c2876852a9e59535f9877ddcbe835","first_computed_at":"2026-05-18T01:08:13.813955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:13.813955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WF8BUy3qUxhOdbfDfxm9xinTi0ulFnxy8wtDipDB82PVrXFIfY7e24HvFg/gAS/Igs9hTktS7SmGg3UACW+oAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:13.814402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99c09575de646916cccd4181b358a6dc913f30dc6a5a71f03474d1e73593aab3","sha256:5721a6edd7299bdae2557e72934ad270f467236d2c7adb6e794665e1ae0d3297"],"state_sha256":"ef5ce05cdc1457b909e23db9cce8767d1c2cd038c9d171dc99bc9780768a24f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKpzEwlk3MQXDT+f2ojOQuXbjLFhRDNoYIvh9Rm2CigDJ326Z6GEiZBJWQ7Kek05oTdEOKxMn04B4Pd08V3XDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:04:55.066216Z","bundle_sha256":"9aa3fbded4f4e6fb93a17a482bbb284875407790230174121b6196d77ad702ae"}}