{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2NZHM56UKTNJNK6GKEDBXRQ3XS","short_pith_number":"pith:2NZHM56U","canonical_record":{"source":{"id":"1503.06857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2015-03-23T21:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"4645d1a7c14cd11e49339a3b6d8e4bb12b8e800663c49a3cb319ecce24bb2e68","abstract_canon_sha256":"86b14b5bb91774c160f28f0072fef0f190187072f1b361ca00de02624326c600"},"schema_version":"1.0"},"canonical_sha256":"d3727677d454da96abc651061bc61bbc9a67511a393f45f459400c3b6b23c22f","source":{"kind":"arxiv","id":"1503.06857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06857","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06857v1","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06857","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"2NZHM56UKTNJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NZHM56UKTNJNK6G","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NZHM56U","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2NZHM56UKTNJNK6GKEDBXRQ3XS","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2015-03-23T21:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"4645d1a7c14cd11e49339a3b6d8e4bb12b8e800663c49a3cb319ecce24bb2e68","abstract_canon_sha256":"86b14b5bb91774c160f28f0072fef0f190187072f1b361ca00de02624326c600"},"schema_version":"1.0"},"canonical_sha256":"d3727677d454da96abc651061bc61bbc9a67511a393f45f459400c3b6b23c22f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.920801Z","signature_b64":"5pYhLX7ZNZr3/W3IWcL1kv6b9kFc2xxi7+YdtuhtzRpiXH5X68FByMatsQZcr4qxs/rL7WFt/F5+3eGq2Gn/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3727677d454da96abc651061bc61bbc9a67511a393f45f459400c3b6b23c22f","last_reissued_at":"2026-05-18T02:20:29.920385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.920385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06857","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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1NiB39mNCa7AaUze5Fho2lNg8p7zf7P9AEEXY5QSoOQLCw/uSA7h8PE5tPrCh2n8XtxKVENqSZQN6rG3zx3hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:49:43.778952Z"},"content_sha256":"23d75bd47a23b56017824fef7a71cb8c112202e82bcb8b057d1b0a59f17d8d95","schema_version":"1.0","event_id":"sha256:23d75bd47a23b56017824fef7a71cb8c112202e82bcb8b057d1b0a59f17d8d95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2NZHM56UKTNJNK6GKEDBXRQ3XS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loop-Free Backpressure Routing Using Link-Reversal Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NI","authors_text":"Anurag Rai, Chih-ping Li, Eytan Modiano, Georgios Paschos","submitted_at":"2015-03-23T21:58:58Z","abstract_excerpt":"The backpressure routing policy is known to be a throughput optimal policy that supports any feasible traffic demand in data networks, but may have poor delay performance when packets traverse loops in the network. In this paper, we study loop-free backpressure routing policies that forward packets along directed acyclic graphs (DAGs) to avoid the looping problem. These policies use link reversal algorithms to improve the DAGs in order to support any achievable traffic demand.\n  For a network with a single commodity, we show that a DAG that supports a given traffic demand can be found after a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06857","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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7micgF+tEQVdd1sEINg2CWhTxtBFpwTUnNHjGZ7Hv3zRBt8NjyDeJ011B6njZtFQjUqsdURXAFIO+UTQRYClCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:49:43.779615Z"},"content_sha256":"cae8b89b5c3d47bdd57af4e02a2108f868da424f5bb1fce293dd90ba60b7f47f","schema_version":"1.0","event_id":"sha256:cae8b89b5c3d47bdd57af4e02a2108f868da424f5bb1fce293dd90ba60b7f47f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/bundle.json","state_url":"https://pith.science/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/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":"2026-05-28T15:49:43Z","links":{"resolver":"https://pith.science/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS","bundle":"https://pith.science/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/bundle.json","state":"https://pith.science/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NZHM56UKTNJNK6GKEDBXRQ3XS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NZHM56UKTNJNK6GKEDBXRQ3XS","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":"86b14b5bb91774c160f28f0072fef0f190187072f1b361ca00de02624326c600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2015-03-23T21:58:58Z","title_canon_sha256":"4645d1a7c14cd11e49339a3b6d8e4bb12b8e800663c49a3cb319ecce24bb2e68"},"schema_version":"1.0","source":{"id":"1503.06857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06857","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06857v1","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06857","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"2NZHM56UKTNJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NZHM56UKTNJNK6G","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NZHM56U","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:cae8b89b5c3d47bdd57af4e02a2108f868da424f5bb1fce293dd90ba60b7f47f","target":"graph","created_at":"2026-05-18T02:20:29Z","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 backpressure routing policy is known to be a throughput optimal policy that supports any feasible traffic demand in data networks, but may have poor delay performance when packets traverse loops in the network. In this paper, we study loop-free backpressure routing policies that forward packets along directed acyclic graphs (DAGs) to avoid the looping problem. These policies use link reversal algorithms to improve the DAGs in order to support any achievable traffic demand.\n  For a network with a single commodity, we show that a DAG that supports a given traffic demand can be found after a ","authors_text":"Anurag Rai, Chih-ping Li, Eytan Modiano, Georgios Paschos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2015-03-23T21:58:58Z","title":"Loop-Free Backpressure Routing Using Link-Reversal Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06857","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":"sha256:23d75bd47a23b56017824fef7a71cb8c112202e82bcb8b057d1b0a59f17d8d95","target":"record","created_at":"2026-05-18T02:20:29Z","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":"86b14b5bb91774c160f28f0072fef0f190187072f1b361ca00de02624326c600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2015-03-23T21:58:58Z","title_canon_sha256":"4645d1a7c14cd11e49339a3b6d8e4bb12b8e800663c49a3cb319ecce24bb2e68"},"schema_version":"1.0","source":{"id":"1503.06857","kind":"arxiv","version":1}},"canonical_sha256":"d3727677d454da96abc651061bc61bbc9a67511a393f45f459400c3b6b23c22f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3727677d454da96abc651061bc61bbc9a67511a393f45f459400c3b6b23c22f","first_computed_at":"2026-05-18T02:20:29.920385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:29.920385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5pYhLX7ZNZr3/W3IWcL1kv6b9kFc2xxi7+YdtuhtzRpiXH5X68FByMatsQZcr4qxs/rL7WFt/F5+3eGq2Gn/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:29.920801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23d75bd47a23b56017824fef7a71cb8c112202e82bcb8b057d1b0a59f17d8d95","sha256:cae8b89b5c3d47bdd57af4e02a2108f868da424f5bb1fce293dd90ba60b7f47f"],"state_sha256":"b6e2ff0215e6e420c224a6b674953e36b34360c53479ff598fad0eb294fa5eb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BTcG14zhQLoqQ0j6GoDfsYItdmPrxFd8+Zc90cyLXXMiKGpeN5KeMtbLSBzAe2oMJPzX5zJmbQvB5bl0JhjRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:49:43.782628Z","bundle_sha256":"e311469ffe7354cb0ac493eb19635895737da1af2517479f253a746cd8290d86"}}