{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MKBUPRBIVFMN23TFJ4OLKC6ESV","short_pith_number":"pith:MKBUPRBI","canonical_record":{"source":{"id":"1602.08290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2016-02-26T12:09:03Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"5c26df799bd1180e3cc59ce86e98cbe87ad074fd0107f9fd97fbe0d727ac710d","abstract_canon_sha256":"7765fbe2b2fa33f01c058ca5c5e01e4ffcf27a68b09ce206fb84ecc4cfdbbe62"},"schema_version":"1.0"},"canonical_sha256":"628347c428a958dd6e654f1cb50bc495608c961e68257fbb80dc9b4bd6c46026","source":{"kind":"arxiv","id":"1602.08290","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08290","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08290v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08290","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"MKBUPRBIVFMN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKBUPRBIVFMN23TF","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKBUPRBI","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MKBUPRBIVFMN23TFJ4OLKC6ESV","target":"record","payload":{"canonical_record":{"source":{"id":"1602.08290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2016-02-26T12:09:03Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"5c26df799bd1180e3cc59ce86e98cbe87ad074fd0107f9fd97fbe0d727ac710d","abstract_canon_sha256":"7765fbe2b2fa33f01c058ca5c5e01e4ffcf27a68b09ce206fb84ecc4cfdbbe62"},"schema_version":"1.0"},"canonical_sha256":"628347c428a958dd6e654f1cb50bc495608c961e68257fbb80dc9b4bd6c46026","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:49.560488Z","signature_b64":"vV3risZTuDNHW1z571Lp88XZRgull6e4eHOlRMOScYdKABRYQVUnScBIXVV5jaGGpFY2DzJkieRIpyHjPK1MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"628347c428a958dd6e654f1cb50bc495608c961e68257fbb80dc9b4bd6c46026","last_reissued_at":"2026-05-18T00:46:49.559828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:49.559828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.08290","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":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKwIODrAwWm7o36oTtLQZq2AxzdOoeEIqzQuBbb/Yky6cIvBMa5ZVtKAkmCjr84V92DQ8BNeCIUqe+DI8j2wDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:02:54.884642Z"},"content_sha256":"25eda792ac25451358801742801700a26130447c3427d55796a63c0e140a8292","schema_version":"1.0","event_id":"sha256:25eda792ac25451358801742801700a26130447c3427d55796a63c0e140a8292"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MKBUPRBIVFMN23TFJ4OLKC6ESV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit back-off rates for achieving target throughputs in CSMA/CA networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.NI","authors_text":"Benny Van Houdt","submitted_at":"2016-02-26T12:09:03Z","abstract_excerpt":"CSMA/CA networks have often been analyzed using a stylized model that is fully characterized by a vector of back-off rates and a conflict graph. Further, for any achievable throughput vector $\\vec \\theta$ the existence of a unique vector $\\vec \\nu(\\vec \\theta)$ of back-off rates that achieves this throughput vector was proven. Although this unique vector can in principle be computed iteratively, the required time complexity grows exponentially in the network size, making this only feasible for small networks.\n  In this paper, we present an explicit formula for the unique vector of back-off rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08290","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":"2026-05-18T00:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4BT9RyrseIFl+1z3Ttm9ZGKRwG9lbrOHyo4OFkD0eRI1n6XOonmP/kllcXJQOGqWZqAaZTlhDcPu1Mfz5BSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:02:54.884985Z"},"content_sha256":"44e0c769f6278de0617f15bf0c9af19da6af899b51931c96ded90a54c1e84460","schema_version":"1.0","event_id":"sha256:44e0c769f6278de0617f15bf0c9af19da6af899b51931c96ded90a54c1e84460"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/bundle.json","state_url":"https://pith.science/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/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":"2026-07-01T21:02:54Z","links":{"resolver":"https://pith.science/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV","bundle":"https://pith.science/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/bundle.json","state":"https://pith.science/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKBUPRBIVFMN23TFJ4OLKC6ESV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MKBUPRBIVFMN23TFJ4OLKC6ESV","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":"7765fbe2b2fa33f01c058ca5c5e01e4ffcf27a68b09ce206fb84ecc4cfdbbe62","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2016-02-26T12:09:03Z","title_canon_sha256":"5c26df799bd1180e3cc59ce86e98cbe87ad074fd0107f9fd97fbe0d727ac710d"},"schema_version":"1.0","source":{"id":"1602.08290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08290","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08290v2","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08290","created_at":"2026-05-18T00:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"MKBUPRBIVFMN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKBUPRBIVFMN23TF","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKBUPRBI","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:44e0c769f6278de0617f15bf0c9af19da6af899b51931c96ded90a54c1e84460","target":"graph","created_at":"2026-05-18T00:46:49Z","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":"CSMA/CA networks have often been analyzed using a stylized model that is fully characterized by a vector of back-off rates and a conflict graph. Further, for any achievable throughput vector $\\vec \\theta$ the existence of a unique vector $\\vec \\nu(\\vec \\theta)$ of back-off rates that achieves this throughput vector was proven. Although this unique vector can in principle be computed iteratively, the required time complexity grows exponentially in the network size, making this only feasible for small networks.\n  In this paper, we present an explicit formula for the unique vector of back-off rat","authors_text":"Benny Van Houdt","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2016-02-26T12:09:03Z","title":"Explicit back-off rates for achieving target throughputs in CSMA/CA networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08290","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":"sha256:25eda792ac25451358801742801700a26130447c3427d55796a63c0e140a8292","target":"record","created_at":"2026-05-18T00:46:49Z","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":"7765fbe2b2fa33f01c058ca5c5e01e4ffcf27a68b09ce206fb84ecc4cfdbbe62","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2016-02-26T12:09:03Z","title_canon_sha256":"5c26df799bd1180e3cc59ce86e98cbe87ad074fd0107f9fd97fbe0d727ac710d"},"schema_version":"1.0","source":{"id":"1602.08290","kind":"arxiv","version":2}},"canonical_sha256":"628347c428a958dd6e654f1cb50bc495608c961e68257fbb80dc9b4bd6c46026","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"628347c428a958dd6e654f1cb50bc495608c961e68257fbb80dc9b4bd6c46026","first_computed_at":"2026-05-18T00:46:49.559828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:49.559828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vV3risZTuDNHW1z571Lp88XZRgull6e4eHOlRMOScYdKABRYQVUnScBIXVV5jaGGpFY2DzJkieRIpyHjPK1MAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:49.560488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25eda792ac25451358801742801700a26130447c3427d55796a63c0e140a8292","sha256:44e0c769f6278de0617f15bf0c9af19da6af899b51931c96ded90a54c1e84460"],"state_sha256":"800e1fe15d885e368a9c8e7e0c7f4a0679e5f5e42f953d446b2f7654d253009e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YijB9stwJJVWkJoB5W9hDftsm8XAF5Wng0uObOixHhK9ItJtyjHytmLDaYSb/zX0T9oBQZrLGSGRqu16QBJmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:02:54.886976Z","bundle_sha256":"88311f33b88fa39eae85f2dcd3a3f147d277983c0f7f3d56cb68161519f12e4a"}}