{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KNIK5JDYAIUFXXRXKGIUGV5FGF","short_pith_number":"pith:KNIK5JDY","canonical_record":{"source":{"id":"1901.09885","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-28T18:58:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ae0f67b35284c47f0e2a0c2e49cf4ed29bd3cdc13245cbebb0bb8dafa202b287","abstract_canon_sha256":"f9670a8bf13d81963fc78336fa459ec20174f0be2df513d2533e6da8e415bf8a"},"schema_version":"1.0"},"canonical_sha256":"5350aea47802285bde3751914357a5315d57ef71d5e471a41e108be11ceabcf7","source":{"kind":"arxiv","id":"1901.09885","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09885","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09885v2","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09885","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_12","alias_value":"KNIK5JDYAIUF","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_16","alias_value":"KNIK5JDYAIUFXXRX","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_8","alias_value":"KNIK5JDY","created_at":"2026-07-05T00:14:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KNIK5JDYAIUFXXRXKGIUGV5FGF","target":"record","payload":{"canonical_record":{"source":{"id":"1901.09885","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-28T18:58:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ae0f67b35284c47f0e2a0c2e49cf4ed29bd3cdc13245cbebb0bb8dafa202b287","abstract_canon_sha256":"f9670a8bf13d81963fc78336fa459ec20174f0be2df513d2533e6da8e415bf8a"},"schema_version":"1.0"},"canonical_sha256":"5350aea47802285bde3751914357a5315d57ef71d5e471a41e108be11ceabcf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:14:43.726347Z","signature_b64":"0wUPGSLMIrIMJiKek9QbY09eD8kj/iNtDNRw+OXdsR2eQWPhXda/zYXY4WYEa1TRLs3aUKbCTEGN1njVjfn4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5350aea47802285bde3751914357a5315d57ef71d5e471a41e108be11ceabcf7","last_reissued_at":"2026-07-05T00:14:43.725929Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:14:43.725929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.09885","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":"2026-07-05T00:14:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m14UVMV5fWRicN9/avTuX0EpIE0gt9nkrvoQTf03NjfyNbXKLHmCrfFKwEpoOfgbZ4Jm7QPbFGFhmBI40pB4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:09:47.399367Z"},"content_sha256":"37e35e4c7f48b3b3f2dc0964cc8f172c5829c139945ae00bf0c7c5c075dd0a76","schema_version":"1.0","event_id":"sha256:37e35e4c7f48b3b3f2dc0964cc8f172c5829c139945ae00bf0c7c5c075dd0a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KNIK5JDYAIUFXXRXKGIUGV5FGF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards an Extremal Network Theory -- Robust GDoF Gain of Transmitter Cooperation over TIN","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Junge Wang, Syed A. Jafar, Yao-Chia Chan","submitted_at":"2019-01-28T18:58:34Z","abstract_excerpt":"Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09885","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.09885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:14:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EnIqgvvKi6/3OK8F+JJFsjx1SPIAt6Jr4yqMHfJK/3xGBt0AMQzD4Ol5HykVpeI8BJ1qREDmbvIeA2WrAPYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:09:47.400190Z"},"content_sha256":"8ac2b56071359a17e6fa48ce5c5d1b57df618966ce4ddab3c9e932e7e07f40c5","schema_version":"1.0","event_id":"sha256:8ac2b56071359a17e6fa48ce5c5d1b57df618966ce4ddab3c9e932e7e07f40c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/bundle.json","state_url":"https://pith.science/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/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":"2026-08-15T16:09:47Z","links":{"resolver":"https://pith.science/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF","bundle":"https://pith.science/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/bundle.json","state":"https://pith.science/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNIK5JDYAIUFXXRXKGIUGV5FGF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KNIK5JDYAIUFXXRXKGIUGV5FGF","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":"f9670a8bf13d81963fc78336fa459ec20174f0be2df513d2533e6da8e415bf8a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-28T18:58:34Z","title_canon_sha256":"ae0f67b35284c47f0e2a0c2e49cf4ed29bd3cdc13245cbebb0bb8dafa202b287"},"schema_version":"1.0","source":{"id":"1901.09885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09885","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09885v2","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09885","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_12","alias_value":"KNIK5JDYAIUF","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_16","alias_value":"KNIK5JDYAIUFXXRX","created_at":"2026-07-05T00:14:43Z"},{"alias_kind":"pith_short_8","alias_value":"KNIK5JDY","created_at":"2026-07-05T00:14:43Z"}],"graph_snapshots":[{"event_id":"sha256:8ac2b56071359a17e6fa48ce5c5d1b57df618966ce4ddab3c9e932e7e07f40c5","target":"graph","created_at":"2026-07-05T00:14:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1901.09885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network t","authors_text":"Junge Wang, Syed A. Jafar, Yao-Chia Chan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-28T18:58:34Z","title":"Towards an Extremal Network Theory -- Robust GDoF Gain of Transmitter Cooperation over TIN"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09885","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":"sha256:37e35e4c7f48b3b3f2dc0964cc8f172c5829c139945ae00bf0c7c5c075dd0a76","target":"record","created_at":"2026-07-05T00:14:43Z","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":"f9670a8bf13d81963fc78336fa459ec20174f0be2df513d2533e6da8e415bf8a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-28T18:58:34Z","title_canon_sha256":"ae0f67b35284c47f0e2a0c2e49cf4ed29bd3cdc13245cbebb0bb8dafa202b287"},"schema_version":"1.0","source":{"id":"1901.09885","kind":"arxiv","version":2}},"canonical_sha256":"5350aea47802285bde3751914357a5315d57ef71d5e471a41e108be11ceabcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5350aea47802285bde3751914357a5315d57ef71d5e471a41e108be11ceabcf7","first_computed_at":"2026-07-05T00:14:43.725929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:14:43.725929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wUPGSLMIrIMJiKek9QbY09eD8kj/iNtDNRw+OXdsR2eQWPhXda/zYXY4WYEa1TRLs3aUKbCTEGN1njVjfn4Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:14:43.726347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37e35e4c7f48b3b3f2dc0964cc8f172c5829c139945ae00bf0c7c5c075dd0a76","sha256:8ac2b56071359a17e6fa48ce5c5d1b57df618966ce4ddab3c9e932e7e07f40c5"],"state_sha256":"4163fa010e080dfd35dd71c6746c6244b0ea57eb033f9d0e7abfa9e4eceadd0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wzo6m2fl057GnuNoFMnSzQhAc5roVZpGLzXFnNemZb8fVZfAqqvtP8XkVF44+3Cb2M18JS4UPpMI1Hld71HBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T16:09:47.419657Z","bundle_sha256":"4a0da540a727796ff59c867c89bde12dc2461236cc8ebdaf2e7ccdf6cbcea68b"}}