{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HAL7VUUPX7J25X3CJWW34IDMGY","short_pith_number":"pith:HAL7VUUP","canonical_record":{"source":{"id":"1611.08660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-26T05:35:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f7c8c3d0a1f9aff38112510047a3854fe69541d5ab611c5d12ddd438b87699fc","abstract_canon_sha256":"6cf2f119442e5eadb67c2c97880fa48f79d0fa2d803926611a1a2dd58184c188"},"schema_version":"1.0"},"canonical_sha256":"3817fad28fbfd3aedf624dadbe206c362ef2e126a10874bfb9b8d20d1aae2bac","source":{"kind":"arxiv","id":"1611.08660","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08660","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08660v1","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08660","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"HAL7VUUPX7J2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HAL7VUUPX7J25X3C","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HAL7VUUP","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HAL7VUUPX7J25X3CJWW34IDMGY","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-26T05:35:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f7c8c3d0a1f9aff38112510047a3854fe69541d5ab611c5d12ddd438b87699fc","abstract_canon_sha256":"6cf2f119442e5eadb67c2c97880fa48f79d0fa2d803926611a1a2dd58184c188"},"schema_version":"1.0"},"canonical_sha256":"3817fad28fbfd3aedf624dadbe206c362ef2e126a10874bfb9b8d20d1aae2bac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:31.492457Z","signature_b64":"UFaTQuCS9CPwPtXgJdctUDq+s8/BF8hD//sAOMkjE4Xj2suASRkvtLBq6zeqvEk3W8OAybM9bl6pyGzAS9Q6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3817fad28fbfd3aedf624dadbe206c362ef2e126a10874bfb9b8d20d1aae2bac","last_reissued_at":"2026-05-18T00:31:31.491746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:31.491746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08660","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":"2026-05-18T00:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NV5Y0O2lQGgcMWvmiAtn25p6NDb/F0VIkZbVCwm55CbTMd3voWoZYRQ9LpbctZy80GH7CEEU5VPJU6YNeli7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:03:22.748711Z"},"content_sha256":"fac75e05d643bf28866e8dfc6923b02eb619de8dee983f6821b9a65ea46a1679","schema_version":"1.0","event_id":"sha256:fac75e05d643bf28866e8dfc6923b02eb619de8dee983f6821b9a65ea46a1679"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HAL7VUUPX7J25X3CJWW34IDMGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the DoF of Two-way $2\\times2\\times2$ Relay Networks with or without Relay Caching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mehdi Ashraphijuo, Vaneet Aggarwal, Xiaodong Wang","submitted_at":"2016-11-26T05:35:54Z","abstract_excerpt":"Two-way relay is potentially an effective approach to spectrum sharing and aggregation by allowing simultaneous bidirectional transmissions between source-destinations pairs. This paper studies the two-way $2\\times2\\times2$ relay network, a class of four-unicast networks, where there are four source/destination nodes and two relay nodes, with each source sending a message to its destination. We show that without relay caching the total degrees of freedom (DoF) is bounded from above by $8/3$, indicating that bidirectional links do not double the DoF (It is known that the total DoF of one-way $2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08660","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":"2026-05-18T00:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HHlHwry5LKxY2fjaj0TDdsIzH9mhx9k38r4UlULq4GrZyoQ2FAoMSYlCVYAy9Or+Vh+RWViPUDrPbTD4Ih3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:03:22.749383Z"},"content_sha256":"05ffb47ae6b9480c69d19b825fe6c1b11d1a60a348feb28a1818f38a9abb894f","schema_version":"1.0","event_id":"sha256:05ffb47ae6b9480c69d19b825fe6c1b11d1a60a348feb28a1818f38a9abb894f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAL7VUUPX7J25X3CJWW34IDMGY/bundle.json","state_url":"https://pith.science/pith/HAL7VUUPX7J25X3CJWW34IDMGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAL7VUUPX7J25X3CJWW34IDMGY/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":"2026-06-07T05:03:22Z","links":{"resolver":"https://pith.science/pith/HAL7VUUPX7J25X3CJWW34IDMGY","bundle":"https://pith.science/pith/HAL7VUUPX7J25X3CJWW34IDMGY/bundle.json","state":"https://pith.science/pith/HAL7VUUPX7J25X3CJWW34IDMGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAL7VUUPX7J25X3CJWW34IDMGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HAL7VUUPX7J25X3CJWW34IDMGY","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":"6cf2f119442e5eadb67c2c97880fa48f79d0fa2d803926611a1a2dd58184c188","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-26T05:35:54Z","title_canon_sha256":"f7c8c3d0a1f9aff38112510047a3854fe69541d5ab611c5d12ddd438b87699fc"},"schema_version":"1.0","source":{"id":"1611.08660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08660","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08660v1","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08660","created_at":"2026-05-18T00:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"HAL7VUUPX7J2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HAL7VUUPX7J25X3C","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HAL7VUUP","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:05ffb47ae6b9480c69d19b825fe6c1b11d1a60a348feb28a1818f38a9abb894f","target":"graph","created_at":"2026-05-18T00:31:31Z","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":"Two-way relay is potentially an effective approach to spectrum sharing and aggregation by allowing simultaneous bidirectional transmissions between source-destinations pairs. This paper studies the two-way $2\\times2\\times2$ relay network, a class of four-unicast networks, where there are four source/destination nodes and two relay nodes, with each source sending a message to its destination. We show that without relay caching the total degrees of freedom (DoF) is bounded from above by $8/3$, indicating that bidirectional links do not double the DoF (It is known that the total DoF of one-way $2","authors_text":"Mehdi Ashraphijuo, Vaneet Aggarwal, Xiaodong Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-26T05:35:54Z","title":"On the DoF of Two-way $2\\times2\\times2$ Relay Networks with or without Relay Caching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08660","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:fac75e05d643bf28866e8dfc6923b02eb619de8dee983f6821b9a65ea46a1679","target":"record","created_at":"2026-05-18T00:31:31Z","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":"6cf2f119442e5eadb67c2c97880fa48f79d0fa2d803926611a1a2dd58184c188","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-26T05:35:54Z","title_canon_sha256":"f7c8c3d0a1f9aff38112510047a3854fe69541d5ab611c5d12ddd438b87699fc"},"schema_version":"1.0","source":{"id":"1611.08660","kind":"arxiv","version":1}},"canonical_sha256":"3817fad28fbfd3aedf624dadbe206c362ef2e126a10874bfb9b8d20d1aae2bac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3817fad28fbfd3aedf624dadbe206c362ef2e126a10874bfb9b8d20d1aae2bac","first_computed_at":"2026-05-18T00:31:31.491746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:31.491746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UFaTQuCS9CPwPtXgJdctUDq+s8/BF8hD//sAOMkjE4Xj2suASRkvtLBq6zeqvEk3W8OAybM9bl6pyGzAS9Q6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:31.492457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fac75e05d643bf28866e8dfc6923b02eb619de8dee983f6821b9a65ea46a1679","sha256:05ffb47ae6b9480c69d19b825fe6c1b11d1a60a348feb28a1818f38a9abb894f"],"state_sha256":"adc5ab042fadb3124f87428dc1d92b07899786e0b5e74bd050a311ad1998945d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2YCp+tMJaThe5PviswcbJszxJk4tqZ4iD8czRdeS07w0IRkUeE+fYkbQh5zeHoVD+yK0X9b8NvqLVrr2DN5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:03:22.753490Z","bundle_sha256":"d57773d3bd3c02641d2fc4bcebf1d3f0d2743e4a0942c9ede6e9b0ae728874c9"}}