{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RBGCMLE657OWZEJ6524VOIYEZN","short_pith_number":"pith:RBGCMLE6","canonical_record":{"source":{"id":"1109.5790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-27T06:56:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ed64015714c909b36d9a5952775be30bf835615640027bfeee07fb9d7c36b2e7","abstract_canon_sha256":"a9188f9c88e01281bff2041071b0c857b8e8f1149bc02c313a46b2909de2e075"},"schema_version":"1.0"},"canonical_sha256":"884c262c9eefdd6c913eeeb9572304cb4cb3b7b5e783dbd44492242ec569f974","source":{"kind":"arxiv","id":"1109.5790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5790","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5790v1","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5790","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"RBGCMLE657OW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBGCMLE657OWZEJ6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBGCMLE6","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RBGCMLE657OWZEJ6524VOIYEZN","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-27T06:56:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ed64015714c909b36d9a5952775be30bf835615640027bfeee07fb9d7c36b2e7","abstract_canon_sha256":"a9188f9c88e01281bff2041071b0c857b8e8f1149bc02c313a46b2909de2e075"},"schema_version":"1.0"},"canonical_sha256":"884c262c9eefdd6c913eeeb9572304cb4cb3b7b5e783dbd44492242ec569f974","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:11.204808Z","signature_b64":"/kzDlmZ8OkbdDnfEG5oFvxm3WZfXZrbdOZ4kuESxgPiZr8f+muS5deCNAtiBMcY1JItZlVJWiY1K/EFnrwFpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"884c262c9eefdd6c913eeeb9572304cb4cb3b7b5e783dbd44492242ec569f974","last_reissued_at":"2026-05-18T04:12:11.204055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:11.204055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5790","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":"2026-05-18T04:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DgbEQ7KYGu9/NMjKlLzD/QUmjrB0TZHiZ5hZRxUrAFEfGuuVbU/JRrmFunvC4EPMrA5Az0oKDom/4mI0R0iAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:41:20.916986Z"},"content_sha256":"5589731616425edbfba2053896da1f5d3e4049ec0c4b8a2c94e319cc62e9841a","schema_version":"1.0","event_id":"sha256:5589731616425edbfba2053896da1f5d3e4049ec0c4b8a2c94e319cc62e9841a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RBGCMLE657OWZEJ6524VOIYEZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Degrees of Freedom of the 2-Hop, 2-User Interference Channel with Feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chinmay S. Vaze, Mahesh K. Varanasi","submitted_at":"2011-09-27T06:56:56Z","abstract_excerpt":"The layered two-hop, two-flow interference network is considered that consists of two sources, two relays and two destinations with the first hop network between he sources and the relays and the second hop network between relays and destinations both being i.i.d. Rayleigh fading Gaussian interference channels. Two feedback models are studied. In the first one, called the delayed channel state information at the sources (delayed CSI-S) model, the sources know all channel coefficients with a finite delay but the relays have no side information whatsoever. In the second feedback model, referred "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5790","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":"2026-05-18T04:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2ka3uzyOYvbFBWtAW9JbtXMITo2f9lNEsone+/bQVS+PyBtG9xmHSxMtJTQRSV1hD5XbUNtI2GydVqAa2XgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:41:20.917358Z"},"content_sha256":"273d603655c1486cb1c8d6b985f87d10177f51a97cc950d7c360233784616033","schema_version":"1.0","event_id":"sha256:273d603655c1486cb1c8d6b985f87d10177f51a97cc950d7c360233784616033"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBGCMLE657OWZEJ6524VOIYEZN/bundle.json","state_url":"https://pith.science/pith/RBGCMLE657OWZEJ6524VOIYEZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBGCMLE657OWZEJ6524VOIYEZN/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":"2026-06-28T08:41:20Z","links":{"resolver":"https://pith.science/pith/RBGCMLE657OWZEJ6524VOIYEZN","bundle":"https://pith.science/pith/RBGCMLE657OWZEJ6524VOIYEZN/bundle.json","state":"https://pith.science/pith/RBGCMLE657OWZEJ6524VOIYEZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBGCMLE657OWZEJ6524VOIYEZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RBGCMLE657OWZEJ6524VOIYEZN","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":"a9188f9c88e01281bff2041071b0c857b8e8f1149bc02c313a46b2909de2e075","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-27T06:56:56Z","title_canon_sha256":"ed64015714c909b36d9a5952775be30bf835615640027bfeee07fb9d7c36b2e7"},"schema_version":"1.0","source":{"id":"1109.5790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5790","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5790v1","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5790","created_at":"2026-05-18T04:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"RBGCMLE657OW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBGCMLE657OWZEJ6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBGCMLE6","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:273d603655c1486cb1c8d6b985f87d10177f51a97cc950d7c360233784616033","target":"graph","created_at":"2026-05-18T04:12:11Z","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 layered two-hop, two-flow interference network is considered that consists of two sources, two relays and two destinations with the first hop network between he sources and the relays and the second hop network between relays and destinations both being i.i.d. Rayleigh fading Gaussian interference channels. Two feedback models are studied. In the first one, called the delayed channel state information at the sources (delayed CSI-S) model, the sources know all channel coefficients with a finite delay but the relays have no side information whatsoever. In the second feedback model, referred ","authors_text":"Chinmay S. Vaze, Mahesh K. Varanasi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-27T06:56:56Z","title":"The Degrees of Freedom of the 2-Hop, 2-User Interference Channel with Feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5790","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":"sha256:5589731616425edbfba2053896da1f5d3e4049ec0c4b8a2c94e319cc62e9841a","target":"record","created_at":"2026-05-18T04:12:11Z","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":"a9188f9c88e01281bff2041071b0c857b8e8f1149bc02c313a46b2909de2e075","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-27T06:56:56Z","title_canon_sha256":"ed64015714c909b36d9a5952775be30bf835615640027bfeee07fb9d7c36b2e7"},"schema_version":"1.0","source":{"id":"1109.5790","kind":"arxiv","version":1}},"canonical_sha256":"884c262c9eefdd6c913eeeb9572304cb4cb3b7b5e783dbd44492242ec569f974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"884c262c9eefdd6c913eeeb9572304cb4cb3b7b5e783dbd44492242ec569f974","first_computed_at":"2026-05-18T04:12:11.204055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:11.204055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/kzDlmZ8OkbdDnfEG5oFvxm3WZfXZrbdOZ4kuESxgPiZr8f+muS5deCNAtiBMcY1JItZlVJWiY1K/EFnrwFpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:11.204808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5589731616425edbfba2053896da1f5d3e4049ec0c4b8a2c94e319cc62e9841a","sha256:273d603655c1486cb1c8d6b985f87d10177f51a97cc950d7c360233784616033"],"state_sha256":"fb49ba7cfbbe33548440368437cf6c4cbffd8e7f1d6411ffbfafbf71c224207b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MK+6iJ57vhMozGgnrCPVvh8F0VdRkyYYCrbmM2WdKc9NK7pREt7fpGZzeWoh2Dr3Ucays3bqkajPiF1HQHY+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:41:20.919272Z","bundle_sha256":"273b64d116a97d1cc9206af2bf7a8639f6647f197ed88732a49b22dd85700bc9"}}