{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SABJWKTSU2NZFWUQTWENRP4KAS","short_pith_number":"pith:SABJWKTS","canonical_record":{"source":{"id":"1601.01488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-07T11:19:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3aee2dd20b54e88cff2fc377f3e63fa9d09c35daffb5cbc97d1efcb347ca1d29","abstract_canon_sha256":"5d604b99fdc1ebd279f6ee31edce57acb05153868730cdcd3fdb4a50c303f64f"},"schema_version":"1.0"},"canonical_sha256":"90029b2a72a69b92da909d88d8bf8a0494b32ff7f8b975a4ad9c45814cb87d0c","source":{"kind":"arxiv","id":"1601.01488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01488","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01488v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01488","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"SABJWKTSU2NZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SABJWKTSU2NZFWUQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SABJWKTS","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SABJWKTSU2NZFWUQTWENRP4KAS","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-07T11:19:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3aee2dd20b54e88cff2fc377f3e63fa9d09c35daffb5cbc97d1efcb347ca1d29","abstract_canon_sha256":"5d604b99fdc1ebd279f6ee31edce57acb05153868730cdcd3fdb4a50c303f64f"},"schema_version":"1.0"},"canonical_sha256":"90029b2a72a69b92da909d88d8bf8a0494b32ff7f8b975a4ad9c45814cb87d0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:13.510084Z","signature_b64":"fg+B+0smotluk0Oqm0YfuzXsp3VEek1sD2Y1kqSjTkdFVyxdRSVIxeNeMm90lLWRkJlyTpJ3Lc9yOkjUjC9lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90029b2a72a69b92da909d88d8bf8a0494b32ff7f8b975a4ad9c45814cb87d0c","last_reissued_at":"2026-05-18T01:23:13.509403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:13.509403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01488","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrVLvgE/Otwynew6pqduwqBHXlqv0zqP4jpOJ/k3d7kei+UOXlUBzk9Jr5K7S4yoq/C8Ch4ABZgHh64P7nfqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:43:57.799991Z"},"content_sha256":"de9e59a1437b6714b2e4c824af46bf11f857ca0a201bf285a5bae80c3a356077","schema_version":"1.0","event_id":"sha256:de9e59a1437b6714b2e4c824af46bf11f857ca0a201bf285a5bae80c3a356077"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SABJWKTSU2NZFWUQTWENRP4KAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Successive Compute-and-Forward over Multi-User Multi-Relay Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrooz Makki, Masoumeh Nasiri-Kenari, Mohsen Hejazi, Seyed Mohammad Azimi-Abarghouyi, Tommy Svensson","submitted_at":"2016-01-07T11:19:07Z","abstract_excerpt":"This paper develops efficient Compute-and-forward (CMF) schemes in multi-user multi-relay networks. To solve the rank failure problem in CMF setups and to achieve full diversity of the network, we introduce two novel CMF methods, namely, extended CMF and successive CMF. The former, having low complexity, is based on recovering multiple equations at relays. The latter utilizes successive interference cancellation (SIC) to enhance the system performance compared to the state-of-the-art schemes. Both methods can be utilized in a network with different number of users, relays, and relay antennas, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01488","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CDgB+qC9IxOfjIpw2lOtaBUHv/7s30md4JGi8ufyZV0BUYC9tB2EWeZVAfz12Yp9L5cmcIp726ik1YpgzXvADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:43:57.800738Z"},"content_sha256":"76552338a7bf770f254c2e83369986037b0da3b67619f7c2fd584da163ee9db9","schema_version":"1.0","event_id":"sha256:76552338a7bf770f254c2e83369986037b0da3b67619f7c2fd584da163ee9db9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SABJWKTSU2NZFWUQTWENRP4KAS/bundle.json","state_url":"https://pith.science/pith/SABJWKTSU2NZFWUQTWENRP4KAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SABJWKTSU2NZFWUQTWENRP4KAS/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":"2026-06-11T11:43:57Z","links":{"resolver":"https://pith.science/pith/SABJWKTSU2NZFWUQTWENRP4KAS","bundle":"https://pith.science/pith/SABJWKTSU2NZFWUQTWENRP4KAS/bundle.json","state":"https://pith.science/pith/SABJWKTSU2NZFWUQTWENRP4KAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SABJWKTSU2NZFWUQTWENRP4KAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SABJWKTSU2NZFWUQTWENRP4KAS","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":"5d604b99fdc1ebd279f6ee31edce57acb05153868730cdcd3fdb4a50c303f64f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-07T11:19:07Z","title_canon_sha256":"3aee2dd20b54e88cff2fc377f3e63fa9d09c35daffb5cbc97d1efcb347ca1d29"},"schema_version":"1.0","source":{"id":"1601.01488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01488","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01488v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01488","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"SABJWKTSU2NZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SABJWKTSU2NZFWUQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SABJWKTS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:76552338a7bf770f254c2e83369986037b0da3b67619f7c2fd584da163ee9db9","target":"graph","created_at":"2026-05-18T01:23:13Z","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":"This paper develops efficient Compute-and-forward (CMF) schemes in multi-user multi-relay networks. To solve the rank failure problem in CMF setups and to achieve full diversity of the network, we introduce two novel CMF methods, namely, extended CMF and successive CMF. The former, having low complexity, is based on recovering multiple equations at relays. The latter utilizes successive interference cancellation (SIC) to enhance the system performance compared to the state-of-the-art schemes. Both methods can be utilized in a network with different number of users, relays, and relay antennas, ","authors_text":"Behrooz Makki, Masoumeh Nasiri-Kenari, Mohsen Hejazi, Seyed Mohammad Azimi-Abarghouyi, Tommy Svensson","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-07T11:19:07Z","title":"Robust Successive Compute-and-Forward over Multi-User Multi-Relay Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01488","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:de9e59a1437b6714b2e4c824af46bf11f857ca0a201bf285a5bae80c3a356077","target":"record","created_at":"2026-05-18T01:23:13Z","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":"5d604b99fdc1ebd279f6ee31edce57acb05153868730cdcd3fdb4a50c303f64f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-07T11:19:07Z","title_canon_sha256":"3aee2dd20b54e88cff2fc377f3e63fa9d09c35daffb5cbc97d1efcb347ca1d29"},"schema_version":"1.0","source":{"id":"1601.01488","kind":"arxiv","version":1}},"canonical_sha256":"90029b2a72a69b92da909d88d8bf8a0494b32ff7f8b975a4ad9c45814cb87d0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90029b2a72a69b92da909d88d8bf8a0494b32ff7f8b975a4ad9c45814cb87d0c","first_computed_at":"2026-05-18T01:23:13.509403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:13.509403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fg+B+0smotluk0Oqm0YfuzXsp3VEek1sD2Y1kqSjTkdFVyxdRSVIxeNeMm90lLWRkJlyTpJ3Lc9yOkjUjC9lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:13.510084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de9e59a1437b6714b2e4c824af46bf11f857ca0a201bf285a5bae80c3a356077","sha256:76552338a7bf770f254c2e83369986037b0da3b67619f7c2fd584da163ee9db9"],"state_sha256":"ae910eeba85c7efa3d5495f3422ec98ebdcb56eff5c286774bd1383e5b025b4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LcqS7kuCs71gk5nZQcMAqpL9LLZ7LxG2MqwRAkyq3qOYElGQENcW/H38veL+wkDRAvHYc+srMH3swoWoUpuyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:43:57.804744Z","bundle_sha256":"e5c7d85baee7ece6f2b2a2ae60b9defb36e765e63d0beb945454ade52c7f25ea"}}