{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MGT2NK5JY2KFODDWOMBQEDUVW6","short_pith_number":"pith:MGT2NK5J","canonical_record":{"source":{"id":"1405.0718","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:11:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"df4c8bf4ddaeffcf7d3112c6d1f595cfd385eee695054a078e1afe3083e74212","abstract_canon_sha256":"689d5fbc4348d7fc246f208f28a7f42305f85125adf5fca8258baa2c1c575f35"},"schema_version":"1.0"},"canonical_sha256":"61a7a6aba9c694570c767303020e95b7be718f9b15c5194aad8093fd653f152f","source":{"kind":"arxiv","id":"1405.0718","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0718","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0718v3","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0718","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"MGT2NK5JY2KF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MGT2NK5JY2KFODDW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MGT2NK5J","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MGT2NK5JY2KFODDWOMBQEDUVW6","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0718","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:11:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"df4c8bf4ddaeffcf7d3112c6d1f595cfd385eee695054a078e1afe3083e74212","abstract_canon_sha256":"689d5fbc4348d7fc246f208f28a7f42305f85125adf5fca8258baa2c1c575f35"},"schema_version":"1.0"},"canonical_sha256":"61a7a6aba9c694570c767303020e95b7be718f9b15c5194aad8093fd653f152f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:02.257834Z","signature_b64":"u2vbOt28PrsCqqjbnnah90uYXBfnU3R3B12x+59J78b/wm2GPpyIPbO7Vuos7VgQKzeccnduADMkdcm57x/FDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61a7a6aba9c694570c767303020e95b7be718f9b15c5194aad8093fd653f152f","last_reissued_at":"2026-05-18T00:23:02.257201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:02.257201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0718","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtR/MXEmJFANzNdTezDHpriKa4jWDFrXJEmyuKbhYCp0pv814PaDPWQO+1onVGyCkdhs9CBus+LIe95xx3p8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:50:43.741016Z"},"content_sha256":"203ceea063bd0e9fa9b8e71d060fc118395a92e7b20638d6f28ae61058426f2d","schema_version":"1.0","event_id":"sha256:203ceea063bd0e9fa9b8e71d060fc118395a92e7b20638d6f28ae61058426f2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MGT2NK5JY2KFODDWOMBQEDUVW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Signal Alignment: On the Achievable DoF for Multi-User MIMO Two-Way Relay Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kangqi Liu, Meixia Tao","submitted_at":"2014-05-04T17:11:01Z","abstract_excerpt":"This paper studies the achievable degrees of freedom for multi-user MIMO two-way relay channels, where there are $K$ source nodes, each equipped with $M$ antennas, one relay node, equipped with $N$ antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: $K$-user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized MIMO two-way X relay channel, and $L$-clu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0718","kind":"arxiv","version":3},"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":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+QWK7yG+sF5VpqRPCntj1/8M5Iw9Y10Nb0/tEWMGaGpdfE14Xec5ltLKiAAl2BXjV3COTWAFI8+nSjADHr0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:50:43.741671Z"},"content_sha256":"d95b81ff1881dcc822fa7496a30ca60068dbc5841f7802520c623f16f6943288","schema_version":"1.0","event_id":"sha256:d95b81ff1881dcc822fa7496a30ca60068dbc5841f7802520c623f16f6943288"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/bundle.json","state_url":"https://pith.science/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/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":"2026-05-26T01:50:43Z","links":{"resolver":"https://pith.science/pith/MGT2NK5JY2KFODDWOMBQEDUVW6","bundle":"https://pith.science/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/bundle.json","state":"https://pith.science/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGT2NK5JY2KFODDWOMBQEDUVW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MGT2NK5JY2KFODDWOMBQEDUVW6","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":"689d5fbc4348d7fc246f208f28a7f42305f85125adf5fca8258baa2c1c575f35","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:11:01Z","title_canon_sha256":"df4c8bf4ddaeffcf7d3112c6d1f595cfd385eee695054a078e1afe3083e74212"},"schema_version":"1.0","source":{"id":"1405.0718","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0718","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0718v3","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0718","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"MGT2NK5JY2KF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MGT2NK5JY2KFODDW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MGT2NK5J","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d95b81ff1881dcc822fa7496a30ca60068dbc5841f7802520c623f16f6943288","target":"graph","created_at":"2026-05-18T00:23:02Z","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 studies the achievable degrees of freedom for multi-user MIMO two-way relay channels, where there are $K$ source nodes, each equipped with $M$ antennas, one relay node, equipped with $N$ antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: $K$-user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized MIMO two-way X relay channel, and $L$-clu","authors_text":"Kangqi Liu, Meixia Tao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:11:01Z","title":"Generalized Signal Alignment: On the Achievable DoF for Multi-User MIMO Two-Way Relay Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0718","kind":"arxiv","version":3},"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":"sha256:203ceea063bd0e9fa9b8e71d060fc118395a92e7b20638d6f28ae61058426f2d","target":"record","created_at":"2026-05-18T00:23:02Z","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":"689d5fbc4348d7fc246f208f28a7f42305f85125adf5fca8258baa2c1c575f35","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:11:01Z","title_canon_sha256":"df4c8bf4ddaeffcf7d3112c6d1f595cfd385eee695054a078e1afe3083e74212"},"schema_version":"1.0","source":{"id":"1405.0718","kind":"arxiv","version":3}},"canonical_sha256":"61a7a6aba9c694570c767303020e95b7be718f9b15c5194aad8093fd653f152f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61a7a6aba9c694570c767303020e95b7be718f9b15c5194aad8093fd653f152f","first_computed_at":"2026-05-18T00:23:02.257201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:02.257201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u2vbOt28PrsCqqjbnnah90uYXBfnU3R3B12x+59J78b/wm2GPpyIPbO7Vuos7VgQKzeccnduADMkdcm57x/FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:02.257834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0718","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:203ceea063bd0e9fa9b8e71d060fc118395a92e7b20638d6f28ae61058426f2d","sha256:d95b81ff1881dcc822fa7496a30ca60068dbc5841f7802520c623f16f6943288"],"state_sha256":"7a518d1aa57df376a4a8c3bb93a7226925ac22e57c42fda56bce7234dd551c76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YKrjIf3QT7POUgVK53w/jI9Dc2jgeZMg2ygkhdJ/4tLhiCY4L1wOjr7aztgz8HO3tzfiSIqj5BRUl5D++HvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:50:43.744628Z","bundle_sha256":"7607796320d14ee70ecf29c82700f741c3507540ec2223bc0d38c1ba705dbbef"}}