{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YXICII5QJZKJPP74UI3EZCAFZJ","short_pith_number":"pith:YXICII5Q","canonical_record":{"source":{"id":"1007.0512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-03T21:26:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9ff14ffe3e45ed313f90e6a3d863fcbed8b46bed0369f2537f5b5a971b4fed8e","abstract_canon_sha256":"082a594dbf296fc27cc20d5379dda4fd6dd20c6965d4e5eef7e50fb68eb97cd7"},"schema_version":"1.0"},"canonical_sha256":"c5d02423b04e5497bffca2364c8805ca755b9c771bffaf6f6bf3aa0071324d51","source":{"kind":"arxiv","id":"1007.0512","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0512","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0512v2","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0512","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"pith_short_12","alias_value":"YXICII5QJZKJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YXICII5QJZKJPP74","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YXICII5Q","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YXICII5QJZKJPP74UI3EZCAFZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-03T21:26:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9ff14ffe3e45ed313f90e6a3d863fcbed8b46bed0369f2537f5b5a971b4fed8e","abstract_canon_sha256":"082a594dbf296fc27cc20d5379dda4fd6dd20c6965d4e5eef7e50fb68eb97cd7"},"schema_version":"1.0"},"canonical_sha256":"c5d02423b04e5497bffca2364c8805ca755b9c771bffaf6f6bf3aa0071324d51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:52.988657Z","signature_b64":"glSSBlalZxO3r+uTymAmM79/IrN5pOeLvppZzNKOwWEMOEh/j4Ja8CaMTX6ULlHFbvCXVXQ7xxHa5jQ/c/f9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5d02423b04e5497bffca2364c8805ca755b9c771bffaf6f6bf3aa0071324d51","last_reissued_at":"2026-05-18T04:02:52.987802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:52.987802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0512","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":"2026-05-18T04:02:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIY4Qt94ilfZCHc41HQMTnbNzSMEXNKG1ZWo62pl0nsDxbJlOaWuxnZCy2biNM/Kc4UMGzy6tD1+zf9Pd7CpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:43:18.445323Z"},"content_sha256":"b51093e7867011fbaa40bb6fca5bf7b5804ea2ebbc5ab4488be89602d5a86f74","schema_version":"1.0","event_id":"sha256:b51093e7867011fbaa40bb6fca5bf7b5804ea2ebbc5ab4488be89602d5a86f74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YXICII5QJZKJPP74UI3EZCAFZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"User Partitioning for Less Overhead in MIMO Interference Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Robert W. Heath Jr, Steven W. Peters","submitted_at":"2010-07-03T21:26:32Z","abstract_excerpt":"This paper presents a study on multiple-antenna interference channels, accounting for general overhead as a function of the number of users and antennas in the network. The model includes both perfect and imperfect channel state information based on channel estimation in the presence of noise. Three low complexity methods are proposed for reducing the impact of overhead in the sum network throughput by partitioning users into orthogonal groups. The first method allocates spectrum to the groups equally, creating an imbalance in the sum rate of each group. The second proposed method allocates sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0512","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":""},"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":"2026-05-18T04:02:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGxhtIjnNcB+eLyInlZmJVE6i36gd+EEdPMPoob9qRx3nMwcjvLlWwS+YIcjInjR1uZELMO9Ru7tjng20A/ZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:43:18.445673Z"},"content_sha256":"d207b19143f57e4345de67b6c1e49b2528d74eeac978a7b7eb00dc1ad26b3b09","schema_version":"1.0","event_id":"sha256:d207b19143f57e4345de67b6c1e49b2528d74eeac978a7b7eb00dc1ad26b3b09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXICII5QJZKJPP74UI3EZCAFZJ/bundle.json","state_url":"https://pith.science/pith/YXICII5QJZKJPP74UI3EZCAFZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXICII5QJZKJPP74UI3EZCAFZJ/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":"2026-06-04T22:43:18Z","links":{"resolver":"https://pith.science/pith/YXICII5QJZKJPP74UI3EZCAFZJ","bundle":"https://pith.science/pith/YXICII5QJZKJPP74UI3EZCAFZJ/bundle.json","state":"https://pith.science/pith/YXICII5QJZKJPP74UI3EZCAFZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXICII5QJZKJPP74UI3EZCAFZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YXICII5QJZKJPP74UI3EZCAFZJ","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":"082a594dbf296fc27cc20d5379dda4fd6dd20c6965d4e5eef7e50fb68eb97cd7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-03T21:26:32Z","title_canon_sha256":"9ff14ffe3e45ed313f90e6a3d863fcbed8b46bed0369f2537f5b5a971b4fed8e"},"schema_version":"1.0","source":{"id":"1007.0512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0512","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0512v2","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0512","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"pith_short_12","alias_value":"YXICII5QJZKJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YXICII5QJZKJPP74","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YXICII5Q","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d207b19143f57e4345de67b6c1e49b2528d74eeac978a7b7eb00dc1ad26b3b09","target":"graph","created_at":"2026-05-18T04:02:52Z","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 presents a study on multiple-antenna interference channels, accounting for general overhead as a function of the number of users and antennas in the network. The model includes both perfect and imperfect channel state information based on channel estimation in the presence of noise. Three low complexity methods are proposed for reducing the impact of overhead in the sum network throughput by partitioning users into orthogonal groups. The first method allocates spectrum to the groups equally, creating an imbalance in the sum rate of each group. The second proposed method allocates sp","authors_text":"Robert W. Heath Jr, Steven W. Peters","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-03T21:26:32Z","title":"User Partitioning for Less Overhead in MIMO Interference Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0512","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:b51093e7867011fbaa40bb6fca5bf7b5804ea2ebbc5ab4488be89602d5a86f74","target":"record","created_at":"2026-05-18T04:02:52Z","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":"082a594dbf296fc27cc20d5379dda4fd6dd20c6965d4e5eef7e50fb68eb97cd7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-03T21:26:32Z","title_canon_sha256":"9ff14ffe3e45ed313f90e6a3d863fcbed8b46bed0369f2537f5b5a971b4fed8e"},"schema_version":"1.0","source":{"id":"1007.0512","kind":"arxiv","version":2}},"canonical_sha256":"c5d02423b04e5497bffca2364c8805ca755b9c771bffaf6f6bf3aa0071324d51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5d02423b04e5497bffca2364c8805ca755b9c771bffaf6f6bf3aa0071324d51","first_computed_at":"2026-05-18T04:02:52.987802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:52.987802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"glSSBlalZxO3r+uTymAmM79/IrN5pOeLvppZzNKOwWEMOEh/j4Ja8CaMTX6ULlHFbvCXVXQ7xxHa5jQ/c/f9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:52.988657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b51093e7867011fbaa40bb6fca5bf7b5804ea2ebbc5ab4488be89602d5a86f74","sha256:d207b19143f57e4345de67b6c1e49b2528d74eeac978a7b7eb00dc1ad26b3b09"],"state_sha256":"50c4698cd82736f145b3c28ea7e79fa3af8eee9aebd55ddd8b0af336169b3b21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxUnd/d3Ailul2jR1xHN4HH3NU6TwosQcisMfeDKTQcVxERx5gg297GsMBnqpuuhDsXtTcILhFdcv3a3jEALDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:43:18.447636Z","bundle_sha256":"671d8f749a49b8d163d1be22ecc8929141c8f756d05d322d69fe29d1750d7381"}}