{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7REG4REDHGHRRTZ46EJHG5XAU3","short_pith_number":"pith:7REG4RED","canonical_record":{"source":{"id":"1105.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-29T12:29:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"df7eb9383c1d7f54758c568d94b0f4e901e92d5078693636538eeeb212fc208c","abstract_canon_sha256":"b5ad580d362a8e79c7649658b4fe5eec230fff7f97393f97d0041ea7bff2b3f5"},"schema_version":"1.0"},"canonical_sha256":"fc486e4483398f18cf3cf1127376e0a6cff755f07d1443954fc05b6678e49bd4","source":{"kind":"arxiv","id":"1105.5782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5782","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5782v1","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5782","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"7REG4REDHGHR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7REG4REDHGHRRTZ4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7REG4RED","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7REG4REDHGHRRTZ46EJHG5XAU3","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-29T12:29:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"df7eb9383c1d7f54758c568d94b0f4e901e92d5078693636538eeeb212fc208c","abstract_canon_sha256":"b5ad580d362a8e79c7649658b4fe5eec230fff7f97393f97d0041ea7bff2b3f5"},"schema_version":"1.0"},"canonical_sha256":"fc486e4483398f18cf3cf1127376e0a6cff755f07d1443954fc05b6678e49bd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:01.576632Z","signature_b64":"ZzLm5drt0dL8VH9bcud/xoKKpMslNYQDR0kutr6rj4L3rgsFZXmp867N30ql0WlVYM7ye59N2/vIFJRTvmkcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc486e4483398f18cf3cf1127376e0a6cff755f07d1443954fc05b6678e49bd4","last_reissued_at":"2026-05-18T04:21:01.576161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:01.576161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5782","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":"2026-05-18T04:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyhEJTdY0kL19vKsS3+c115h/Q5odlGsiQ3jmfVNSbp9KCH+2NAVJbpQ9Vp6/LOEuza2uX1EXz7e7jgCq2HKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:21:22.442222Z"},"content_sha256":"98e563b690cd60a9c8cc011882040f9340144442127cbe4a7ed3479a23d97fce","schema_version":"1.0","event_id":"sha256:98e563b690cd60a9c8cc011882040f9340144442127cbe4a7ed3479a23d97fce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7REG4REDHGHRRTZ46EJHG5XAU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grassmannian Predictive Coding for Limited Feedback in Multiple Antenna Wireless Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Robert W. Heath Jr, Takao Inoue","submitted_at":"2011-05-29T12:29:16Z","abstract_excerpt":"Limited feedback is a paradigm for the feedback of channel state information in wireless systems. In multiple antenna wireless systems, limited feedback usually entails quantizing a source that lives on the Grassmann manifold. Most work on limited feedback beamforming considered single-shot quantization. In wireless systems, however, the channel is temporally correlated, which can be used to reduce feedback requirements. Unfortunately, conventional predictive quantization does not incorporate the non-Euclidean structure of the Grassmann manifold. In this paper, we propose a Grassmannian predic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5782","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":"2026-05-18T04:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTCI0IVWcKrinnWU1S3ec5rX3sESzfe/UlqVL84zbA3PuZEF+BthTRCJsTCkbcGWb+zKp2OjC2B54pp2nnlcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:21:22.442582Z"},"content_sha256":"157de19867101c2d0d07d723fe9bd3940f034ba9ede3864612747a844a3f99a8","schema_version":"1.0","event_id":"sha256:157de19867101c2d0d07d723fe9bd3940f034ba9ede3864612747a844a3f99a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7REG4REDHGHRRTZ46EJHG5XAU3/bundle.json","state_url":"https://pith.science/pith/7REG4REDHGHRRTZ46EJHG5XAU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7REG4REDHGHRRTZ46EJHG5XAU3/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":"2026-06-05T12:21:22Z","links":{"resolver":"https://pith.science/pith/7REG4REDHGHRRTZ46EJHG5XAU3","bundle":"https://pith.science/pith/7REG4REDHGHRRTZ46EJHG5XAU3/bundle.json","state":"https://pith.science/pith/7REG4REDHGHRRTZ46EJHG5XAU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7REG4REDHGHRRTZ46EJHG5XAU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7REG4REDHGHRRTZ46EJHG5XAU3","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":"b5ad580d362a8e79c7649658b4fe5eec230fff7f97393f97d0041ea7bff2b3f5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-29T12:29:16Z","title_canon_sha256":"df7eb9383c1d7f54758c568d94b0f4e901e92d5078693636538eeeb212fc208c"},"schema_version":"1.0","source":{"id":"1105.5782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5782","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5782v1","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5782","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"7REG4REDHGHR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7REG4REDHGHRRTZ4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7REG4RED","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:157de19867101c2d0d07d723fe9bd3940f034ba9ede3864612747a844a3f99a8","target":"graph","created_at":"2026-05-18T04:21:01Z","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":"Limited feedback is a paradigm for the feedback of channel state information in wireless systems. In multiple antenna wireless systems, limited feedback usually entails quantizing a source that lives on the Grassmann manifold. Most work on limited feedback beamforming considered single-shot quantization. In wireless systems, however, the channel is temporally correlated, which can be used to reduce feedback requirements. Unfortunately, conventional predictive quantization does not incorporate the non-Euclidean structure of the Grassmann manifold. In this paper, we propose a Grassmannian predic","authors_text":"Robert W. Heath Jr, Takao Inoue","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-29T12:29:16Z","title":"Grassmannian Predictive Coding for Limited Feedback in Multiple Antenna Wireless Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5782","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":"sha256:98e563b690cd60a9c8cc011882040f9340144442127cbe4a7ed3479a23d97fce","target":"record","created_at":"2026-05-18T04:21:01Z","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":"b5ad580d362a8e79c7649658b4fe5eec230fff7f97393f97d0041ea7bff2b3f5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-29T12:29:16Z","title_canon_sha256":"df7eb9383c1d7f54758c568d94b0f4e901e92d5078693636538eeeb212fc208c"},"schema_version":"1.0","source":{"id":"1105.5782","kind":"arxiv","version":1}},"canonical_sha256":"fc486e4483398f18cf3cf1127376e0a6cff755f07d1443954fc05b6678e49bd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc486e4483398f18cf3cf1127376e0a6cff755f07d1443954fc05b6678e49bd4","first_computed_at":"2026-05-18T04:21:01.576161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:01.576161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZzLm5drt0dL8VH9bcud/xoKKpMslNYQDR0kutr6rj4L3rgsFZXmp867N30ql0WlVYM7ye59N2/vIFJRTvmkcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:01.576632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98e563b690cd60a9c8cc011882040f9340144442127cbe4a7ed3479a23d97fce","sha256:157de19867101c2d0d07d723fe9bd3940f034ba9ede3864612747a844a3f99a8"],"state_sha256":"7c4e795e7c1d52a1a206f25c6ac49e0d576b0587b82e99cb5d3ddc7cec94961d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFY/m8VHG5jvepvagjDq60UMOgx3vRqQJznk0PfJTML4OpDtnxoXT+aTk0+lIT0XqYy0ZGYWvomiuMi6bF5mDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:21:22.444513Z","bundle_sha256":"dfb0fedcf7564373610700bbe7313a511ffd8ad37a95d79b294ac181e95cc7c1"}}