{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:64AOOYYHXV2QCLD7NGKH5ISZKW","short_pith_number":"pith:64AOOYYH","canonical_record":{"source":{"id":"1609.03601","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-12T20:57:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"59cf006b69b7a239c810f78b7911ddfbe40c18ffe88cb1792c49a75659186244","abstract_canon_sha256":"e9844461b893503a2b46ba2d7a36993a9101a32a404300a7c5ca4f6f1df1775d"},"schema_version":"1.0"},"canonical_sha256":"f700e76307bd75012c7f69947ea259559bbcfae0a6aafc061505a36678d7945b","source":{"kind":"arxiv","id":"1609.03601","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03601","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03601v3","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03601","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"64AOOYYHXV2Q","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"64AOOYYHXV2QCLD7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"64AOOYYH","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:64AOOYYHXV2QCLD7NGKH5ISZKW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03601","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-12T20:57:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"59cf006b69b7a239c810f78b7911ddfbe40c18ffe88cb1792c49a75659186244","abstract_canon_sha256":"e9844461b893503a2b46ba2d7a36993a9101a32a404300a7c5ca4f6f1df1775d"},"schema_version":"1.0"},"canonical_sha256":"f700e76307bd75012c7f69947ea259559bbcfae0a6aafc061505a36678d7945b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:29.013166Z","signature_b64":"Uzwv6zbUB3c5YwDOi6D+aiW9KafLw78csgHCtNMxEflISada+uxriLJpkaI/w+iBFDD7ftXD2WpwkKoAGOWbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f700e76307bd75012c7f69947ea259559bbcfae0a6aafc061505a36678d7945b","last_reissued_at":"2026-05-18T00:39:29.012704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:29.012704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03601","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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c44TJ+rRAkaJ4VdbgjpVOhnLR2X2JeOBDYIcRvd8OZVGznd45iuGdRAM+rwauZc9BgYmr9O8cpzrevtSVyvlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:41:59.456072Z"},"content_sha256":"b483dddc5f9da7c31db89913619361b477aed9197fbbec7e28cdcd279258b9e9","schema_version":"1.0","event_id":"sha256:b483dddc5f9da7c31db89913619361b477aed9197fbbec7e28cdcd279258b9e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:64AOOYYHXV2QCLD7NGKH5ISZKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noisy Beam Alignment Techniques for Reciprocal MIMO Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"David J. Love, Dennis Ogbe, Vasanthan Raghavan","submitted_at":"2016-09-12T20:57:07Z","abstract_excerpt":"Future multi-input multi-output (MIMO) wireless communications systems will use beamforming as a first-step towards realizing the capacity requirements necessitated by the exponential increase in data demands. The focus of this work is on beam alignment for time-division duplexing (TDD) systems, for which we propose a number of novel algorithms. These algorithms seek to obtain good estimates of the optimal beamformer/combiner pair (which are the dominant singular vectors of the channel matrix). They are motivated by the power method, an iterative algorithm to determine eigenvalues and eigenvec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03601","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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/PmO+HvRdl0rsbil4w+mJtdtnbw2/P0Hiu1eQhhebfoPuh2/2L9Kplim9Y63kKF3ZI6PsPGFcaxKFzFT8oIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:41:59.456417Z"},"content_sha256":"09ba8dbe5bd192f922be10b71d1afab11fb37ffc5a0d2333563fd5259dac3b0f","schema_version":"1.0","event_id":"sha256:09ba8dbe5bd192f922be10b71d1afab11fb37ffc5a0d2333563fd5259dac3b0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/bundle.json","state_url":"https://pith.science/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/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":"2026-06-02T18:41:59Z","links":{"resolver":"https://pith.science/pith/64AOOYYHXV2QCLD7NGKH5ISZKW","bundle":"https://pith.science/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/bundle.json","state":"https://pith.science/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64AOOYYHXV2QCLD7NGKH5ISZKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:64AOOYYHXV2QCLD7NGKH5ISZKW","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":"e9844461b893503a2b46ba2d7a36993a9101a32a404300a7c5ca4f6f1df1775d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-12T20:57:07Z","title_canon_sha256":"59cf006b69b7a239c810f78b7911ddfbe40c18ffe88cb1792c49a75659186244"},"schema_version":"1.0","source":{"id":"1609.03601","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03601","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03601v3","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03601","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"64AOOYYHXV2Q","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"64AOOYYHXV2QCLD7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"64AOOYYH","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:09ba8dbe5bd192f922be10b71d1afab11fb37ffc5a0d2333563fd5259dac3b0f","target":"graph","created_at":"2026-05-18T00:39:29Z","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":"Future multi-input multi-output (MIMO) wireless communications systems will use beamforming as a first-step towards realizing the capacity requirements necessitated by the exponential increase in data demands. The focus of this work is on beam alignment for time-division duplexing (TDD) systems, for which we propose a number of novel algorithms. These algorithms seek to obtain good estimates of the optimal beamformer/combiner pair (which are the dominant singular vectors of the channel matrix). They are motivated by the power method, an iterative algorithm to determine eigenvalues and eigenvec","authors_text":"David J. Love, Dennis Ogbe, Vasanthan Raghavan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-12T20:57:07Z","title":"Noisy Beam Alignment Techniques for Reciprocal MIMO Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03601","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:b483dddc5f9da7c31db89913619361b477aed9197fbbec7e28cdcd279258b9e9","target":"record","created_at":"2026-05-18T00:39:29Z","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":"e9844461b893503a2b46ba2d7a36993a9101a32a404300a7c5ca4f6f1df1775d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-12T20:57:07Z","title_canon_sha256":"59cf006b69b7a239c810f78b7911ddfbe40c18ffe88cb1792c49a75659186244"},"schema_version":"1.0","source":{"id":"1609.03601","kind":"arxiv","version":3}},"canonical_sha256":"f700e76307bd75012c7f69947ea259559bbcfae0a6aafc061505a36678d7945b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f700e76307bd75012c7f69947ea259559bbcfae0a6aafc061505a36678d7945b","first_computed_at":"2026-05-18T00:39:29.012704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:29.012704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uzwv6zbUB3c5YwDOi6D+aiW9KafLw78csgHCtNMxEflISada+uxriLJpkaI/w+iBFDD7ftXD2WpwkKoAGOWbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:29.013166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03601","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b483dddc5f9da7c31db89913619361b477aed9197fbbec7e28cdcd279258b9e9","sha256:09ba8dbe5bd192f922be10b71d1afab11fb37ffc5a0d2333563fd5259dac3b0f"],"state_sha256":"c8891bfef610480b2e71da1a99af0906b73978e6818d285bf2072198937691ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INpvkMQHd/Nsh7SjZ04z/0gP6Ohz+EEs3vk3e4oBoUrFo9i5h+xw1+Tp9WpmN/tOm4vF3n2TtBQYjtYpvXmTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:41:59.458251Z","bundle_sha256":"801ae19f8e6786270b93fc87e9c46e4a73a30090252daea7e0f3b6db423a8a5a"}}