{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MG64E7O56T6KJ7XF7CZC6FPOTM","short_pith_number":"pith:MG64E7O5","canonical_record":{"source":{"id":"2110.10756","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2021-10-20T19:59:33Z","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"title_canon_sha256":"34cba15c8b7532eb80c603c876d9f1652f5083cddf26e1497ada8476f1215948","abstract_canon_sha256":"9fd0f639fdc211c4e0783fbb71becfb3714599e332ce58c1d513234ea7a78ae5"},"schema_version":"1.0"},"canonical_sha256":"61bdc27dddf4fca4fee5f8b22f15ee9b3b23ec86e10bf0e888bdca863e7f5ff1","source":{"kind":"arxiv","id":"2110.10756","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.10756","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"2110.10756v1","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.10756","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"MG64E7O56T6K","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_16","alias_value":"MG64E7O56T6KJ7XF","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_8","alias_value":"MG64E7O5","created_at":"2026-07-05T05:01:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MG64E7O56T6KJ7XF7CZC6FPOTM","target":"record","payload":{"canonical_record":{"source":{"id":"2110.10756","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2021-10-20T19:59:33Z","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"title_canon_sha256":"34cba15c8b7532eb80c603c876d9f1652f5083cddf26e1497ada8476f1215948","abstract_canon_sha256":"9fd0f639fdc211c4e0783fbb71becfb3714599e332ce58c1d513234ea7a78ae5"},"schema_version":"1.0"},"canonical_sha256":"61bdc27dddf4fca4fee5f8b22f15ee9b3b23ec86e10bf0e888bdca863e7f5ff1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:01:16.375101Z","signature_b64":"bzTT27XwDaLPGmOk/8teXTezniJ5Ee3svKIjciW313JIMp3ATslzUVv/qIdJGGnnbwFL/shUg0VQnwWq/sEDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61bdc27dddf4fca4fee5f8b22f15ee9b3b23ec86e10bf0e888bdca863e7f5ff1","last_reissued_at":"2026-07-05T05:01:16.374533Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:01:16.374533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.10756","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":"2026-07-05T05:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g05gb8p96SrCbQhkmfsPm4uh2SCM8CTmXTCkNXqpE/d61bncgmxzf6aP1beNzJyRzS5t5F9XdjPyv1erZeWsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:12:45.655045Z"},"content_sha256":"35c811dffc59d4751b93f01536202225b85e8d70a0c6516000b04e547b6cb880","schema_version":"1.0","event_id":"sha256:35c811dffc59d4751b93f01536202225b85e8d70a0c6516000b04e547b6cb880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MG64E7O56T6KJ7XF7CZC6FPOTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ambiguities in Direction-of-Arrival Estimation with Linear Arrays","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC"],"primary_cat":"eess.SP","authors_text":"Frederic Matter, Marc E. Pfetsch, Marius Pesavento, Tobias Fischer","submitted_at":"2021-10-20T19:59:33Z","abstract_excerpt":"In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10756","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.10756/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFdqNxJ6Z4abTrZJOF1ukn2XZf6v4MzX859zNvYL+CSrtOwlQl5cO6Iu1/lGMg9gpeGuFEBu1xsbztomobMVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:12:45.655461Z"},"content_sha256":"ccc6a24d7a305bd1c48a0c5fef312c5b9958dc9b3f8b8cc99a547fe977b92cef","schema_version":"1.0","event_id":"sha256:ccc6a24d7a305bd1c48a0c5fef312c5b9958dc9b3f8b8cc99a547fe977b92cef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/bundle.json","state_url":"https://pith.science/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/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":"2026-07-08T19:12:45Z","links":{"resolver":"https://pith.science/pith/MG64E7O56T6KJ7XF7CZC6FPOTM","bundle":"https://pith.science/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/bundle.json","state":"https://pith.science/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MG64E7O56T6KJ7XF7CZC6FPOTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MG64E7O56T6KJ7XF7CZC6FPOTM","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":"9fd0f639fdc211c4e0783fbb71becfb3714599e332ce58c1d513234ea7a78ae5","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2021-10-20T19:59:33Z","title_canon_sha256":"34cba15c8b7532eb80c603c876d9f1652f5083cddf26e1497ada8476f1215948"},"schema_version":"1.0","source":{"id":"2110.10756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.10756","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"2110.10756v1","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.10756","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"MG64E7O56T6K","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_16","alias_value":"MG64E7O56T6KJ7XF","created_at":"2026-07-05T05:01:16Z"},{"alias_kind":"pith_short_8","alias_value":"MG64E7O5","created_at":"2026-07-05T05:01:16Z"}],"graph_snapshots":[{"event_id":"sha256:ccc6a24d7a305bd1c48a0c5fef312c5b9958dc9b3f8b8cc99a547fe977b92cef","target":"graph","created_at":"2026-07-05T05:01:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.10756/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of","authors_text":"Frederic Matter, Marc E. Pfetsch, Marius Pesavento, Tobias Fischer","cross_cats":["cs.IT","math.IT","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2021-10-20T19:59:33Z","title":"Ambiguities in Direction-of-Arrival Estimation with Linear Arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10756","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":"sha256:35c811dffc59d4751b93f01536202225b85e8d70a0c6516000b04e547b6cb880","target":"record","created_at":"2026-07-05T05:01:16Z","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":"9fd0f639fdc211c4e0783fbb71becfb3714599e332ce58c1d513234ea7a78ae5","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2021-10-20T19:59:33Z","title_canon_sha256":"34cba15c8b7532eb80c603c876d9f1652f5083cddf26e1497ada8476f1215948"},"schema_version":"1.0","source":{"id":"2110.10756","kind":"arxiv","version":1}},"canonical_sha256":"61bdc27dddf4fca4fee5f8b22f15ee9b3b23ec86e10bf0e888bdca863e7f5ff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61bdc27dddf4fca4fee5f8b22f15ee9b3b23ec86e10bf0e888bdca863e7f5ff1","first_computed_at":"2026-07-05T05:01:16.374533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:01:16.374533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bzTT27XwDaLPGmOk/8teXTezniJ5Ee3svKIjciW313JIMp3ATslzUVv/qIdJGGnnbwFL/shUg0VQnwWq/sEDCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:01:16.375101Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.10756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35c811dffc59d4751b93f01536202225b85e8d70a0c6516000b04e547b6cb880","sha256:ccc6a24d7a305bd1c48a0c5fef312c5b9958dc9b3f8b8cc99a547fe977b92cef"],"state_sha256":"150909510220cf62a59f6c6f2334a7bc396eeee676dbd0ea5805ca766e0d3daf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+GcEXfjy1OzQZr8BMm9zPe097K93ca3r/3GCKQ7OP08KvRlLFgre9XfKtoi61CveOB8Bwps4NSVBUqWUF2KAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T19:12:45.657427Z","bundle_sha256":"3646e27cfddfd66b69853e9a694c555460f5481e2682e7a6104db5dba100dd04"}}