{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:55RFNFGLFKPIQ5CFWO33TKSUTB","short_pith_number":"pith:55RFNFGL","schema_version":"1.0","canonical_sha256":"ef625694cb2a9e887445b3b7b9aa549871650e387a5421741b77109813c61e49","source":{"kind":"arxiv","id":"2402.03787","version":2},"attestation_state":"computed","paper":{"title":"The beltway problem over orthogonal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Dan Edidin, Oscar Mickelin, Tamir Bendory","submitted_at":"2024-02-06T08:01:31Z","abstract_excerpt":"The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle. This problem can be viewed as a special case of the crystallographic phase retrieval problem of recovering a sparse signal from its periodic autocorrelation. Based on this interpretation, and motivated by cryo-electron microscopy, we suggest a natural generalization to orthogonal groups: recovering a sparse signal, up to an orthogonal transformation, from its autocorrelation over the orthogonal group. If the support of the signal is collision-free, we bound the number of solu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2402.03787","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2024-02-06T08:01:31Z","cross_cats_sorted":[],"title_canon_sha256":"b39867bae7a7b3f64363a912adf284e91038c54d4760ecdaa72bc33be417b790","abstract_canon_sha256":"302ad66fc9ca691593cbc4887357478032c0f5c07accd898d57ff787c9ce1809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:28.749277Z","signature_b64":"1XBhU4OoSKirwP2kzODvo/P2GjWi3UtHSsT1CKEwOZqkMROR6b9HhswQvle+EPU4ciEUn7Jpg2eP7KsQMbzGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef625694cb2a9e887445b3b7b9aa549871650e387a5421741b77109813c61e49","last_reissued_at":"2026-07-05T08:49:28.748726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:28.748726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The beltway problem over orthogonal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Dan Edidin, Oscar Mickelin, Tamir Bendory","submitted_at":"2024-02-06T08:01:31Z","abstract_excerpt":"The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle. This problem can be viewed as a special case of the crystallographic phase retrieval problem of recovering a sparse signal from its periodic autocorrelation. Based on this interpretation, and motivated by cryo-electron microscopy, we suggest a natural generalization to orthogonal groups: recovering a sparse signal, up to an orthogonal transformation, from its autocorrelation over the orthogonal group. If the support of the signal is collision-free, we bound the number of solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.03787","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.03787/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.03787","created_at":"2026-07-05T08:49:28.748789+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.03787v2","created_at":"2026-07-05T08:49:28.748789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.03787","created_at":"2026-07-05T08:49:28.748789+00:00"},{"alias_kind":"pith_short_12","alias_value":"55RFNFGLFKPI","created_at":"2026-07-05T08:49:28.748789+00:00"},{"alias_kind":"pith_short_16","alias_value":"55RFNFGLFKPIQ5CF","created_at":"2026-07-05T08:49:28.748789+00:00"},{"alias_kind":"pith_short_8","alias_value":"55RFNFGL","created_at":"2026-07-05T08:49:28.748789+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17434","citing_title":"Recovering a group from few orbits","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB","json":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB.json","graph_json":"https://pith.science/api/pith-number/55RFNFGLFKPIQ5CFWO33TKSUTB/graph.json","events_json":"https://pith.science/api/pith-number/55RFNFGLFKPIQ5CFWO33TKSUTB/events.json","paper":"https://pith.science/paper/55RFNFGL"},"agent_actions":{"view_html":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB","download_json":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB.json","view_paper":"https://pith.science/paper/55RFNFGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.03787&json=true","fetch_graph":"https://pith.science/api/pith-number/55RFNFGLFKPIQ5CFWO33TKSUTB/graph.json","fetch_events":"https://pith.science/api/pith-number/55RFNFGLFKPIQ5CFWO33TKSUTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB/action/storage_attestation","attest_author":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB/action/author_attestation","sign_citation":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB/action/citation_signature","submit_replication":"https://pith.science/pith/55RFNFGLFKPIQ5CFWO33TKSUTB/action/replication_record"}},"created_at":"2026-07-05T08:49:28.748789+00:00","updated_at":"2026-07-05T08:49:28.748789+00:00"}