{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VJKZR27QKBV3QSZ63RJPVWKDDR","short_pith_number":"pith:VJKZR27Q","schema_version":"1.0","canonical_sha256":"aa5598ebf0506bb84b3edc52fad9431c5174fbae0356974765ae46e4e4b624c7","source":{"kind":"arxiv","id":"1803.05531","version":2},"attestation_state":"computed","paper":{"title":"Low coherence unit norm tight frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT"],"primary_cat":"cs.IT","authors_text":"Jesse Oldroyd, Somantika Datta","submitted_at":"2018-03-14T23:04:58Z","abstract_excerpt":"Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two distinct vectors is equal to the Welch bound. This guarantees that the maximum coherence between pairs of vectors is minimized. Despite their usefulness and widespread applications, ETFs of a given size $N$ are only guaranteed to exist in $\\mathbb{R}^{d}$ or $\\mathbb{C}^{d}$ if $N = d + 1$. This leads to the problem of finding approximations of ETFs of $N$ vector"},"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":"1803.05531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-14T23:04:58Z","cross_cats_sorted":["math.FA","math.IT"],"title_canon_sha256":"c925f48b8595f65e664b50c821d152eec500e1d72cf287b755602be31925a21c","abstract_canon_sha256":"558c4d27b5dd5c3f33619dedc5b02198e06c5d0ba288fe7de7d6dbe870699cac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:02.163610Z","signature_b64":"F744tbBDipji1mKERhNSsYeGO69HL1PQHsOnhTA2ykTElW4RYxgCYhYvkBkEMKI0WVQWfWbN/2CpDH/XlUSICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa5598ebf0506bb84b3edc52fad9431c5174fbae0356974765ae46e4e4b624c7","last_reissued_at":"2026-05-18T00:19:02.162733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:02.162733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low coherence unit norm tight frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT"],"primary_cat":"cs.IT","authors_text":"Jesse Oldroyd, Somantika Datta","submitted_at":"2018-03-14T23:04:58Z","abstract_excerpt":"Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two distinct vectors is equal to the Welch bound. This guarantees that the maximum coherence between pairs of vectors is minimized. Despite their usefulness and widespread applications, ETFs of a given size $N$ are only guaranteed to exist in $\\mathbb{R}^{d}$ or $\\mathbb{C}^{d}$ if $N = d + 1$. This leads to the problem of finding approximations of ETFs of $N$ vector"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05531","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.05531","created_at":"2026-05-18T00:19:02.162844+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05531v2","created_at":"2026-05-18T00:19:02.162844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05531","created_at":"2026-05-18T00:19:02.162844+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJKZR27QKBV3","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJKZR27QKBV3QSZ6","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJKZR27Q","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR","json":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR.json","graph_json":"https://pith.science/api/pith-number/VJKZR27QKBV3QSZ63RJPVWKDDR/graph.json","events_json":"https://pith.science/api/pith-number/VJKZR27QKBV3QSZ63RJPVWKDDR/events.json","paper":"https://pith.science/paper/VJKZR27Q"},"agent_actions":{"view_html":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR","download_json":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR.json","view_paper":"https://pith.science/paper/VJKZR27Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05531&json=true","fetch_graph":"https://pith.science/api/pith-number/VJKZR27QKBV3QSZ63RJPVWKDDR/graph.json","fetch_events":"https://pith.science/api/pith-number/VJKZR27QKBV3QSZ63RJPVWKDDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR/action/storage_attestation","attest_author":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR/action/author_attestation","sign_citation":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR/action/citation_signature","submit_replication":"https://pith.science/pith/VJKZR27QKBV3QSZ63RJPVWKDDR/action/replication_record"}},"created_at":"2026-05-18T00:19:02.162844+00:00","updated_at":"2026-05-18T00:19:02.162844+00:00"}