{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:THEOTKZD34CXSC3BVYFDBX7SID","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":"4443f78f99ce4440f75d1f198aa3d790a2afe9c878ad69439d623c687f3b9932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T20:15:37Z","title_canon_sha256":"65b4735f96cd9602d6fa1e3cac9500e208a63f4f0def3752394be638e6a2c44c"},"schema_version":"1.0","source":{"id":"1303.1159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1159","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1159v1","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1159","created_at":"2026-05-18T03:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"THEOTKZD34CX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"THEOTKZD34CXSC3B","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"THEOTKZD","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:e445a558956506021cf8703bf5be8bd0d184240842ebdb8df0724ba80360e9d6","target":"graph","created_at":"2026-05-18T03:31:45Z","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":"We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R2 was previously defined using polar coordinates and was used to characterize tight frames in R2 in a geometric fashion. Reformulating the definition of a diagram vector in R2 we provide a natural extension of this notion to Rn and Cn. Using the diagram vectors we give a characterization of tight frames in Rn or Cn. Further we provide a characterization of when a unit-norm frame in Rn or Cn can be scaled to a tight frame. This classifica","authors_text":"Cortney Logan, Jonathan Sheperd, Kyanne Mayfield, Martin S. Copenhaver, Matthew J. Petro, Sivaram K. Narayan, Yeon Hyang Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T20:15:37Z","title":"Diagram vectors and Tight Frame Scaling in Finite Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1159","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":"sha256:25277632e575df730615cb677f64aa4dc4098ca3f6fddce457113dbd9e4fffd6","target":"record","created_at":"2026-05-18T03:31:45Z","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":"4443f78f99ce4440f75d1f198aa3d790a2afe9c878ad69439d623c687f3b9932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-05T20:15:37Z","title_canon_sha256":"65b4735f96cd9602d6fa1e3cac9500e208a63f4f0def3752394be638e6a2c44c"},"schema_version":"1.0","source":{"id":"1303.1159","kind":"arxiv","version":1}},"canonical_sha256":"99c8e9ab23df05790b61ae0a30dff240e7e0b44f896af060ccc5ec75402c526d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99c8e9ab23df05790b61ae0a30dff240e7e0b44f896af060ccc5ec75402c526d","first_computed_at":"2026-05-18T03:31:45.488525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:45.488525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLxHxm8NuwADQ2liG0ZstLrqrJva8kTMnmiMWmjW/Jlu2nr4drSGIzz6JHDxQ3ls1zGxE+lqFWLsp6mNyakVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:45.489142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25277632e575df730615cb677f64aa4dc4098ca3f6fddce457113dbd9e4fffd6","sha256:e445a558956506021cf8703bf5be8bd0d184240842ebdb8df0724ba80360e9d6"],"state_sha256":"6f3888f950d8c37d0792f6797ad71db051de6a45c52ee4418c6d023dcc3283c6"}