{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q2FR2RRCD2D57XJYBHWAI6CGF7","short_pith_number":"pith:Q2FR2RRC","canonical_record":{"source":{"id":"1204.1880","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-09T14:04:02Z","cross_cats_sorted":["cs.IT","cs.NA","math.FA","math.IT"],"title_canon_sha256":"8798bcf038baba3a87107515c8ca1474a7861033cf4eda99ea8a0bb470678e08","abstract_canon_sha256":"155fefae3ee7711d4daee626f7c1bd687946f45cc2ec0dff95f7baa3ee4e94f4"},"schema_version":"1.0"},"canonical_sha256":"868b1d46221e87dfdd3809ec0478462ff649e7c8f111e37d1fa092ca7b3a08fc","source":{"kind":"arxiv","id":"1204.1880","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1880","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1880v3","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1880","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"Q2FR2RRCD2D5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q2FR2RRCD2D57XJY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q2FR2RRC","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q2FR2RRCD2D57XJYBHWAI6CGF7","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1880","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-09T14:04:02Z","cross_cats_sorted":["cs.IT","cs.NA","math.FA","math.IT"],"title_canon_sha256":"8798bcf038baba3a87107515c8ca1474a7861033cf4eda99ea8a0bb470678e08","abstract_canon_sha256":"155fefae3ee7711d4daee626f7c1bd687946f45cc2ec0dff95f7baa3ee4e94f4"},"schema_version":"1.0"},"canonical_sha256":"868b1d46221e87dfdd3809ec0478462ff649e7c8f111e37d1fa092ca7b3a08fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.659594Z","signature_b64":"5bGZza/wQWJTPEf6kacrHYcCJr8fpABd/xaQ75aP1+HM0L+BHtG+P42ktgUEME16oVzD8sNpNw5gjEYLUTwICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"868b1d46221e87dfdd3809ec0478462ff649e7c8f111e37d1fa092ca7b3a08fc","last_reissued_at":"2026-05-18T03:57:52.659147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.659147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1880","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":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOocFU4DYw5IHdLtfUMffLlrmVvfz/rsNhhsZvDl3JvhD4qJlMktuVE5xp4eop0KcoetCYlnTEf5QKLEH1/lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:49:31.532175Z"},"content_sha256":"31c16277c870cb877c7b2e1172215475861a5f47e2f84bf396896c3a9fc5b7ea","schema_version":"1.0","event_id":"sha256:31c16277c870cb877c7b2e1172215475861a5f47e2f84bf396896c3a9fc5b7ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q2FR2RRCD2D57XJYBHWAI6CGF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalable Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.FA","math.IT"],"primary_cat":"math.NA","authors_text":"Elizabeth K. Tuley, Friedrich Philipp, Gitta Kutyniok, Kasso A. Okoudjou","submitted_at":"2012-04-09T14:04:02Z","abstract_excerpt":"Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1880","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":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qf1kRIiuGPwHMwed+Iih8YrX6H5vvq7fNKc+xP7oWi/JXEieEDRWAMRa1aCM6Os84+NNz3t7cT/CYnzDri3wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:49:31.532538Z"},"content_sha256":"0142620e2f02a3540b2ada95da2d9a1d340d8e96890c634946a29af21a1700ee","schema_version":"1.0","event_id":"sha256:0142620e2f02a3540b2ada95da2d9a1d340d8e96890c634946a29af21a1700ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/bundle.json","state_url":"https://pith.science/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/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":"2026-06-02T02:49:31Z","links":{"resolver":"https://pith.science/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7","bundle":"https://pith.science/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/bundle.json","state":"https://pith.science/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2FR2RRCD2D57XJYBHWAI6CGF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q2FR2RRCD2D57XJYBHWAI6CGF7","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":"155fefae3ee7711d4daee626f7c1bd687946f45cc2ec0dff95f7baa3ee4e94f4","cross_cats_sorted":["cs.IT","cs.NA","math.FA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-09T14:04:02Z","title_canon_sha256":"8798bcf038baba3a87107515c8ca1474a7861033cf4eda99ea8a0bb470678e08"},"schema_version":"1.0","source":{"id":"1204.1880","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1880","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1880v3","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1880","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"Q2FR2RRCD2D5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q2FR2RRCD2D57XJY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q2FR2RRC","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:0142620e2f02a3540b2ada95da2d9a1d340d8e96890c634946a29af21a1700ee","target":"graph","created_at":"2026-05-18T03:57:52Z","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":"Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces.","authors_text":"Elizabeth K. Tuley, Friedrich Philipp, Gitta Kutyniok, Kasso A. Okoudjou","cross_cats":["cs.IT","cs.NA","math.FA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-09T14:04:02Z","title":"Scalable Frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1880","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":"sha256:31c16277c870cb877c7b2e1172215475861a5f47e2f84bf396896c3a9fc5b7ea","target":"record","created_at":"2026-05-18T03:57:52Z","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":"155fefae3ee7711d4daee626f7c1bd687946f45cc2ec0dff95f7baa3ee4e94f4","cross_cats_sorted":["cs.IT","cs.NA","math.FA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-09T14:04:02Z","title_canon_sha256":"8798bcf038baba3a87107515c8ca1474a7861033cf4eda99ea8a0bb470678e08"},"schema_version":"1.0","source":{"id":"1204.1880","kind":"arxiv","version":3}},"canonical_sha256":"868b1d46221e87dfdd3809ec0478462ff649e7c8f111e37d1fa092ca7b3a08fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"868b1d46221e87dfdd3809ec0478462ff649e7c8f111e37d1fa092ca7b3a08fc","first_computed_at":"2026-05-18T03:57:52.659147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:52.659147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bGZza/wQWJTPEf6kacrHYcCJr8fpABd/xaQ75aP1+HM0L+BHtG+P42ktgUEME16oVzD8sNpNw5gjEYLUTwICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:52.659594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1880","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31c16277c870cb877c7b2e1172215475861a5f47e2f84bf396896c3a9fc5b7ea","sha256:0142620e2f02a3540b2ada95da2d9a1d340d8e96890c634946a29af21a1700ee"],"state_sha256":"c3209a170561eb7000a508466745a0092adad27b98176125a3d9ce95f6ba101a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqQ7WV9HsiM6ZEHGel0t7u2aQs+QFW1UbEFFMOWcmiTZJjyPZ4sf7VU3GikN0G15Wc5yne9a181cid/1ZkbJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:49:31.534415Z","bundle_sha256":"7db0cf158ee3a10c480dca8e13e08aa84eb92220796f13c1ec4414f076f59123"}}