{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YULUQVJVW2PSDOEDTN77RIIKEW","short_pith_number":"pith:YULUQVJV","canonical_record":{"source":{"id":"1405.6656","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-26T17:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"1d28bee8791078bdfe44946c0fbaaa085e8d9c5cd21a13c67c51863076eb9032","abstract_canon_sha256":"260cc455430dc7e6788d258070f6da5ac3735a01fcb4ce832e00e3a479419c45"},"schema_version":"1.0"},"canonical_sha256":"c517485535b69f21b8839b7ff8a10a258b7d9aaef2ad3d4ad2d57aa5a260b42c","source":{"kind":"arxiv","id":"1405.6656","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6656","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6656v5","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6656","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"YULUQVJVW2PS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YULUQVJVW2PSDOED","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YULUQVJV","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YULUQVJVW2PSDOEDTN77RIIKEW","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6656","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-26T17:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"1d28bee8791078bdfe44946c0fbaaa085e8d9c5cd21a13c67c51863076eb9032","abstract_canon_sha256":"260cc455430dc7e6788d258070f6da5ac3735a01fcb4ce832e00e3a479419c45"},"schema_version":"1.0"},"canonical_sha256":"c517485535b69f21b8839b7ff8a10a258b7d9aaef2ad3d4ad2d57aa5a260b42c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:47.490308Z","signature_b64":"eLoVd4vq3MquwfGqgGAky6bTbVRMHxdI0xqQnne8PeTzGKei9AnnkazJw/k75IuE01TU5DaVmDID23Cg0fNjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c517485535b69f21b8839b7ff8a10a258b7d9aaef2ad3d4ad2d57aa5a260b42c","last_reissued_at":"2026-05-18T01:20:47.489917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:47.489917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6656","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SqfTblvw2BiHiaZ2aQt7f3cosIJdmydWQ/40HFKOGHHtkNaHXV0Gjygq/Jrm/ARE+/Y6naXKdwI9HhN2zc5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:25:47.296022Z"},"content_sha256":"bc8cd126a4973409117b96874a55165f3560eaac3996d4eb0530e7ffd5d48091","schema_version":"1.0","event_id":"sha256:bc8cd126a4973409117b96874a55165f3560eaac3996d4eb0530e7ffd5d48091"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YULUQVJVW2PSDOEDTN77RIIKEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Unconditional Constants for Hilbert Space Frame Expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Peter G. Casazza, Richard G. Lynch, Travis Bemrose, Victor Kaftal","submitted_at":"2014-05-26T17:30:00Z","abstract_excerpt":"The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has made it impossible to get accurate quantitative estimates for problems which require using subsequences of a frame. We will prove some new results in frame theory by showing that the unconditional constants of the frame expansion of a vector in a Hilbert space are bounded by $\\sqrt{\\frac{B}{A}}$, where $A,B$ are the frame bounds of the frame. Tight frames thu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6656","kind":"arxiv","version":5},"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":"2026-05-18T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8AGABSmdvuSJB/yDm3QQKvSc28RONBXyb09rOyelqMZJhyZI436wyGC0wlYk4jfYGkMbUQKRrw4xHOeY1/hBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:25:47.296375Z"},"content_sha256":"6a78698d73c01497087567250869481c2d3fb49a150d364290ffd4e3d34e761a","schema_version":"1.0","event_id":"sha256:6a78698d73c01497087567250869481c2d3fb49a150d364290ffd4e3d34e761a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YULUQVJVW2PSDOEDTN77RIIKEW/bundle.json","state_url":"https://pith.science/pith/YULUQVJVW2PSDOEDTN77RIIKEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YULUQVJVW2PSDOEDTN77RIIKEW/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":"2026-06-01T09:25:47Z","links":{"resolver":"https://pith.science/pith/YULUQVJVW2PSDOEDTN77RIIKEW","bundle":"https://pith.science/pith/YULUQVJVW2PSDOEDTN77RIIKEW/bundle.json","state":"https://pith.science/pith/YULUQVJVW2PSDOEDTN77RIIKEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YULUQVJVW2PSDOEDTN77RIIKEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YULUQVJVW2PSDOEDTN77RIIKEW","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":"260cc455430dc7e6788d258070f6da5ac3735a01fcb4ce832e00e3a479419c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-26T17:30:00Z","title_canon_sha256":"1d28bee8791078bdfe44946c0fbaaa085e8d9c5cd21a13c67c51863076eb9032"},"schema_version":"1.0","source":{"id":"1405.6656","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6656","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6656v5","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6656","created_at":"2026-05-18T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"YULUQVJVW2PS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YULUQVJVW2PSDOED","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YULUQVJV","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:6a78698d73c01497087567250869481c2d3fb49a150d364290ffd4e3d34e761a","target":"graph","created_at":"2026-05-18T01:20:47Z","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":"The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has made it impossible to get accurate quantitative estimates for problems which require using subsequences of a frame. We will prove some new results in frame theory by showing that the unconditional constants of the frame expansion of a vector in a Hilbert space are bounded by $\\sqrt{\\frac{B}{A}}$, where $A,B$ are the frame bounds of the frame. Tight frames thu","authors_text":"Peter G. Casazza, Richard G. Lynch, Travis Bemrose, Victor Kaftal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-26T17:30:00Z","title":"The Unconditional Constants for Hilbert Space Frame Expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6656","kind":"arxiv","version":5},"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:bc8cd126a4973409117b96874a55165f3560eaac3996d4eb0530e7ffd5d48091","target":"record","created_at":"2026-05-18T01:20:47Z","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":"260cc455430dc7e6788d258070f6da5ac3735a01fcb4ce832e00e3a479419c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-26T17:30:00Z","title_canon_sha256":"1d28bee8791078bdfe44946c0fbaaa085e8d9c5cd21a13c67c51863076eb9032"},"schema_version":"1.0","source":{"id":"1405.6656","kind":"arxiv","version":5}},"canonical_sha256":"c517485535b69f21b8839b7ff8a10a258b7d9aaef2ad3d4ad2d57aa5a260b42c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c517485535b69f21b8839b7ff8a10a258b7d9aaef2ad3d4ad2d57aa5a260b42c","first_computed_at":"2026-05-18T01:20:47.489917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:47.489917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eLoVd4vq3MquwfGqgGAky6bTbVRMHxdI0xqQnne8PeTzGKei9AnnkazJw/k75IuE01TU5DaVmDID23Cg0fNjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:47.490308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6656","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc8cd126a4973409117b96874a55165f3560eaac3996d4eb0530e7ffd5d48091","sha256:6a78698d73c01497087567250869481c2d3fb49a150d364290ffd4e3d34e761a"],"state_sha256":"2f7d3aa36e381ef39338742741ae5eb40bfa66e708ac2cf5a8bb3f409b843332"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZ2lPm3Drqd2jtPlC7x+XVXQtFSgCMns6Nd0QvVLyBxeEm2DFYl810B18kijk3apEqu8iwj0shyiH8oi72C/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:25:47.298257Z","bundle_sha256":"250312aeb0433d8a02dc898e6c5e521542e540c920d347b9394a079694895cba"}}