{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:TAV5WA4S433I54DJSJ7C4JO5VQ","short_pith_number":"pith:TAV5WA4S","canonical_record":{"source":{"id":"math/0508646","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2005-08-31T17:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"f30d8311f60ff5e5447a8ed25f52d7e6eb09693006c82bcd97f6928f66693ddb","abstract_canon_sha256":"8ccc6a75f326cae4868345e5076112c080ccdf176edf3ed8765977aaff0e9f2a"},"schema_version":"1.0"},"canonical_sha256":"982bdb0392e6f68ef069927e2e25ddac330f93599d47db67cb50987476074088","source":{"kind":"arxiv","id":"math/0508646","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508646","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508646v2","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508646","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TAV5WA4S433I","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_16","alias_value":"TAV5WA4S433I54DJ","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_8","alias_value":"TAV5WA4S","created_at":"2026-07-04T14:40:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:TAV5WA4S433I54DJSJ7C4JO5VQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0508646","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2005-08-31T17:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"f30d8311f60ff5e5447a8ed25f52d7e6eb09693006c82bcd97f6928f66693ddb","abstract_canon_sha256":"8ccc6a75f326cae4868345e5076112c080ccdf176edf3ed8765977aaff0e9f2a"},"schema_version":"1.0"},"canonical_sha256":"982bdb0392e6f68ef069927e2e25ddac330f93599d47db67cb50987476074088","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:21.123627Z","signature_b64":"HTVuXiQXMFkyI6eZrJcZc5FTNYrlnCx4cxwznV4mq46fNoKRm80yZbFwd8pVZzKyJEQS/99sIDM4o+UvhQUZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982bdb0392e6f68ef069927e2e25ddac330f93599d47db67cb50987476074088","last_reissued_at":"2026-07-04T14:40:21.123279Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:21.123279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0508646","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGqfEYyUaq8GKNSxWzddV78CKzTyO599JFil0aQufPzYzHTXeLNZpt9BvHYr67OVfu2ha8Anfe0EnnX/avmECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:51:38.579130Z"},"content_sha256":"8bd5068adb770db17d40581df81179ccc072315efd57c252394cda262a355dac","schema_version":"1.0","event_id":"sha256:8bd5068adb770db17d40581df81179ccc072315efd57c252394cda262a355dac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:TAV5WA4S433I54DJSJ7C4JO5VQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Schur-Horn theorem for operators and frames with prescribed norms and frame operator","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D.Stojanoff, J. Antezana, M.Ruiz, P. Massey","submitted_at":"2005-08-31T17:12:32Z","abstract_excerpt":"Let $\\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\\mathcal H$, and a bounded sequence $\\mathbf{c} = \\{c_k \\}_{k \\in \\mathbb N}$ of non negative real numbers, the pair $(S, \\mathbf{c})$ is frame admissible, if there exists a frame $\\{f_k \\}_{k \\in \\mathbb{N}} $ on $\\mathcal H$ with frame operator $S$, such that $\\|f_k \\|^2 = c_k$, $k \\in \\mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508646","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/math/0508646/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgHxhPoVc9tLoER2dvnB9xMMQFFcT/z1OzP3R8mbDTpQWG9/s4EdS1Yn4+VbG8LrMLZdOS5cznU+LoCYCnZ1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:51:38.579424Z"},"content_sha256":"7122b116098e6055d3476d2c7027e15c97cef82d7ae28c257b3e94d57edfab97","schema_version":"1.0","event_id":"sha256:7122b116098e6055d3476d2c7027e15c97cef82d7ae28c257b3e94d57edfab97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/bundle.json","state_url":"https://pith.science/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/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":"2026-08-06T13:51:38Z","links":{"resolver":"https://pith.science/pith/TAV5WA4S433I54DJSJ7C4JO5VQ","bundle":"https://pith.science/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/bundle.json","state":"https://pith.science/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAV5WA4S433I54DJSJ7C4JO5VQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:TAV5WA4S433I54DJSJ7C4JO5VQ","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":"8ccc6a75f326cae4868345e5076112c080ccdf176edf3ed8765977aaff0e9f2a","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2005-08-31T17:12:32Z","title_canon_sha256":"f30d8311f60ff5e5447a8ed25f52d7e6eb09693006c82bcd97f6928f66693ddb"},"schema_version":"1.0","source":{"id":"math/0508646","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508646","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508646v2","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508646","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TAV5WA4S433I","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_16","alias_value":"TAV5WA4S433I54DJ","created_at":"2026-07-04T14:40:21Z"},{"alias_kind":"pith_short_8","alias_value":"TAV5WA4S","created_at":"2026-07-04T14:40:21Z"}],"graph_snapshots":[{"event_id":"sha256:7122b116098e6055d3476d2c7027e15c97cef82d7ae28c257b3e94d57edfab97","target":"graph","created_at":"2026-07-04T14:40:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0508646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\\mathcal H$, and a bounded sequence $\\mathbf{c} = \\{c_k \\}_{k \\in \\mathbb N}$ of non negative real numbers, the pair $(S, \\mathbf{c})$ is frame admissible, if there exists a frame $\\{f_k \\}_{k \\in \\mathbb{N}} $ on $\\mathcal H$ with frame operator $S$, such that $\\|f_k \\|^2 = c_k$, $k \\in \\mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditi","authors_text":"D.Stojanoff, J. Antezana, M.Ruiz, P. Massey","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2005-08-31T17:12:32Z","title":"The Schur-Horn theorem for operators and frames with prescribed norms and frame operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508646","kind":"arxiv","version":2},"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":"sha256:8bd5068adb770db17d40581df81179ccc072315efd57c252394cda262a355dac","target":"record","created_at":"2026-07-04T14:40:21Z","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":"8ccc6a75f326cae4868345e5076112c080ccdf176edf3ed8765977aaff0e9f2a","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2005-08-31T17:12:32Z","title_canon_sha256":"f30d8311f60ff5e5447a8ed25f52d7e6eb09693006c82bcd97f6928f66693ddb"},"schema_version":"1.0","source":{"id":"math/0508646","kind":"arxiv","version":2}},"canonical_sha256":"982bdb0392e6f68ef069927e2e25ddac330f93599d47db67cb50987476074088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"982bdb0392e6f68ef069927e2e25ddac330f93599d47db67cb50987476074088","first_computed_at":"2026-07-04T14:40:21.123279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:21.123279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HTVuXiQXMFkyI6eZrJcZc5FTNYrlnCx4cxwznV4mq46fNoKRm80yZbFwd8pVZzKyJEQS/99sIDM4o+UvhQUZCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:21.123627Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508646","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd5068adb770db17d40581df81179ccc072315efd57c252394cda262a355dac","sha256:7122b116098e6055d3476d2c7027e15c97cef82d7ae28c257b3e94d57edfab97"],"state_sha256":"ae4d3df242a26c63bdf24963f7f697de6cd5716d7530e1741520594888dd6b1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTOffNzEf5S0mDpzrr+IHwFF/RCdJtWCUX11Tka/v6jIaLd/5iK9CWLKlW32zu8H9uAS/LWh2IckS6/5KNX5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:51:38.582445Z","bundle_sha256":"29edddfe50501bdce5ec92dc8614147c79c9befd99a76e70e56605994c129850"}}