{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ASZJND23RF2MCHSOIUDUJE3NKV","short_pith_number":"pith:ASZJND23","canonical_record":{"source":{"id":"1901.01360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-05T03:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"e1ca54328d1afb9e19f0148a4a2dbde9eb6a0028512e40773b2f94e210b055b7","abstract_canon_sha256":"048d5b27feaf3698402f6f6f44950f2af6e49aadb41dd20808b000d74641ce7e"},"schema_version":"1.0"},"canonical_sha256":"04b2968f5b8974c11e4e450744936d5577abdabbd4cdbd149c5fd0a01a0e746e","source":{"kind":"arxiv","id":"1901.01360","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01360","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01360v1","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01360","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"ASZJND23RF2M","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ASZJND23RF2MCHSO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ASZJND23","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ASZJND23RF2MCHSOIUDUJE3NKV","target":"record","payload":{"canonical_record":{"source":{"id":"1901.01360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-05T03:46:23Z","cross_cats_sorted":[],"title_canon_sha256":"e1ca54328d1afb9e19f0148a4a2dbde9eb6a0028512e40773b2f94e210b055b7","abstract_canon_sha256":"048d5b27feaf3698402f6f6f44950f2af6e49aadb41dd20808b000d74641ce7e"},"schema_version":"1.0"},"canonical_sha256":"04b2968f5b8974c11e4e450744936d5577abdabbd4cdbd149c5fd0a01a0e746e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:52.136814Z","signature_b64":"5MAhkEYyYXlPAa/awDcC5jbzbM1NuV9MzE2pOQ5ozBIjhgEgw9b9Ok5buroQNhoRmVdeTMGX69pqSz8uBNd0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04b2968f5b8974c11e4e450744936d5577abdabbd4cdbd149c5fd0a01a0e746e","last_reissued_at":"2026-05-17T23:56:52.136292Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:52.136292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.01360","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izEQ5EROPrwthFhNH7T4ExIse8e6wI7pYereSi5ViSB5pna+SLsfscNRQND30NSQmqOn0B/gzCEe5y1nR/PbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:51:18.171951Z"},"content_sha256":"fcc792bad4d00e799dafedbed1cb30994b32294a8333144e03a1976d077c91f7","schema_version":"1.0","event_id":"sha256:fcc792bad4d00e799dafedbed1cb30994b32294a8333144e03a1976d077c91f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ASZJND23RF2MCHSOIUDUJE3NKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On weaving frames in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dongwei Li","submitted_at":"2019-01-05T03:46:23Z","abstract_excerpt":"In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a condition associated with synthesis operators of frames such that the sequence of frames is woven. Finally, for a family of woven frames, we show that they are stable under invertible operators and small perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01360","kind":"arxiv","version":1},"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":"2026-05-17T23:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvDu0b5H88y5Qklsf/rdx7TdirbxlnZ6C5huyL1OhkL1rH8ByhaSssdC9Aoxl35oRAMUac/4MJgSMKoVBraXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:51:18.172466Z"},"content_sha256":"9787b8336436faaf4ba2c001fe2594c7d12c4b536bbdc58f5f9b3ae0d3ee3de5","schema_version":"1.0","event_id":"sha256:9787b8336436faaf4ba2c001fe2594c7d12c4b536bbdc58f5f9b3ae0d3ee3de5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASZJND23RF2MCHSOIUDUJE3NKV/bundle.json","state_url":"https://pith.science/pith/ASZJND23RF2MCHSOIUDUJE3NKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASZJND23RF2MCHSOIUDUJE3NKV/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":"2026-05-27T00:51:18Z","links":{"resolver":"https://pith.science/pith/ASZJND23RF2MCHSOIUDUJE3NKV","bundle":"https://pith.science/pith/ASZJND23RF2MCHSOIUDUJE3NKV/bundle.json","state":"https://pith.science/pith/ASZJND23RF2MCHSOIUDUJE3NKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASZJND23RF2MCHSOIUDUJE3NKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ASZJND23RF2MCHSOIUDUJE3NKV","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":"048d5b27feaf3698402f6f6f44950f2af6e49aadb41dd20808b000d74641ce7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-05T03:46:23Z","title_canon_sha256":"e1ca54328d1afb9e19f0148a4a2dbde9eb6a0028512e40773b2f94e210b055b7"},"schema_version":"1.0","source":{"id":"1901.01360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01360","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01360v1","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01360","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"ASZJND23RF2M","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ASZJND23RF2MCHSO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ASZJND23","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9787b8336436faaf4ba2c001fe2594c7d12c4b536bbdc58f5f9b3ae0d3ee3de5","target":"graph","created_at":"2026-05-17T23:56:52Z","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":"In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a condition associated with synthesis operators of frames such that the sequence of frames is woven. Finally, for a family of woven frames, we show that they are stable under invertible operators and small perturbations.","authors_text":"Dongwei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-05T03:46:23Z","title":"On weaving frames in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01360","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:fcc792bad4d00e799dafedbed1cb30994b32294a8333144e03a1976d077c91f7","target":"record","created_at":"2026-05-17T23:56:52Z","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":"048d5b27feaf3698402f6f6f44950f2af6e49aadb41dd20808b000d74641ce7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-01-05T03:46:23Z","title_canon_sha256":"e1ca54328d1afb9e19f0148a4a2dbde9eb6a0028512e40773b2f94e210b055b7"},"schema_version":"1.0","source":{"id":"1901.01360","kind":"arxiv","version":1}},"canonical_sha256":"04b2968f5b8974c11e4e450744936d5577abdabbd4cdbd149c5fd0a01a0e746e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04b2968f5b8974c11e4e450744936d5577abdabbd4cdbd149c5fd0a01a0e746e","first_computed_at":"2026-05-17T23:56:52.136292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:52.136292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MAhkEYyYXlPAa/awDcC5jbzbM1NuV9MzE2pOQ5ozBIjhgEgw9b9Ok5buroQNhoRmVdeTMGX69pqSz8uBNd0Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:52.136814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcc792bad4d00e799dafedbed1cb30994b32294a8333144e03a1976d077c91f7","sha256:9787b8336436faaf4ba2c001fe2594c7d12c4b536bbdc58f5f9b3ae0d3ee3de5"],"state_sha256":"d07e68dfc6ce3119254941307f56437cb6033cf5dab771a59b1afcbda5711bb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGcjQc+LRXgfrDenyaZUotuYBdiGVp6tidRybrHGWMTDsjtq5Blu239tyCbPoYPpuQqYYMnzOsAV2gupNN8CAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:51:18.176010Z","bundle_sha256":"238d3f3cb8b95f5c3140bda972b55e1020d287d6864785b79965550c2c60a1e8"}}