{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZWNTMINZMQICYJ6OADG4QQ5WZZ","short_pith_number":"pith:ZWNTMINZ","canonical_record":{"source":{"id":"1809.09465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T13:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"5c796193926224908bd7ca6ba8c2843efb8cab6f515e04d35486ef0a4ef0faa2","abstract_canon_sha256":"1f4c12e5686cddd7809b1f586656ba1cdd246ef7c2bade5ccac913b7533bf8e3"},"schema_version":"1.0"},"canonical_sha256":"cd9b3621b964102c27ce00cdc843b6ce466d2755c3724f07bb08d72ea55ff717","source":{"kind":"arxiv","id":"1809.09465","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09465","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09465v2","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09465","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZWNTMINZMQIC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZWNTMINZMQICYJ6O","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZWNTMINZ","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZWNTMINZMQICYJ6OADG4QQ5WZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T13:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"5c796193926224908bd7ca6ba8c2843efb8cab6f515e04d35486ef0a4ef0faa2","abstract_canon_sha256":"1f4c12e5686cddd7809b1f586656ba1cdd246ef7c2bade5ccac913b7533bf8e3"},"schema_version":"1.0"},"canonical_sha256":"cd9b3621b964102c27ce00cdc843b6ce466d2755c3724f07bb08d72ea55ff717","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:46.126301Z","signature_b64":"csH0K6CLNlvxUmh64imk71Wlaut1Lc1Nah8EALwwD76bmfSmM2EgbW5cLc/ds1LuvigDAThnh9rGNqw92fWcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd9b3621b964102c27ce00cdc843b6ce466d2755c3724f07bb08d72ea55ff717","last_reissued_at":"2026-05-17T23:46:46.125817Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:46.125817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09465","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":"2026-05-17T23:46:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mc0JwMM1fWvmRU1uqD3Tke99BSSCybU8vGbZDYztYG4vpCZoAk8BVPP84ZMTIRNuvTNi1oNbQO04RGHP8bMaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:22:44.016599Z"},"content_sha256":"bfb50025942e60ce6e2e6bc7b85cff26137db2730723eae2877f63d35011e368","schema_version":"1.0","event_id":"sha256:bfb50025942e60ce6e2e6bc7b85cff26137db2730723eae2877f63d35011e368"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZWNTMINZMQICYJ6OADG4QQ5WZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of woven frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Animesh Bhandari, Saikat Mukherjee","submitted_at":"2018-09-25T13:29:32Z","abstract_excerpt":"In a separable Hilbert space $\\mathcal H$, two frames $\\{f_i\\}_{i \\in I}$ and $\\{g_i\\}_{i \\in I}$ are said to be woven if there are constants $0<A \\leq B$ so that for every $\\sigma \\subset I$, $\\{f_i\\}_{i \\in \\sigma} \\cup \\{g_i\\}_{i \\in \\sigma ^c}$ forms a frame for $\\mathcal H$ with the universal bounds $A, B$. This article provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09465","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":""},"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":"2026-05-17T23:46:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8O8PMfJUhDAaU3PpE0Brznw7PYwMqCQEdcmys1cXy+rS1C2B/NiII2Qe5I3jWHrwI6fCqkWQ2ViWt05vmTbnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:22:44.016941Z"},"content_sha256":"3c1e42a59ef7a89da3a26566d2280938ba6c26e408674fd1186788e3b998c1d0","schema_version":"1.0","event_id":"sha256:3c1e42a59ef7a89da3a26566d2280938ba6c26e408674fd1186788e3b998c1d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/bundle.json","state_url":"https://pith.science/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/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":"2026-06-21T09:22:44Z","links":{"resolver":"https://pith.science/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ","bundle":"https://pith.science/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/bundle.json","state":"https://pith.science/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWNTMINZMQICYJ6OADG4QQ5WZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZWNTMINZMQICYJ6OADG4QQ5WZZ","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":"1f4c12e5686cddd7809b1f586656ba1cdd246ef7c2bade5ccac913b7533bf8e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T13:29:32Z","title_canon_sha256":"5c796193926224908bd7ca6ba8c2843efb8cab6f515e04d35486ef0a4ef0faa2"},"schema_version":"1.0","source":{"id":"1809.09465","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09465","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09465v2","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09465","created_at":"2026-05-17T23:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZWNTMINZMQIC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZWNTMINZMQICYJ6O","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZWNTMINZ","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:3c1e42a59ef7a89da3a26566d2280938ba6c26e408674fd1186788e3b998c1d0","target":"graph","created_at":"2026-05-17T23:46:46Z","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 a separable Hilbert space $\\mathcal H$, two frames $\\{f_i\\}_{i \\in I}$ and $\\{g_i\\}_{i \\in I}$ are said to be woven if there are constants $0<A \\leq B$ so that for every $\\sigma \\subset I$, $\\{f_i\\}_{i \\in \\sigma} \\cup \\{g_i\\}_{i \\in \\sigma ^c}$ forms a frame for $\\mathcal H$ with the universal bounds $A, B$. This article provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.","authors_text":"Animesh Bhandari, Saikat Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T13:29:32Z","title":"Characterizations of woven frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09465","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:bfb50025942e60ce6e2e6bc7b85cff26137db2730723eae2877f63d35011e368","target":"record","created_at":"2026-05-17T23:46:46Z","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":"1f4c12e5686cddd7809b1f586656ba1cdd246ef7c2bade5ccac913b7533bf8e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-25T13:29:32Z","title_canon_sha256":"5c796193926224908bd7ca6ba8c2843efb8cab6f515e04d35486ef0a4ef0faa2"},"schema_version":"1.0","source":{"id":"1809.09465","kind":"arxiv","version":2}},"canonical_sha256":"cd9b3621b964102c27ce00cdc843b6ce466d2755c3724f07bb08d72ea55ff717","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd9b3621b964102c27ce00cdc843b6ce466d2755c3724f07bb08d72ea55ff717","first_computed_at":"2026-05-17T23:46:46.125817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:46.125817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csH0K6CLNlvxUmh64imk71Wlaut1Lc1Nah8EALwwD76bmfSmM2EgbW5cLc/ds1LuvigDAThnh9rGNqw92fWcAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:46.126301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09465","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfb50025942e60ce6e2e6bc7b85cff26137db2730723eae2877f63d35011e368","sha256:3c1e42a59ef7a89da3a26566d2280938ba6c26e408674fd1186788e3b998c1d0"],"state_sha256":"6cef618a2cf7c33abe4f628a806a8cdb49eca225aea6b66aa967092c7e5a65d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CAdIsdTDm4Y04Pix+78VgCJbtModNuoK5J5NTv5/sUe5hcMcN4MtprWNScOHGo/wUZQlXrB6e+vYJIgkAR5JBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:22:44.019035Z","bundle_sha256":"a5e1e550c95a472e03fbb648b7daa7eddee0644e1cad14e3a628953fc9e87ecf"}}