{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XXFFDXKIDCLG5PWWWSS6ZVYKKF","short_pith_number":"pith:XXFFDXKI","canonical_record":{"source":{"id":"1805.00208","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T06:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"2b1dcf5a620800c16e28736ae21687b90af3f807a8bab9f4398d7a2e1cbecc40","abstract_canon_sha256":"2a25a92911a8aad9ed37351074510b80dd05742e1e47f3e6030792cfffa98257"},"schema_version":"1.0"},"canonical_sha256":"bdca51dd4818966ebed6b4a5ecd70a515ba8f93c1360f110888fbfd3d0d63f01","source":{"kind":"arxiv","id":"1805.00208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00208","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00208v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00208","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"XXFFDXKIDCLG","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XXFFDXKIDCLG5PWW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XXFFDXKI","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XXFFDXKIDCLG5PWWWSS6ZVYKKF","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00208","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T06:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"2b1dcf5a620800c16e28736ae21687b90af3f807a8bab9f4398d7a2e1cbecc40","abstract_canon_sha256":"2a25a92911a8aad9ed37351074510b80dd05742e1e47f3e6030792cfffa98257"},"schema_version":"1.0"},"canonical_sha256":"bdca51dd4818966ebed6b4a5ecd70a515ba8f93c1360f110888fbfd3d0d63f01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:10.263017Z","signature_b64":"IWe5uSR9dSUD+vOwP21sTf2o/+zLioWVPSuDCBmUEHgsfAUtTlXcVlZPRtODlxZWxD9RLfoYOvqyXvMhQIfiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdca51dd4818966ebed6b4a5ecd70a515ba8f93c1360f110888fbfd3d0d63f01","last_reissued_at":"2026-05-18T00:17:10.262384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:10.262384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00208","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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0Gm+Ch0iu1OhJgUsfq0fRBShW0/0Q86yL5qPYNXEQ1XbK6yx61eBonLIfnGOpOv9IN7NZthuuWIS30JTIkmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:18:49.458695Z"},"content_sha256":"00f987066dcee4d2a2131e2cedbd183ec050322980376252ab03f84fe059788b","schema_version":"1.0","event_id":"sha256:00f987066dcee4d2a2131e2cedbd183ec050322980376252ab03f84fe059788b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XXFFDXKIDCLG5PWWWSS6ZVYKKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some properties of Controlled Fusion Frames","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Habib shakoory, Naghi Behzadi, Reza Ahmadi, Susan Nami","submitted_at":"2018-05-01T06:46:25Z","abstract_excerpt":"Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper we have introduced and displayed some new concepts and results on controlled fusion frames for Hilbert spaces. It is shown that controlled fusion frames as a generalization of fusion frames give a generalized way to obtain numerical advantage in the sense of reconditioning to check the fusion frame condition. For this end, we introduce the notion of Q-duality for Controlled fusion frames. Also, we sur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00208","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":"2026-05-18T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+GhcsyJl1SsgPfSHrqqKBWlb+1+aL2vYx2BdFHjyNguf/TA7LquCY0dxhv7crvE6tO5gPT1XhGinGmZdufzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:18:49.459303Z"},"content_sha256":"ef27034aa9c72b320e153eb036b46d6f04b97f7ddebb1dad55eb96ad2579b29f","schema_version":"1.0","event_id":"sha256:ef27034aa9c72b320e153eb036b46d6f04b97f7ddebb1dad55eb96ad2579b29f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/bundle.json","state_url":"https://pith.science/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/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":"2026-06-07T10:18:49Z","links":{"resolver":"https://pith.science/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF","bundle":"https://pith.science/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/bundle.json","state":"https://pith.science/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXFFDXKIDCLG5PWWWSS6ZVYKKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XXFFDXKIDCLG5PWWWSS6ZVYKKF","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":"2a25a92911a8aad9ed37351074510b80dd05742e1e47f3e6030792cfffa98257","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T06:46:25Z","title_canon_sha256":"2b1dcf5a620800c16e28736ae21687b90af3f807a8bab9f4398d7a2e1cbecc40"},"schema_version":"1.0","source":{"id":"1805.00208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00208","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00208v1","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00208","created_at":"2026-05-18T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"XXFFDXKIDCLG","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XXFFDXKIDCLG5PWW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XXFFDXKI","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:ef27034aa9c72b320e153eb036b46d6f04b97f7ddebb1dad55eb96ad2579b29f","target":"graph","created_at":"2026-05-18T00:17:10Z","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":"Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper we have introduced and displayed some new concepts and results on controlled fusion frames for Hilbert spaces. It is shown that controlled fusion frames as a generalization of fusion frames give a generalized way to obtain numerical advantage in the sense of reconditioning to check the fusion frame condition. For this end, we introduce the notion of Q-duality for Controlled fusion frames. Also, we sur","authors_text":"Habib shakoory, Naghi Behzadi, Reza Ahmadi, Susan Nami","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T06:46:25Z","title":"Some properties of Controlled Fusion Frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00208","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":"sha256:00f987066dcee4d2a2131e2cedbd183ec050322980376252ab03f84fe059788b","target":"record","created_at":"2026-05-18T00:17:10Z","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":"2a25a92911a8aad9ed37351074510b80dd05742e1e47f3e6030792cfffa98257","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-05-01T06:46:25Z","title_canon_sha256":"2b1dcf5a620800c16e28736ae21687b90af3f807a8bab9f4398d7a2e1cbecc40"},"schema_version":"1.0","source":{"id":"1805.00208","kind":"arxiv","version":1}},"canonical_sha256":"bdca51dd4818966ebed6b4a5ecd70a515ba8f93c1360f110888fbfd3d0d63f01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdca51dd4818966ebed6b4a5ecd70a515ba8f93c1360f110888fbfd3d0d63f01","first_computed_at":"2026-05-18T00:17:10.262384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:10.262384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWe5uSR9dSUD+vOwP21sTf2o/+zLioWVPSuDCBmUEHgsfAUtTlXcVlZPRtODlxZWxD9RLfoYOvqyXvMhQIfiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:10.263017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f987066dcee4d2a2131e2cedbd183ec050322980376252ab03f84fe059788b","sha256:ef27034aa9c72b320e153eb036b46d6f04b97f7ddebb1dad55eb96ad2579b29f"],"state_sha256":"9d5e72206142f371bbf42fbbd8218259eb1518c1287746fdbd9d7db793a22f1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLpiwRVtxbkHxWpnX0DA+QAsIgYx1+XBDdxfdrn/6PB6wIbPMWYbG9MstLbtax/EhUyEVw/wDdV0oYv/nJtxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:18:49.461491Z","bundle_sha256":"fc83d4fb533591076e6b344bae119776f2f00d451080330daee7515c6eb86f20"}}