{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:53UVNKSPSYYU47VSIOSTV6ZT37","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":"c8e2c6b3bfdc4a9e228bcaa9e0b043ff09f61587c08ef45312cb522cc859e631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-05T21:31:22Z","title_canon_sha256":"50e17292d07a02cc503408533c8f7dbf96aecac6e52832c82acd2ed2d988bd2e"},"schema_version":"1.0","source":{"id":"1204.1359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1359","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1359v1","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1359","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"53UVNKSPSYYU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"53UVNKSPSYYU47VS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"53UVNKSP","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0283c9d1969335c31fcf2d3b949ef44f50f2c44b125723da05cc036b3a55f6a0","target":"graph","created_at":"2026-05-18T03:58:25Z","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":"Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g-frames will be defined and we will show that c","authors_text":"Abolhassan Fereydooni, Asghar Rahimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-05T21:31:22Z","title":"Controlled G-Frames and Their G-Multipliers in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1359","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:b60ec53d36255c35b41497ada00d44322197e34eb202daf1fd5721be3c3f8961","target":"record","created_at":"2026-05-18T03:58:25Z","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":"c8e2c6b3bfdc4a9e228bcaa9e0b043ff09f61587c08ef45312cb522cc859e631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-04-05T21:31:22Z","title_canon_sha256":"50e17292d07a02cc503408533c8f7dbf96aecac6e52832c82acd2ed2d988bd2e"},"schema_version":"1.0","source":{"id":"1204.1359","kind":"arxiv","version":1}},"canonical_sha256":"eee956aa4f96314e7eb243a53afb33dfc5870022ee346bf2417c26ba8598ad71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eee956aa4f96314e7eb243a53afb33dfc5870022ee346bf2417c26ba8598ad71","first_computed_at":"2026-05-18T03:58:25.865241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:25.865241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hnBr3mIrIeOQPAHwf6Hvg9z6aHjfyM1Pf0aOfHhkHF2Cj9FLFeAJXr08Pci1FnAxLBBmYZdLP0zgr3+AUaFGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:25.865925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b60ec53d36255c35b41497ada00d44322197e34eb202daf1fd5721be3c3f8961","sha256:0283c9d1969335c31fcf2d3b949ef44f50f2c44b125723da05cc036b3a55f6a0"],"state_sha256":"8db5d11da3916d3115d15d5e07930c85495d6a824694a68e38e6aee8acfe1de2"}