{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:REVYWJZZCE7ZDEA2CDJ533DJKH","short_pith_number":"pith:REVYWJZZ","canonical_record":{"source":{"id":"0911.2783","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T15:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"ef202cd84fbe06a9c73aa24561501c30891271a11580c06a6d739907adc79bd7","abstract_canon_sha256":"4afcb8182d7d64e9bb9e50c6f2127915fbe85ed7a932cd6efa07b236c6d16287"},"schema_version":"1.0"},"canonical_sha256":"892b8b2739113f91901a10d3ddec6951e444b9d32685fbcae3e9253b6423a6c7","source":{"kind":"arxiv","id":"0911.2783","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2783","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2783v3","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2783","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"REVYWJZZCE7Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"REVYWJZZCE7ZDEA2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"REVYWJZZ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:REVYWJZZCE7ZDEA2CDJ533DJKH","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2783","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T15:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"ef202cd84fbe06a9c73aa24561501c30891271a11580c06a6d739907adc79bd7","abstract_canon_sha256":"4afcb8182d7d64e9bb9e50c6f2127915fbe85ed7a932cd6efa07b236c6d16287"},"schema_version":"1.0"},"canonical_sha256":"892b8b2739113f91901a10d3ddec6951e444b9d32685fbcae3e9253b6423a6c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:42.682470Z","signature_b64":"jNTUNGqCE5R0XCZJrRG/khxi9o/lwBNxOn7tiKFE6xmE0R2wa0HYvPHo9V2SCz/xAFNNsIyLMRw49+NhKvDVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"892b8b2739113f91901a10d3ddec6951e444b9d32685fbcae3e9253b6423a6c7","last_reissued_at":"2026-05-18T03:53:42.681944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:42.681944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2783","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jlS5i8tbTxFwSytRcP4aDpszcbHsExp9QIz1B/gzoaN+rPScKocfRllwhvIOCQmUpJHb/LO/lDPkebWoUc+qBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:32:17.599270Z"},"content_sha256":"da83885cf2bf7bc63da7ac88d24870cf46a23da94f611efd9e1463454bf8b6e5","schema_version":"1.0","event_id":"sha256:da83885cf2bf7bc63da7ac88d24870cf46a23da94f611efd9e1463454bf8b6e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:REVYWJZZCE7ZDEA2CDJ533DJKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unconditional convergence and invertibility of multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Stoeva, P. Balazs","submitted_at":"2009-11-14T15:54:19Z","abstract_excerpt":"In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2783","kind":"arxiv","version":3},"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":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9O4LjOFPws3FEpw7rO0LBzEEdG1NGQ8m1aWLYfOzgBUOCwg++Aa7buU6G3VGN2zem31wQXwZEmxFf1mCLVI7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:32:17.599644Z"},"content_sha256":"e3342a62ef1884a599e069c12f8e517e3dd4b4159950dcdf4e61c28ac486d6ea","schema_version":"1.0","event_id":"sha256:e3342a62ef1884a599e069c12f8e517e3dd4b4159950dcdf4e61c28ac486d6ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/bundle.json","state_url":"https://pith.science/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/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":"2026-06-05T21:32:17Z","links":{"resolver":"https://pith.science/pith/REVYWJZZCE7ZDEA2CDJ533DJKH","bundle":"https://pith.science/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/bundle.json","state":"https://pith.science/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REVYWJZZCE7ZDEA2CDJ533DJKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:REVYWJZZCE7ZDEA2CDJ533DJKH","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":"4afcb8182d7d64e9bb9e50c6f2127915fbe85ed7a932cd6efa07b236c6d16287","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T15:54:19Z","title_canon_sha256":"ef202cd84fbe06a9c73aa24561501c30891271a11580c06a6d739907adc79bd7"},"schema_version":"1.0","source":{"id":"0911.2783","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2783","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2783v3","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2783","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"REVYWJZZCE7Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"REVYWJZZCE7ZDEA2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"REVYWJZZ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:e3342a62ef1884a599e069c12f8e517e3dd4b4159950dcdf4e61c28ac486d6ea","target":"graph","created_at":"2026-05-18T03:53:42Z","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 the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when","authors_text":"D. Stoeva, P. Balazs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T15:54:19Z","title":"Unconditional convergence and invertibility of multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2783","kind":"arxiv","version":3},"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:da83885cf2bf7bc63da7ac88d24870cf46a23da94f611efd9e1463454bf8b6e5","target":"record","created_at":"2026-05-18T03:53:42Z","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":"4afcb8182d7d64e9bb9e50c6f2127915fbe85ed7a932cd6efa07b236c6d16287","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-14T15:54:19Z","title_canon_sha256":"ef202cd84fbe06a9c73aa24561501c30891271a11580c06a6d739907adc79bd7"},"schema_version":"1.0","source":{"id":"0911.2783","kind":"arxiv","version":3}},"canonical_sha256":"892b8b2739113f91901a10d3ddec6951e444b9d32685fbcae3e9253b6423a6c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"892b8b2739113f91901a10d3ddec6951e444b9d32685fbcae3e9253b6423a6c7","first_computed_at":"2026-05-18T03:53:42.681944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:42.681944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jNTUNGqCE5R0XCZJrRG/khxi9o/lwBNxOn7tiKFE6xmE0R2wa0HYvPHo9V2SCz/xAFNNsIyLMRw49+NhKvDVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:42.682470Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2783","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da83885cf2bf7bc63da7ac88d24870cf46a23da94f611efd9e1463454bf8b6e5","sha256:e3342a62ef1884a599e069c12f8e517e3dd4b4159950dcdf4e61c28ac486d6ea"],"state_sha256":"a48491ed4bf5b71b10dece3821ee570c55d2613645bceede312fdd39cea9be21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uu+p9P6mEWOy7NNf3VR9S+PLlglPwF2V5uwHreorwp7QNYsAg/ja9s2tNIB+3ZiJXQirSkd+Ok5IRFEurKlaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:32:17.601834Z","bundle_sha256":"29ab31f83a5bd0179c1c318e4e04e258af546706a0164c0c05d916a48e65ed5a"}}