{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VQUMUYU6WZBXX4DV3MIXWJES7X","short_pith_number":"pith:VQUMUYU6","canonical_record":{"source":{"id":"2108.02465","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-05T09:10:42Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"42c848e54d2a18c2b75d5f41dfff4db920df3a9f6e8e8d1ba0255f175b4e02d2","abstract_canon_sha256":"fe6284e822cd67c11f1ddca96afb528816ba86d0cfbade67bb48e77361aaff13"},"schema_version":"1.0"},"canonical_sha256":"ac28ca629eb6437bf075db117b2492fdc9d7396dd916765f185760c17632c687","source":{"kind":"arxiv","id":"2108.02465","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02465","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02465v4","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02465","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"VQUMUYU6WZBX","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_16","alias_value":"VQUMUYU6WZBXX4DV","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_8","alias_value":"VQUMUYU6","created_at":"2026-07-05T05:12:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VQUMUYU6WZBXX4DV3MIXWJES7X","target":"record","payload":{"canonical_record":{"source":{"id":"2108.02465","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-05T09:10:42Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"42c848e54d2a18c2b75d5f41dfff4db920df3a9f6e8e8d1ba0255f175b4e02d2","abstract_canon_sha256":"fe6284e822cd67c11f1ddca96afb528816ba86d0cfbade67bb48e77361aaff13"},"schema_version":"1.0"},"canonical_sha256":"ac28ca629eb6437bf075db117b2492fdc9d7396dd916765f185760c17632c687","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:12:48.918567Z","signature_b64":"344uCvAt2CxrgFVUT3ieQ2DrLwfL07R4EWhp7Vzn9/nniAdo/sAV2pTx/J/Uf5Hc81wfNNkmux8ubFaNcnkzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac28ca629eb6437bf075db117b2492fdc9d7396dd916765f185760c17632c687","last_reissued_at":"2026-07-05T05:12:48.918151Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:12:48.918151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.02465","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFq9Ql6/PtyVssBjaKsiVs2XmMRXkze3RV/CmCzZNNh0AI8A7Id8VMnbjA67lyoW2QDsPlm6gjYtm73xjlbWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:44:38.635347Z"},"content_sha256":"4c9af9ed1bb3ae4026b85036a4c8518836f6f845d5d065d01d6ebee859da983e","schema_version":"1.0","event_id":"sha256:4c9af9ed1bb3ae4026b85036a4c8518836f6f845d5d065d01d6ebee859da983e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VQUMUYU6WZBXX4DV3MIXWJES7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Regularization via Frame Decompositions with Applications in Tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lukas Weissinger, Ronny Ramlau, Simon Hubmer","submitted_at":"2021-08-05T09:10:42Z","abstract_excerpt":"In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class of continuous regularization methods and derive convergence rates under both a-priori and a-posteriori parameter choice rules. Furthermore, we apply our derived results to a standard tomography problem based on the Radon transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02465","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.02465/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qgrjRGPXce4kMffrUNESYATntd7jGzsO0x8G2vV+OBxTD8c0QPVU4qumzl1OLaEzcR8bIjdaWpMbcezw/DvbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:44:38.635841Z"},"content_sha256":"7184e48297065e5fb6c0f8e21b67034a52dd7d8c2bd4707747d716bb7a0bd09e","schema_version":"1.0","event_id":"sha256:7184e48297065e5fb6c0f8e21b67034a52dd7d8c2bd4707747d716bb7a0bd09e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/bundle.json","state_url":"https://pith.science/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/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":"2026-08-11T03:44:38Z","links":{"resolver":"https://pith.science/pith/VQUMUYU6WZBXX4DV3MIXWJES7X","bundle":"https://pith.science/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/bundle.json","state":"https://pith.science/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQUMUYU6WZBXX4DV3MIXWJES7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VQUMUYU6WZBXX4DV3MIXWJES7X","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":"fe6284e822cd67c11f1ddca96afb528816ba86d0cfbade67bb48e77361aaff13","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-05T09:10:42Z","title_canon_sha256":"42c848e54d2a18c2b75d5f41dfff4db920df3a9f6e8e8d1ba0255f175b4e02d2"},"schema_version":"1.0","source":{"id":"2108.02465","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02465","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02465v4","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02465","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"VQUMUYU6WZBX","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_16","alias_value":"VQUMUYU6WZBXX4DV","created_at":"2026-07-05T05:12:48Z"},{"alias_kind":"pith_short_8","alias_value":"VQUMUYU6","created_at":"2026-07-05T05:12:48Z"}],"graph_snapshots":[{"event_id":"sha256:7184e48297065e5fb6c0f8e21b67034a52dd7d8c2bd4707747d716bb7a0bd09e","target":"graph","created_at":"2026-07-05T05:12:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.02465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class of continuous regularization methods and derive convergence rates under both a-priori and a-posteriori parameter choice rules. Furthermore, we apply our derived results to a standard tomography problem based on the Radon transform.","authors_text":"Lukas Weissinger, Ronny Ramlau, Simon Hubmer","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-05T09:10:42Z","title":"On Regularization via Frame Decompositions with Applications in Tomography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02465","kind":"arxiv","version":4},"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":"sha256:4c9af9ed1bb3ae4026b85036a4c8518836f6f845d5d065d01d6ebee859da983e","target":"record","created_at":"2026-07-05T05:12:48Z","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":"fe6284e822cd67c11f1ddca96afb528816ba86d0cfbade67bb48e77361aaff13","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-05T09:10:42Z","title_canon_sha256":"42c848e54d2a18c2b75d5f41dfff4db920df3a9f6e8e8d1ba0255f175b4e02d2"},"schema_version":"1.0","source":{"id":"2108.02465","kind":"arxiv","version":4}},"canonical_sha256":"ac28ca629eb6437bf075db117b2492fdc9d7396dd916765f185760c17632c687","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac28ca629eb6437bf075db117b2492fdc9d7396dd916765f185760c17632c687","first_computed_at":"2026-07-05T05:12:48.918151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:12:48.918151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"344uCvAt2CxrgFVUT3ieQ2DrLwfL07R4EWhp7Vzn9/nniAdo/sAV2pTx/J/Uf5Hc81wfNNkmux8ubFaNcnkzCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:12:48.918567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.02465","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c9af9ed1bb3ae4026b85036a4c8518836f6f845d5d065d01d6ebee859da983e","sha256:7184e48297065e5fb6c0f8e21b67034a52dd7d8c2bd4707747d716bb7a0bd09e"],"state_sha256":"c1382ae54dcd9acdc1980ac561231a48efe0bab1006493042a7d25af7462c848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"beBaBLd8jyztoweVzhrPciZYHuqpsKZS+tfUXcOWiIoebNz++kTAfflvNKLwgBk6f9e7IPD1pM6G85ZN1GoLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:44:38.639712Z","bundle_sha256":"18e9ad018b5bcda7d2d6f563e6dcb644305f3d2933b27be8f955f70020a5d26b"}}