{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CERS3MTCGQTV23UQOEEXJEUCK3","short_pith_number":"pith:CERS3MTC","canonical_record":{"source":{"id":"1106.5812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-28T22:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"062b387c357bf8c7ed8b8207597828b8ab012e542142ce426fa161965aa2bb87","abstract_canon_sha256":"1ef36d68b32742b2c0002de5f2544325bb2a5a5f680ab0ee9b088e34ee3289eb"},"schema_version":"1.0"},"canonical_sha256":"11232db26234275d6e90710974928256f18160d270a79b51eba500e4f3677386","source":{"kind":"arxiv","id":"1106.5812","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5812","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5812v1","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5812","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"CERS3MTCGQTV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CERS3MTCGQTV23UQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CERS3MTC","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CERS3MTCGQTV23UQOEEXJEUCK3","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-28T22:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"062b387c357bf8c7ed8b8207597828b8ab012e542142ce426fa161965aa2bb87","abstract_canon_sha256":"1ef36d68b32742b2c0002de5f2544325bb2a5a5f680ab0ee9b088e34ee3289eb"},"schema_version":"1.0"},"canonical_sha256":"11232db26234275d6e90710974928256f18160d270a79b51eba500e4f3677386","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:00.705197Z","signature_b64":"IAPUjX2f0JEyc/0s8IqnhaSnutDcj0N1Qns0MbhSkBRf30jrjDY7r5xd2ERm4AYlxl+X9/kmVXf2IwbgaTnYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11232db26234275d6e90710974928256f18160d270a79b51eba500e4f3677386","last_reissued_at":"2026-05-18T02:20:00.704582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:00.704582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5812","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":"2026-05-18T02:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/5dYNDsaCdIURevmdQ5ErF2OPJRzUz4Ce94M62/5XCEW+na0N88IZfp/GKm1nFuQSEQh08iTMZ8khId+RHeuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:41:40.419415Z"},"content_sha256":"4238359696940296330cc95290f5c9aa2bb4f6fcfdb1d9b822bf1d2416fc8bbd","schema_version":"1.0","event_id":"sha256:4238359696940296330cc95290f5c9aa2bb4f6fcfdb1d9b822bf1d2416fc8bbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CERS3MTCGQTV23UQOEEXJEUCK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Iteratively Regularized Gau{\\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Martin Burger, Robert St\\\"uck, Thorsten Hohage","submitted_at":"2011-06-28T22:20:28Z","abstract_excerpt":"This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5812","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":"2026-05-18T02:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyeMFNe9grvlXqGTurRFSjbEs5bYX2vqMOiwNsCoT9lh6GjYWuXEl1BlfRDKLHtQf84BWg9nhsakgDDovfhOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:41:40.419800Z"},"content_sha256":"b6282632d46fa6827572658f1a2d50588f3edccb8114c5f1ebfc166e3ae296aa","schema_version":"1.0","event_id":"sha256:b6282632d46fa6827572658f1a2d50588f3edccb8114c5f1ebfc166e3ae296aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CERS3MTCGQTV23UQOEEXJEUCK3/bundle.json","state_url":"https://pith.science/pith/CERS3MTCGQTV23UQOEEXJEUCK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CERS3MTCGQTV23UQOEEXJEUCK3/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":"2026-05-31T03:41:40Z","links":{"resolver":"https://pith.science/pith/CERS3MTCGQTV23UQOEEXJEUCK3","bundle":"https://pith.science/pith/CERS3MTCGQTV23UQOEEXJEUCK3/bundle.json","state":"https://pith.science/pith/CERS3MTCGQTV23UQOEEXJEUCK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CERS3MTCGQTV23UQOEEXJEUCK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CERS3MTCGQTV23UQOEEXJEUCK3","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":"1ef36d68b32742b2c0002de5f2544325bb2a5a5f680ab0ee9b088e34ee3289eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-28T22:20:28Z","title_canon_sha256":"062b387c357bf8c7ed8b8207597828b8ab012e542142ce426fa161965aa2bb87"},"schema_version":"1.0","source":{"id":"1106.5812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5812","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5812v1","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5812","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"CERS3MTCGQTV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CERS3MTCGQTV23UQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CERS3MTC","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:b6282632d46fa6827572658f1a2d50588f3edccb8114c5f1ebfc166e3ae296aa","target":"graph","created_at":"2026-05-18T02:20:00Z","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":"This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with non","authors_text":"Martin Burger, Robert St\\\"uck, Thorsten Hohage","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-28T22:20:28Z","title":"The Iteratively Regularized Gau{\\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5812","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":"sha256:4238359696940296330cc95290f5c9aa2bb4f6fcfdb1d9b822bf1d2416fc8bbd","target":"record","created_at":"2026-05-18T02:20:00Z","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":"1ef36d68b32742b2c0002de5f2544325bb2a5a5f680ab0ee9b088e34ee3289eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-28T22:20:28Z","title_canon_sha256":"062b387c357bf8c7ed8b8207597828b8ab012e542142ce426fa161965aa2bb87"},"schema_version":"1.0","source":{"id":"1106.5812","kind":"arxiv","version":1}},"canonical_sha256":"11232db26234275d6e90710974928256f18160d270a79b51eba500e4f3677386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11232db26234275d6e90710974928256f18160d270a79b51eba500e4f3677386","first_computed_at":"2026-05-18T02:20:00.704582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:00.704582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAPUjX2f0JEyc/0s8IqnhaSnutDcj0N1Qns0MbhSkBRf30jrjDY7r5xd2ERm4AYlxl+X9/kmVXf2IwbgaTnYBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:00.705197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4238359696940296330cc95290f5c9aa2bb4f6fcfdb1d9b822bf1d2416fc8bbd","sha256:b6282632d46fa6827572658f1a2d50588f3edccb8114c5f1ebfc166e3ae296aa"],"state_sha256":"b8934d5ba2f9e5aa941790d59879b08391336538cc6f55cbee579c8020cc71c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2r3QQG9+FufvdDFRDVBf8Y+Ctr7FEyNscU0D6J1SzD9STue37S3o5Aw5Ja1nIUahJ1xFrTsnuOVhe7lTzSxzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:41:40.422611Z","bundle_sha256":"879ddc35a0b8b4de4fa046df40bd6629fc76f760b3002e6f86f266abbcdcc72b"}}