{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T3UYMVUBUOO3IHADOTTM2P7CEW","short_pith_number":"pith:T3UYMVUB","canonical_record":{"source":{"id":"1908.03006","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-08T10:38:01Z","cross_cats_sorted":["cs.LG","cs.NA","math.OC"],"title_canon_sha256":"49a7b9758769f7bec12dfb69764d758f09137994aac8f1846a9d15742d03375b","abstract_canon_sha256":"b201313fe9b3a8df6951e7465a6f171de02e06e7feab44bdb8b53282d16f2668"},"schema_version":"1.0"},"canonical_sha256":"9ee9865681a39db41c0374e6cd3fe225b13af0d442c10fe159272f86a61c9fe5","source":{"kind":"arxiv","id":"1908.03006","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03006","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03006v3","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03006","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"T3UYMVUBUOO3","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"T3UYMVUBUOO3IHAD","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"T3UYMVUB","created_at":"2026-07-05T02:13:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T3UYMVUBUOO3IHADOTTM2P7CEW","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03006","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-08T10:38:01Z","cross_cats_sorted":["cs.LG","cs.NA","math.OC"],"title_canon_sha256":"49a7b9758769f7bec12dfb69764d758f09137994aac8f1846a9d15742d03375b","abstract_canon_sha256":"b201313fe9b3a8df6951e7465a6f171de02e06e7feab44bdb8b53282d16f2668"},"schema_version":"1.0"},"canonical_sha256":"9ee9865681a39db41c0374e6cd3fe225b13af0d442c10fe159272f86a61c9fe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:13:11.109675Z","signature_b64":"VU36rxTq3pSs5rSLURPi/6da/girdMeW2wq8oAx8RQGLdFRVDUhOoeYhgRaJ1ngWAnTY3nzBOu67tdr70YYUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee9865681a39db41c0374e6cd3fe225b13af0d442c10fe159272f86a61c9fe5","last_reissued_at":"2026-07-05T02:13:11.109308Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:13:11.109308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03006","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":"2026-07-05T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/e+psgP1L7iNs0kVqTm0Wl6/APueN3fPAqJRpb133WlQn7tndTrhsztnez+6/a7DKzw/iDkPOa64hURFEzABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:16:48.187792Z"},"content_sha256":"da3104a91c702a0b1e8bf44d3dcffcd983591bd523e085281fa97222318288e7","schema_version":"1.0","event_id":"sha256:da3104a91c702a0b1e8bf44d3dcffcd983591bd523e085281fa97222318288e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T3UYMVUBUOO3IHADOTTM2P7CEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Augmented NETT Regularization of Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Daniel Obmann, Johannes Schwab, Linh Nguyen, Markus Haltmeier","submitted_at":"2019-08-08T10:38:01Z","abstract_excerpt":"We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the data manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03006/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":"2026-07-05T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7WSxa2i6zoVM157wxfo5vGWozSERTk+AP26oi0RW9luIPXAQ9bWEDOkWGhlRg7FQlgeHhTIyJrH5x/+wkzR7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:16:48.188917Z"},"content_sha256":"19eb605d23136872b380ca2a319a99baf050642d4c80a60eb1d5c400a13221fe","schema_version":"1.0","event_id":"sha256:19eb605d23136872b380ca2a319a99baf050642d4c80a60eb1d5c400a13221fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/bundle.json","state_url":"https://pith.science/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/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":"2026-08-16T11:16:48Z","links":{"resolver":"https://pith.science/pith/T3UYMVUBUOO3IHADOTTM2P7CEW","bundle":"https://pith.science/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/bundle.json","state":"https://pith.science/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3UYMVUBUOO3IHADOTTM2P7CEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T3UYMVUBUOO3IHADOTTM2P7CEW","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":"b201313fe9b3a8df6951e7465a6f171de02e06e7feab44bdb8b53282d16f2668","cross_cats_sorted":["cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-08T10:38:01Z","title_canon_sha256":"49a7b9758769f7bec12dfb69764d758f09137994aac8f1846a9d15742d03375b"},"schema_version":"1.0","source":{"id":"1908.03006","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03006","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03006v3","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03006","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"T3UYMVUBUOO3","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"T3UYMVUBUOO3IHAD","created_at":"2026-07-05T02:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"T3UYMVUB","created_at":"2026-07-05T02:13:11Z"}],"graph_snapshots":[{"event_id":"sha256:19eb605d23136872b380ca2a319a99baf050642d4c80a60eb1d5c400a13221fe","target":"graph","created_at":"2026-07-05T02:13:11Z","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/1908.03006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the data manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possi","authors_text":"Daniel Obmann, Johannes Schwab, Linh Nguyen, Markus Haltmeier","cross_cats":["cs.LG","cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-08T10:38:01Z","title":"Augmented NETT Regularization of Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03006","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:da3104a91c702a0b1e8bf44d3dcffcd983591bd523e085281fa97222318288e7","target":"record","created_at":"2026-07-05T02:13:11Z","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":"b201313fe9b3a8df6951e7465a6f171de02e06e7feab44bdb8b53282d16f2668","cross_cats_sorted":["cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-08T10:38:01Z","title_canon_sha256":"49a7b9758769f7bec12dfb69764d758f09137994aac8f1846a9d15742d03375b"},"schema_version":"1.0","source":{"id":"1908.03006","kind":"arxiv","version":3}},"canonical_sha256":"9ee9865681a39db41c0374e6cd3fe225b13af0d442c10fe159272f86a61c9fe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ee9865681a39db41c0374e6cd3fe225b13af0d442c10fe159272f86a61c9fe5","first_computed_at":"2026-07-05T02:13:11.109308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:11.109308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VU36rxTq3pSs5rSLURPi/6da/girdMeW2wq8oAx8RQGLdFRVDUhOoeYhgRaJ1ngWAnTY3nzBOu67tdr70YYUBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:11.109675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03006","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da3104a91c702a0b1e8bf44d3dcffcd983591bd523e085281fa97222318288e7","sha256:19eb605d23136872b380ca2a319a99baf050642d4c80a60eb1d5c400a13221fe"],"state_sha256":"33fda81349dda793d1c5524c52f61b1a72ec26a82abbc65cd6582efca33d5811"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1xgdwb3ErnRaO0UZ2VRoy4MK00bSg1j6KS3KTwb6+gp8+Q0cKUacMPLybPfnvIxY+mc9AkwKQXypsLc4XAoBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:16:48.195830Z","bundle_sha256":"a12d798470c16420421129a9b3ee12fef5b771cc2cd9a8264ae03e2bb231b377"}}