{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XL65XDHEBRKXO53VEHUY3NXR4Y","short_pith_number":"pith:XL65XDHE","canonical_record":{"source":{"id":"2011.03627","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-06T23:05:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"defe18e018fb214e76e26d5e26acf1f7e9bdd7735458fbad2c6c2f0624d18caa","abstract_canon_sha256":"2e5341f86952b691c149508d0ed95176cf592ecc028b614f7de96d86a16a4176"},"schema_version":"1.0"},"canonical_sha256":"bafddb8ce40c5577777521e98db6f1e63fe65a46ae691d4d32762fb62b7c2d77","source":{"kind":"arxiv","id":"2011.03627","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03627","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03627v2","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03627","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"XL65XDHEBRKX","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_16","alias_value":"XL65XDHEBRKXO53V","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_8","alias_value":"XL65XDHE","created_at":"2026-07-05T03:31:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XL65XDHEBRKXO53VEHUY3NXR4Y","target":"record","payload":{"canonical_record":{"source":{"id":"2011.03627","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-06T23:05:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"defe18e018fb214e76e26d5e26acf1f7e9bdd7735458fbad2c6c2f0624d18caa","abstract_canon_sha256":"2e5341f86952b691c149508d0ed95176cf592ecc028b614f7de96d86a16a4176"},"schema_version":"1.0"},"canonical_sha256":"bafddb8ce40c5577777521e98db6f1e63fe65a46ae691d4d32762fb62b7c2d77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:23.115285Z","signature_b64":"UINObjysSJH8n3mxkW//RKqqxoYoxXimnbtxQdFjsM8GlBVEM4VKNCBHDpyvkLLQjqiKTlI3Cr3dkHnlCH4NBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bafddb8ce40c5577777521e98db6f1e63fe65a46ae691d4d32762fb62b7c2d77","last_reissued_at":"2026-07-05T03:31:23.114810Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:23.114810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.03627","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bKHUdTyOGXT1xeZDd0zQdF9TGDKp+phQhf5moFgSai+Z9Zuj+KiGLmM4Orxn3swoulj2dMMJLSONtDHG7NEBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:55:54.853806Z"},"content_sha256":"1b15f64da22814ab6e93cf1586e0d4ef9371281c8ebf00980af4def52c735a99","schema_version":"1.0","event_id":"sha256:1b15f64da22814ab6e93cf1586e0d4ef9371281c8ebf00980af4def52c735a99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XL65XDHEBRKXO53VEHUY3NXR4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discretization of learned NETT regularization for solving inverse problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Markus Haltmeier, Stephan Antholzer","submitted_at":"2020-11-06T23:05:48Z","abstract_excerpt":"Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains a trained neural network as regularizer in generalized Tikhonov regularization. The existing analysis of NETT considers fixed operator and fixed regularizer and analyzes the convergence as the noise level in the data approaches zero. In this paper, we extend the frameworks and analysis considerably to ref"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03627","kind":"arxiv","version":2},"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/2011.03627/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":"2026-07-05T03:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rAP7ruS03WxU/OJWGdVSC1lmx7QKheojCGRlRgTD2gNoP54qOqBrpHlscTH9vgW1KVvGD1oRViy+P//cPHMXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:55:54.854431Z"},"content_sha256":"1b4d9ed858375038f96bfd63fd290359847f87e33604fd84dde4dea472aff4c7","schema_version":"1.0","event_id":"sha256:1b4d9ed858375038f96bfd63fd290359847f87e33604fd84dde4dea472aff4c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/bundle.json","state_url":"https://pith.science/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/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":"2026-08-19T22:55:54Z","links":{"resolver":"https://pith.science/pith/XL65XDHEBRKXO53VEHUY3NXR4Y","bundle":"https://pith.science/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/bundle.json","state":"https://pith.science/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XL65XDHEBRKXO53VEHUY3NXR4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XL65XDHEBRKXO53VEHUY3NXR4Y","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":"2e5341f86952b691c149508d0ed95176cf592ecc028b614f7de96d86a16a4176","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-06T23:05:48Z","title_canon_sha256":"defe18e018fb214e76e26d5e26acf1f7e9bdd7735458fbad2c6c2f0624d18caa"},"schema_version":"1.0","source":{"id":"2011.03627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03627","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03627v2","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03627","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"XL65XDHEBRKX","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_16","alias_value":"XL65XDHEBRKXO53V","created_at":"2026-07-05T03:31:23Z"},{"alias_kind":"pith_short_8","alias_value":"XL65XDHE","created_at":"2026-07-05T03:31:23Z"}],"graph_snapshots":[{"event_id":"sha256:1b4d9ed858375038f96bfd63fd290359847f87e33604fd84dde4dea472aff4c7","target":"graph","created_at":"2026-07-05T03:31:23Z","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/2011.03627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains a trained neural network as regularizer in generalized Tikhonov regularization. The existing analysis of NETT considers fixed operator and fixed regularizer and analyzes the convergence as the noise level in the data approaches zero. In this paper, we extend the frameworks and analysis considerably to ref","authors_text":"Markus Haltmeier, Stephan Antholzer","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-06T23:05:48Z","title":"Discretization of learned NETT regularization for solving inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03627","kind":"arxiv","version":2},"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":"sha256:1b15f64da22814ab6e93cf1586e0d4ef9371281c8ebf00980af4def52c735a99","target":"record","created_at":"2026-07-05T03:31:23Z","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":"2e5341f86952b691c149508d0ed95176cf592ecc028b614f7de96d86a16a4176","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-06T23:05:48Z","title_canon_sha256":"defe18e018fb214e76e26d5e26acf1f7e9bdd7735458fbad2c6c2f0624d18caa"},"schema_version":"1.0","source":{"id":"2011.03627","kind":"arxiv","version":2}},"canonical_sha256":"bafddb8ce40c5577777521e98db6f1e63fe65a46ae691d4d32762fb62b7c2d77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bafddb8ce40c5577777521e98db6f1e63fe65a46ae691d4d32762fb62b7c2d77","first_computed_at":"2026-07-05T03:31:23.114810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:23.114810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UINObjysSJH8n3mxkW//RKqqxoYoxXimnbtxQdFjsM8GlBVEM4VKNCBHDpyvkLLQjqiKTlI3Cr3dkHnlCH4NBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:23.115285Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.03627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b15f64da22814ab6e93cf1586e0d4ef9371281c8ebf00980af4def52c735a99","sha256:1b4d9ed858375038f96bfd63fd290359847f87e33604fd84dde4dea472aff4c7"],"state_sha256":"e97750256e71baf846d9143549e4c702ac4d92cc9a9d7184fe57d480f1028710"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FAnZXGpg5XeiPdWxfRytJlvkx4StzW4u14DRZY89AJRFi9yBN56T5i0JpfMs97To2/UcJJmnly2QKuRd/SK2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:55:54.857976Z","bundle_sha256":"3cfc40fba9db9ed49cc78e48ccbba982b1b611d02406b30281416e5c610bc10d"}}