{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3QSAND5KFEP5INNAQRFYZOD35J","short_pith_number":"pith:3QSAND5K","canonical_record":{"source":{"id":"2605.12041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-12T12:24:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ce846542904f47410fee6c545b4074b2cffa5102613bdfd80efa77c796ebf17f","abstract_canon_sha256":"e75db0c2f718851ca748fc387f1a1a53c7dc26fd046ee13221ae62ef429301f2"},"schema_version":"1.0"},"canonical_sha256":"dc24068faa291fd435a0844b8cb87bea4d7d051e40829c096e7a142a586cdcca","source":{"kind":"arxiv","id":"2605.12041","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12041","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12041v2","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12041","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"3QSAND5KFEP5","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_16","alias_value":"3QSAND5KFEP5INNA","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_8","alias_value":"3QSAND5K","created_at":"2026-06-25T01:17:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3QSAND5KFEP5INNAQRFYZOD35J","target":"record","payload":{"canonical_record":{"source":{"id":"2605.12041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-12T12:24:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ce846542904f47410fee6c545b4074b2cffa5102613bdfd80efa77c796ebf17f","abstract_canon_sha256":"e75db0c2f718851ca748fc387f1a1a53c7dc26fd046ee13221ae62ef429301f2"},"schema_version":"1.0"},"canonical_sha256":"dc24068faa291fd435a0844b8cb87bea4d7d051e40829c096e7a142a586cdcca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:17:53.887867Z","signature_b64":"+S9DookKGv+I/6czukb6IGKpw/b4QJU+LRUSWeGVH/uVV132inzwzFDnXmws2JNkgO3v5Yx3FpvzvYOdijAUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc24068faa291fd435a0844b8cb87bea4d7d051e40829c096e7a142a586cdcca","last_reissued_at":"2026-06-25T01:17:53.887397Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:17:53.887397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.12041","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":"2026-06-25T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dnZAjZU6qts3thc/+7GD/XU8h3XsWWO8BuKdbUsfm/1NQBYlIcV4oEo5vqU4/5uNZGM0Y+PX4j5rPRRx/FlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T07:43:40.660745Z"},"content_sha256":"626703e0b9dca8d4758810935457ca8ac345857d190d2b5391ac4dbb5d326c5c","schema_version":"1.0","event_id":"sha256:626703e0b9dca8d4758810935457ca8ac345857d190d2b5391ac4dbb5d326c5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3QSAND5KFEP5INNAQRFYZOD35J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient TV regularization of large-scale linear inverse problems via the SCD semismooth* Newton method with applications in tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Helmut Gfrerer, Jaakko Kultima, Ronny Ramlau, Simon Hubmer, Stefan Kindermann, Tanja Tarvainen","submitted_at":"2026-05-12T12:24:48Z","abstract_excerpt":"In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via smooth approximations, which are inexact, or using non-smooth optimization techniques, which can often be numerically expensive, in particular for large-scale problems. Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits local"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the semismooth* Newton method can be applied efficiently to the non-smooth TV penalty term without requiring excessive computational resources or losing the superlinear convergence in practice for large-scale problems.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An efficient semismooth* Newton method is presented for minimizing Tikhonov functionals with total variation regularization, offering superlinear convergence for large-scale tomographic imaging problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"aeca7ecc9360baf7620b54e77aaebaea7b6f7a869371c08e3a6815f0d85eee79"},"source":{"id":"2605.12041","kind":"arxiv","version":2},"verdict":{"id":"dc26d5ca-1e83-46ad-b7e3-2c2ec5c5b812","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T04:28:57.077867Z","strongest_claim":"Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees.","one_line_summary":"An efficient semismooth* Newton method is presented for minimizing Tikhonov functionals with total variation regularization, offering superlinear convergence for large-scale tomographic imaging problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the semismooth* Newton method can be applied efficiently to the non-smooth TV penalty term without requiring excessive computational resources or losing the superlinear convergence in practice for large-scale problems.","pith_extraction_headline":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.12041/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-26T15:44:08.059454Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T17:01:26.457713Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T11:35:44.793616Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:01:58.423812Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f8ba8d8066a3522b779133d0242a50171fa7c124eb68d4dd14c6c2cddf09ae53"},"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":"dc26d5ca-1e83-46ad-b7e3-2c2ec5c5b812"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fTCtdm/HWMro+uN13Zj+GIO8OEWyMgtyBMLJxoHybKIUifzXVx353JeEQ7NRW9ekwXB/qqGD8w4jBvgkZVqnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T07:43:40.661224Z"},"content_sha256":"fa63127df717b714ecc4899768612ddda091b0fdf8de69578ab9ab4c35e1c030","schema_version":"1.0","event_id":"sha256:fa63127df717b714ecc4899768612ddda091b0fdf8de69578ab9ab4c35e1c030"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QSAND5KFEP5INNAQRFYZOD35J/bundle.json","state_url":"https://pith.science/pith/3QSAND5KFEP5INNAQRFYZOD35J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QSAND5KFEP5INNAQRFYZOD35J/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":"2026-07-22T07:43:40Z","links":{"resolver":"https://pith.science/pith/3QSAND5KFEP5INNAQRFYZOD35J","bundle":"https://pith.science/pith/3QSAND5KFEP5INNAQRFYZOD35J/bundle.json","state":"https://pith.science/pith/3QSAND5KFEP5INNAQRFYZOD35J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QSAND5KFEP5INNAQRFYZOD35J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3QSAND5KFEP5INNAQRFYZOD35J","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":"e75db0c2f718851ca748fc387f1a1a53c7dc26fd046ee13221ae62ef429301f2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-12T12:24:48Z","title_canon_sha256":"ce846542904f47410fee6c545b4074b2cffa5102613bdfd80efa77c796ebf17f"},"schema_version":"1.0","source":{"id":"2605.12041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12041","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12041v2","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12041","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"3QSAND5KFEP5","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_16","alias_value":"3QSAND5KFEP5INNA","created_at":"2026-06-25T01:17:53Z"},{"alias_kind":"pith_short_8","alias_value":"3QSAND5K","created_at":"2026-06-25T01:17:53Z"}],"graph_snapshots":[{"event_id":"sha256:fa63127df717b714ecc4899768612ddda091b0fdf8de69578ab9ab4c35e1c030","target":"graph","created_at":"2026-06-25T01:17:53Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the semismooth* Newton method can be applied efficiently to the non-smooth TV penalty term without requiring excessive computational resources or losing the superlinear convergence in practice for large-scale problems."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"An efficient semismooth* Newton method is presented for minimizing Tikhonov functionals with total variation regularization, offering superlinear convergence for large-scale tomographic imaging problems."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems."}],"snapshot_sha256":"aeca7ecc9360baf7620b54e77aaebaea7b6f7a869371c08e3a6815f0d85eee79"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-26T15:44:08.059454Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T17:01:26.457713Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-20T11:35:44.793616Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T23:01:58.423812Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.12041/integrity.json","findings":[],"snapshot_sha256":"f8ba8d8066a3522b779133d0242a50171fa7c124eb68d4dd14c6c2cddf09ae53","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via smooth approximations, which are inexact, or using non-smooth optimization techniques, which can often be numerically expensive, in particular for large-scale problems. Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits local","authors_text":"Helmut Gfrerer, Jaakko Kultima, Ronny Ramlau, Simon Hubmer, Stefan Kindermann, Tanja Tarvainen","cross_cats":["cs.NA"],"headline":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-12T12:24:48Z","title":"Efficient TV regularization of large-scale linear inverse problems via the SCD semismooth* Newton method with applications in tomography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12041","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T04:28:57.077867Z","id":"dc26d5ca-1e83-46ad-b7e3-2c2ec5c5b812","model_set":{"reader":"grok-4.3"},"one_line_summary":"An efficient semismooth* Newton method is presented for minimizing Tikhonov functionals with total variation regularization, offering superlinear convergence for large-scale tomographic imaging problems.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The SCD semismooth* Newton method minimizes TV-regularized Tikhonov functionals efficiently for large-scale linear inverse problems.","strongest_claim":"Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees.","weakest_assumption":"That the semismooth* Newton method can be applied efficiently to the non-smooth TV penalty term without requiring excessive computational resources or losing the superlinear convergence in practice for large-scale problems."}},"verdict_id":"dc26d5ca-1e83-46ad-b7e3-2c2ec5c5b812"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:626703e0b9dca8d4758810935457ca8ac345857d190d2b5391ac4dbb5d326c5c","target":"record","created_at":"2026-06-25T01:17:53Z","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":"e75db0c2f718851ca748fc387f1a1a53c7dc26fd046ee13221ae62ef429301f2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-12T12:24:48Z","title_canon_sha256":"ce846542904f47410fee6c545b4074b2cffa5102613bdfd80efa77c796ebf17f"},"schema_version":"1.0","source":{"id":"2605.12041","kind":"arxiv","version":2}},"canonical_sha256":"dc24068faa291fd435a0844b8cb87bea4d7d051e40829c096e7a142a586cdcca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc24068faa291fd435a0844b8cb87bea4d7d051e40829c096e7a142a586cdcca","first_computed_at":"2026-06-25T01:17:53.887397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:17:53.887397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+S9DookKGv+I/6czukb6IGKpw/b4QJU+LRUSWeGVH/uVV132inzwzFDnXmws2JNkgO3v5Yx3FpvzvYOdijAUBQ==","signature_status":"signed_v1","signed_at":"2026-06-25T01:17:53.887867Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:626703e0b9dca8d4758810935457ca8ac345857d190d2b5391ac4dbb5d326c5c","sha256:fa63127df717b714ecc4899768612ddda091b0fdf8de69578ab9ab4c35e1c030"],"state_sha256":"9a100e45e18dcb8d53bf902c94d94c4005577f522102fe148d1aa4f6edd363f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+kGNWrdcMD2fY0Bkkvc80BNLW63Nj+yc4aMwUSQYtkSunwjN6wgML114chkUURIafnSoFlPM7TNzCsiBt62Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T07:43:40.664045Z","bundle_sha256":"1671d6ab3ed1eab0d0efd9b4567cb137f7cee020e8d4dcd8460363a845616223"}}