{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AQ67W6SB2A2K6H7TSVXAT2EBGR","short_pith_number":"pith:AQ67W6SB","canonical_record":{"source":{"id":"1309.7152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-27T08:41:22Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e510059d609e0f9cbd62e5526e856ab46409d3c2db0632438a0c6f423d9329cf","abstract_canon_sha256":"49921ee42eafefcf5e74c38de95b5e322ad83d627325bf99a4ed978b8c56f17a"},"schema_version":"1.0"},"canonical_sha256":"043dfb7a41d034af1ff3956e09e8813458dc787c3d181706893ff57fdeaf5c48","source":{"kind":"arxiv","id":"1309.7152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7152","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7152v1","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7152","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"AQ67W6SB2A2K","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AQ67W6SB2A2K6H7T","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AQ67W6SB","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AQ67W6SB2A2K6H7TSVXAT2EBGR","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-27T08:41:22Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e510059d609e0f9cbd62e5526e856ab46409d3c2db0632438a0c6f423d9329cf","abstract_canon_sha256":"49921ee42eafefcf5e74c38de95b5e322ad83d627325bf99a4ed978b8c56f17a"},"schema_version":"1.0"},"canonical_sha256":"043dfb7a41d034af1ff3956e09e8813458dc787c3d181706893ff57fdeaf5c48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:00.063155Z","signature_b64":"tRZhyI8BtmBKthaiLjXQtQT+zQu+lKUe540BRkHygRvUc0qz87u9oFC3LAeSmMEtqbfHGJsMKYU48ztHMybvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"043dfb7a41d034af1ff3956e09e8813458dc787c3d181706893ff57fdeaf5c48","last_reissued_at":"2026-05-18T03:12:00.062251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:00.062251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7152","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":"2026-05-18T03:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/tYgSiBU2Q4O9U7vxt3uzbV77N09gNIvDDscKLX62WOL6pPYZl0ciQbrr1kUtLup+3pvYdE4R6lVR0c3tO5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:11:11.798164Z"},"content_sha256":"23526843add4aa1def9585a89b674ee52d924510e87def308f4851a489046d44","schema_version":"1.0","event_id":"sha256:23526843add4aa1def9585a89b674ee52d924510e87def308f4851a489046d44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AQ67W6SB2A2K6H7TSVXAT2EBGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Solutions of One-Dimensional TGV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Christiane P\\\"oschl, Otmar Scherzer","submitted_at":"2013-09-27T08:41:22Z","abstract_excerpt":"L2-TGV-regularization has been introduced by Bredies, Kunisch, and Pock. This regularization method requires careful tuning of two regularization parameters. The focus of this paper is to derive analytical results, which allow for characterizing parameter settings, which make this method in fact different from L2-TV (the ROF-model) and L2-TV2 regularization, respectively. In this paper we also provide explicit solutions of TGV-denoising for particular one-dimensional function data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7152","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":"2026-05-18T03:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaxcInD7MFOlb7UtLDxjsy0G4klgc4nUyx7vCE/NZwmXHYA7l/Pi/AKZJ84QH4AFr4hs074oLv5S0yyeZaXyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:11:11.798866Z"},"content_sha256":"4855e6652d8a8a09ea662bd76c2ef181b4573bb7a94bf0895aa15a1d0e734193","schema_version":"1.0","event_id":"sha256:4855e6652d8a8a09ea662bd76c2ef181b4573bb7a94bf0895aa15a1d0e734193"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/bundle.json","state_url":"https://pith.science/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/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":"2026-05-31T06:11:11Z","links":{"resolver":"https://pith.science/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR","bundle":"https://pith.science/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/bundle.json","state":"https://pith.science/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQ67W6SB2A2K6H7TSVXAT2EBGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AQ67W6SB2A2K6H7TSVXAT2EBGR","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":"49921ee42eafefcf5e74c38de95b5e322ad83d627325bf99a4ed978b8c56f17a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-27T08:41:22Z","title_canon_sha256":"e510059d609e0f9cbd62e5526e856ab46409d3c2db0632438a0c6f423d9329cf"},"schema_version":"1.0","source":{"id":"1309.7152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7152","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7152v1","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7152","created_at":"2026-05-18T03:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"AQ67W6SB2A2K","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AQ67W6SB2A2K6H7T","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AQ67W6SB","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:4855e6652d8a8a09ea662bd76c2ef181b4573bb7a94bf0895aa15a1d0e734193","target":"graph","created_at":"2026-05-18T03:12:00Z","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":"L2-TGV-regularization has been introduced by Bredies, Kunisch, and Pock. This regularization method requires careful tuning of two regularization parameters. The focus of this paper is to derive analytical results, which allow for characterizing parameter settings, which make this method in fact different from L2-TV (the ROF-model) and L2-TV2 regularization, respectively. In this paper we also provide explicit solutions of TGV-denoising for particular one-dimensional function data.","authors_text":"Christiane P\\\"oschl, Otmar Scherzer","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-27T08:41:22Z","title":"Exact Solutions of One-Dimensional TGV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7152","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":"sha256:23526843add4aa1def9585a89b674ee52d924510e87def308f4851a489046d44","target":"record","created_at":"2026-05-18T03:12:00Z","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":"49921ee42eafefcf5e74c38de95b5e322ad83d627325bf99a4ed978b8c56f17a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-27T08:41:22Z","title_canon_sha256":"e510059d609e0f9cbd62e5526e856ab46409d3c2db0632438a0c6f423d9329cf"},"schema_version":"1.0","source":{"id":"1309.7152","kind":"arxiv","version":1}},"canonical_sha256":"043dfb7a41d034af1ff3956e09e8813458dc787c3d181706893ff57fdeaf5c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"043dfb7a41d034af1ff3956e09e8813458dc787c3d181706893ff57fdeaf5c48","first_computed_at":"2026-05-18T03:12:00.062251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:00.062251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRZhyI8BtmBKthaiLjXQtQT+zQu+lKUe540BRkHygRvUc0qz87u9oFC3LAeSmMEtqbfHGJsMKYU48ztHMybvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:00.063155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23526843add4aa1def9585a89b674ee52d924510e87def308f4851a489046d44","sha256:4855e6652d8a8a09ea662bd76c2ef181b4573bb7a94bf0895aa15a1d0e734193"],"state_sha256":"adc2ac6ade7f55d27fed07a0355fd15b10d6b42ac907b5d594e12cc39ba9803f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52rWuvKbMFg6OFIfR/lGj6wdJtgz89izXoB0cujt9GlndogXGnbp1NujVhv7NmxXh307jTezurTTHWFrAvNrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:11:11.802388Z","bundle_sha256":"c0710f5901b0d6dedd65f41d755de45b800bb5b13af97c63101376c28be34a57"}}