{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T37VGFXX6E6ECHDARWAJL5P7HI","short_pith_number":"pith:T37VGFXX","canonical_record":{"source":{"id":"1906.09919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T13:04:09Z","cross_cats_sorted":["eess.SP"],"title_canon_sha256":"ccfa0e4b72b3f08217454ac658b07fd101eb84915c6e21a3ffc46b7e03e1bb8f","abstract_canon_sha256":"2d9b64ef840e4a27a99ad660fedbce1f302a2d870c4ace5ed5e3051f4686997a"},"schema_version":"1.0"},"canonical_sha256":"9eff5316f7f13c411c608d8095f5ff3a1dc7c8c8528041a81627b1ba9d963f94","source":{"kind":"arxiv","id":"1906.09919","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09919","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09919v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09919","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"T37VGFXX6E6E","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T37VGFXX6E6ECHDA","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T37VGFXX","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T37VGFXX6E6ECHDARWAJL5P7HI","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T13:04:09Z","cross_cats_sorted":["eess.SP"],"title_canon_sha256":"ccfa0e4b72b3f08217454ac658b07fd101eb84915c6e21a3ffc46b7e03e1bb8f","abstract_canon_sha256":"2d9b64ef840e4a27a99ad660fedbce1f302a2d870c4ace5ed5e3051f4686997a"},"schema_version":"1.0"},"canonical_sha256":"9eff5316f7f13c411c608d8095f5ff3a1dc7c8c8528041a81627b1ba9d963f94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:36.158188Z","signature_b64":"NI4iktz3suu2eGC4vWXtosLFvCBXPuXdiRfG2BwWuYvqc+9swk63zVReF022S80xSCdySBK5XUMFdm5MfOeLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9eff5316f7f13c411c608d8095f5ff3a1dc7c8c8528041a81627b1ba9d963f94","last_reissued_at":"2026-05-17T23:42:36.157438Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:36.157438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09919","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":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C64CViOo44UkRoTlLBWaU/xFnS+xeV3icIr8rk1YTePaGKeU3BiMijdQRt+Q73jbItlK8N8w1jAfdMeEG9sVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:09:56.931957Z"},"content_sha256":"8785330d9ee1e0ab69ff2431dfd92a26329b8e6e08a55515642592589bc3f518","schema_version":"1.0","event_id":"sha256:8785330d9ee1e0ab69ff2431dfd92a26329b8e6e08a55515642592589bc3f518"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T37VGFXX6E6ECHDARWAJL5P7HI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the linear convergence rates of exchange and continuous methods for total variation minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["eess.SP"],"primary_cat":"math.OC","authors_text":"Axel Flinth (IMT), Fr\\'ed\\'eric de Gournay (IMT, ITAV), Pierre Weiss (IMT","submitted_at":"2019-06-24T13:04:09Z","abstract_excerpt":"We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M($\\Omega$) of Radon measures on a subset $\\Omega$ of R d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09919","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":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MfdCGi1Ei1Y58DU4pALN/uDXwBgk1On+fEczyVgTJcBDZmwUc15C4jqa4054TTcZd/ET1Nox93zirhRE3J6SAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:09:56.932309Z"},"content_sha256":"732751433b42ae342d9e34e242a0b23379af19502f0e5f4072d65a1b814077c4","schema_version":"1.0","event_id":"sha256:732751433b42ae342d9e34e242a0b23379af19502f0e5f4072d65a1b814077c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T37VGFXX6E6ECHDARWAJL5P7HI/bundle.json","state_url":"https://pith.science/pith/T37VGFXX6E6ECHDARWAJL5P7HI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T37VGFXX6E6ECHDARWAJL5P7HI/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":"2026-05-28T10:09:56Z","links":{"resolver":"https://pith.science/pith/T37VGFXX6E6ECHDARWAJL5P7HI","bundle":"https://pith.science/pith/T37VGFXX6E6ECHDARWAJL5P7HI/bundle.json","state":"https://pith.science/pith/T37VGFXX6E6ECHDARWAJL5P7HI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T37VGFXX6E6ECHDARWAJL5P7HI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T37VGFXX6E6ECHDARWAJL5P7HI","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":"2d9b64ef840e4a27a99ad660fedbce1f302a2d870c4ace5ed5e3051f4686997a","cross_cats_sorted":["eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T13:04:09Z","title_canon_sha256":"ccfa0e4b72b3f08217454ac658b07fd101eb84915c6e21a3ffc46b7e03e1bb8f"},"schema_version":"1.0","source":{"id":"1906.09919","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09919","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09919v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09919","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"T37VGFXX6E6E","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T37VGFXX6E6ECHDA","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T37VGFXX","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:732751433b42ae342d9e34e242a0b23379af19502f0e5f4072d65a1b814077c4","target":"graph","created_at":"2026-05-17T23:42:36Z","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":"We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M($\\Omega$) of Radon measures on a subset $\\Omega$ of R d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach.","authors_text":"Axel Flinth (IMT), Fr\\'ed\\'eric de Gournay (IMT, ITAV), Pierre Weiss (IMT","cross_cats":["eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T13:04:09Z","title":"On the linear convergence rates of exchange and continuous methods for total variation minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09919","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":"sha256:8785330d9ee1e0ab69ff2431dfd92a26329b8e6e08a55515642592589bc3f518","target":"record","created_at":"2026-05-17T23:42:36Z","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":"2d9b64ef840e4a27a99ad660fedbce1f302a2d870c4ace5ed5e3051f4686997a","cross_cats_sorted":["eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T13:04:09Z","title_canon_sha256":"ccfa0e4b72b3f08217454ac658b07fd101eb84915c6e21a3ffc46b7e03e1bb8f"},"schema_version":"1.0","source":{"id":"1906.09919","kind":"arxiv","version":1}},"canonical_sha256":"9eff5316f7f13c411c608d8095f5ff3a1dc7c8c8528041a81627b1ba9d963f94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9eff5316f7f13c411c608d8095f5ff3a1dc7c8c8528041a81627b1ba9d963f94","first_computed_at":"2026-05-17T23:42:36.157438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:36.157438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NI4iktz3suu2eGC4vWXtosLFvCBXPuXdiRfG2BwWuYvqc+9swk63zVReF022S80xSCdySBK5XUMFdm5MfOeLAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:36.158188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09919","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8785330d9ee1e0ab69ff2431dfd92a26329b8e6e08a55515642592589bc3f518","sha256:732751433b42ae342d9e34e242a0b23379af19502f0e5f4072d65a1b814077c4"],"state_sha256":"db8ec3342999f5fe2e46276c4d89782bcc8a9906a66e2a3011fdaadea6f0030c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLWWNjV9cW4cn36YAztcVobaYZIaIp9qVGr+NI0Zi25m39f2Fk4fX8uOtl4HD7KStt3opIHh8DWPmKs0dvqxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:09:56.934276Z","bundle_sha256":"d234c262f0c13fec2dce2318ac292aac7c6e9ab921fcc5b8ad315f33de2e290f"}}