{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5JCMYJUBLAZS6KC5EHB2N5X6FK","short_pith_number":"pith:5JCMYJUB","canonical_record":{"source":{"id":"1512.09235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T07:32:42Z","cross_cats_sorted":[],"title_canon_sha256":"34de5026dda89e10a7585a9ce92d96dc70083530f68a90fbf3e451dc6e3478e9","abstract_canon_sha256":"1e31d30cb0082e5c2f137bd69441d10203801ae0f9cf55233d23ca02e2821688"},"schema_version":"1.0"},"canonical_sha256":"ea44cc268158332f285d21c3a6f6fe2a9b05b4726ceffa8fd13a403ad1952318","source":{"kind":"arxiv","id":"1512.09235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09235","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09235v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09235","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"5JCMYJUBLAZS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5JCMYJUBLAZS6KC5","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5JCMYJUB","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5JCMYJUBLAZS6KC5EHB2N5X6FK","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T07:32:42Z","cross_cats_sorted":[],"title_canon_sha256":"34de5026dda89e10a7585a9ce92d96dc70083530f68a90fbf3e451dc6e3478e9","abstract_canon_sha256":"1e31d30cb0082e5c2f137bd69441d10203801ae0f9cf55233d23ca02e2821688"},"schema_version":"1.0"},"canonical_sha256":"ea44cc268158332f285d21c3a6f6fe2a9b05b4726ceffa8fd13a403ad1952318","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:32.940841Z","signature_b64":"a5BWNYNgSz5fGhNkXR8aW/x01KlgW6mcbX/ePG+O+3BDkz8oTF87BsGVPOokGPO5Yf7AVNJFGkn/BQaExVAiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea44cc268158332f285d21c3a6f6fe2a9b05b4726ceffa8fd13a403ad1952318","last_reissued_at":"2026-05-18T01:23:32.939896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:32.939896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09235","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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gB6x7SZBYf3ATqmsaJcWujI1hUNzFR0PyjCOj2ymPsaJT90z+j2L5+Af1SiEL89/2rHcSN+7oPmtsnN3VMYaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:21:37.531200Z"},"content_sha256":"8853ab7d899b098b933a63566829d8bdd50bbb2a445059fe7219e089bfa2cea0","schema_version":"1.0","event_id":"sha256:8853ab7d899b098b933a63566829d8bdd50bbb2a445059fe7219e089bfa2cea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5JCMYJUBLAZS6KC5EHB2N5X6FK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A primal-dual fixed-point algorithm for minimization of the sum of three convex separable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jianguo Huang, Peijun Chen, Xiaoqun Zhang","submitted_at":"2015-12-31T07:32:42Z","abstract_excerpt":"Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In this paper, we propose a primal-dual fixed-point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three block problems is a fully splitting symmetric scheme, only involving explicit gradient and linear operators without inner iteration, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09235","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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aqEXBSgmBHjsCr6VGQINOCsDOM490mEwXLeggDF4mRCQgTKK6Q8C+C8OLSJv+lDjCd1/zK7MJEFFQ1ONH7t7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:21:37.531571Z"},"content_sha256":"9e01c3bf9fba54453f5176daf12b1808225293e4a915fd37015aefc6ef169509","schema_version":"1.0","event_id":"sha256:9e01c3bf9fba54453f5176daf12b1808225293e4a915fd37015aefc6ef169509"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/bundle.json","state_url":"https://pith.science/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/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":"2026-06-03T11:21:37Z","links":{"resolver":"https://pith.science/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK","bundle":"https://pith.science/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/bundle.json","state":"https://pith.science/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JCMYJUBLAZS6KC5EHB2N5X6FK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5JCMYJUBLAZS6KC5EHB2N5X6FK","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":"1e31d30cb0082e5c2f137bd69441d10203801ae0f9cf55233d23ca02e2821688","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T07:32:42Z","title_canon_sha256":"34de5026dda89e10a7585a9ce92d96dc70083530f68a90fbf3e451dc6e3478e9"},"schema_version":"1.0","source":{"id":"1512.09235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09235","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09235v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09235","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"5JCMYJUBLAZS","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5JCMYJUBLAZS6KC5","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5JCMYJUB","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:9e01c3bf9fba54453f5176daf12b1808225293e4a915fd37015aefc6ef169509","target":"graph","created_at":"2026-05-18T01:23:32Z","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":"Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In this paper, we propose a primal-dual fixed-point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three block problems is a fully splitting symmetric scheme, only involving explicit gradient and linear operators without inner iteration, w","authors_text":"Jianguo Huang, Peijun Chen, Xiaoqun Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T07:32:42Z","title":"A primal-dual fixed-point algorithm for minimization of the sum of three convex separable functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09235","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":"sha256:8853ab7d899b098b933a63566829d8bdd50bbb2a445059fe7219e089bfa2cea0","target":"record","created_at":"2026-05-18T01:23:32Z","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":"1e31d30cb0082e5c2f137bd69441d10203801ae0f9cf55233d23ca02e2821688","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T07:32:42Z","title_canon_sha256":"34de5026dda89e10a7585a9ce92d96dc70083530f68a90fbf3e451dc6e3478e9"},"schema_version":"1.0","source":{"id":"1512.09235","kind":"arxiv","version":1}},"canonical_sha256":"ea44cc268158332f285d21c3a6f6fe2a9b05b4726ceffa8fd13a403ad1952318","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea44cc268158332f285d21c3a6f6fe2a9b05b4726ceffa8fd13a403ad1952318","first_computed_at":"2026-05-18T01:23:32.939896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.939896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5BWNYNgSz5fGhNkXR8aW/x01KlgW6mcbX/ePG+O+3BDkz8oTF87BsGVPOokGPO5Yf7AVNJFGkn/BQaExVAiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.940841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8853ab7d899b098b933a63566829d8bdd50bbb2a445059fe7219e089bfa2cea0","sha256:9e01c3bf9fba54453f5176daf12b1808225293e4a915fd37015aefc6ef169509"],"state_sha256":"2e4faf5ec952cc95e699778ac4d68cc1239fc2f257e6f1380bc5dde483ba948b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXs4BmxkhwD9dy+sggiR4eZDEnj9PWXFKQVFaQdbp8XougfXP6GDyZdd3aYGXe9AtSfAMUCsfL+JZ/n5/CVmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:21:37.533447Z","bundle_sha256":"1d9619ecd75a14a1601c3d24e1ce7d97f2db70945d1f25612e152d80895abf51"}}