{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ","short_pith_number":"pith:AW6NJEZ3","canonical_record":{"source":{"id":"1612.06265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T16:59:37Z","cross_cats_sorted":[],"title_canon_sha256":"7d54e0800964e3c48f67fd8e4af55e2a75a3691659176903e48c8e33f9cbf865","abstract_canon_sha256":"1e560895904dace9cd2d8ea7d6f0e2867c96b1a0e772e57feafdc221e78515af"},"schema_version":"1.0"},"canonical_sha256":"05bcd4933b2393e16d32d10d8867721276225843276b030df0d3f73f7f8b34d5","source":{"kind":"arxiv","id":"1612.06265","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06265","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06265v2","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06265","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"AW6NJEZ3EOJ6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AW6NJEZ3EOJ6C3JS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AW6NJEZ3","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T16:59:37Z","cross_cats_sorted":[],"title_canon_sha256":"7d54e0800964e3c48f67fd8e4af55e2a75a3691659176903e48c8e33f9cbf865","abstract_canon_sha256":"1e560895904dace9cd2d8ea7d6f0e2867c96b1a0e772e57feafdc221e78515af"},"schema_version":"1.0"},"canonical_sha256":"05bcd4933b2393e16d32d10d8867721276225843276b030df0d3f73f7f8b34d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.296256Z","signature_b64":"B/kZmn6iFhAQ0OSgYERZKajisaCe0nhkbqtaCIJr291yCPjsvtAjJf9WGJMmDPnb11VHQWKtiyLGzITXZ30zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05bcd4933b2393e16d32d10d8867721276225843276b030df0d3f73f7f8b34d5","last_reissued_at":"2026-05-18T00:41:53.295761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.295761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06265","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":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QDa+Clx52pH97fx1SkW5nkEvJIIbu4wL4fhPEhmBReJ7g6LOw7Me9lArHOCpXAV9CG08JlHQIGWTmg2361nLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:37:59.059010Z"},"content_sha256":"64f6e367e3e7e825473dda785413e4cd1c6eb8fb83a73ad81ac94fe2b1cf851e","schema_version":"1.0","event_id":"sha256:64f6e367e3e7e825473dda785413e4cd1c6eb8fb83a73ad81ac94fe2b1cf851e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proximal difference-of-convex algorithm with extrapolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Wen, Ting Kei Pong, Xiaojun Chen","submitted_at":"2016-12-19T16:59:37Z","abstract_excerpt":"We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) [26], the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in [27]. This decomposition has been proposed in numerous work such as [1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06265","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":""},"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":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQNzbMk5KDbK4QKSZkdSuaJBPcoYPknCdgKaBDvyme7lk7g0pso9wxhD+aPz+fJcA/oQ/qI8S5Qv7sibyqT3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:37:59.059460Z"},"content_sha256":"3494ace24712a98af23b6bf444c64fa48f48c99975958ccfbf062cbc263ffce6","schema_version":"1.0","event_id":"sha256:3494ace24712a98af23b6bf444c64fa48f48c99975958ccfbf062cbc263ffce6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/bundle.json","state_url":"https://pith.science/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/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":"2026-05-26T16:37:59Z","links":{"resolver":"https://pith.science/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ","bundle":"https://pith.science/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/bundle.json","state":"https://pith.science/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AW6NJEZ3EOJ6C3JS2EGYQZ3SCJ","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":"1e560895904dace9cd2d8ea7d6f0e2867c96b1a0e772e57feafdc221e78515af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T16:59:37Z","title_canon_sha256":"7d54e0800964e3c48f67fd8e4af55e2a75a3691659176903e48c8e33f9cbf865"},"schema_version":"1.0","source":{"id":"1612.06265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06265","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06265v2","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06265","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"AW6NJEZ3EOJ6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AW6NJEZ3EOJ6C3JS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AW6NJEZ3","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:3494ace24712a98af23b6bf444c64fa48f48c99975958ccfbf062cbc263ffce6","target":"graph","created_at":"2026-05-18T00:41:53Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) [26], the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in [27]. This decomposition has been proposed in numerous work such as [1","authors_text":"Bo Wen, Ting Kei Pong, Xiaojun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T16:59:37Z","title":"A proximal difference-of-convex algorithm with extrapolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06265","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":"sha256:64f6e367e3e7e825473dda785413e4cd1c6eb8fb83a73ad81ac94fe2b1cf851e","target":"record","created_at":"2026-05-18T00:41:53Z","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":"1e560895904dace9cd2d8ea7d6f0e2867c96b1a0e772e57feafdc221e78515af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-19T16:59:37Z","title_canon_sha256":"7d54e0800964e3c48f67fd8e4af55e2a75a3691659176903e48c8e33f9cbf865"},"schema_version":"1.0","source":{"id":"1612.06265","kind":"arxiv","version":2}},"canonical_sha256":"05bcd4933b2393e16d32d10d8867721276225843276b030df0d3f73f7f8b34d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05bcd4933b2393e16d32d10d8867721276225843276b030df0d3f73f7f8b34d5","first_computed_at":"2026-05-18T00:41:53.295761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:53.295761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B/kZmn6iFhAQ0OSgYERZKajisaCe0nhkbqtaCIJr291yCPjsvtAjJf9WGJMmDPnb11VHQWKtiyLGzITXZ30zDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:53.296256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64f6e367e3e7e825473dda785413e4cd1c6eb8fb83a73ad81ac94fe2b1cf851e","sha256:3494ace24712a98af23b6bf444c64fa48f48c99975958ccfbf062cbc263ffce6"],"state_sha256":"0fc81a34bd74cfff9260454f017c24f31be5923b4c8e2e91ad11d654fcdc17f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4QAgah+x1p3AHi7OonbZnLpDIiQa7SewZpevPJftqJdc5xFDut1NOh4YYOXzdSjprJ52imw7q9Z4XkBqQOFDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:37:59.062042Z","bundle_sha256":"9dab20b19f41e9f3cd4b71a46a140dfe153f51db1ffa600bd5a43b39f0e1280a"}}