{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P6GMAID72AK32EIVYNIZJ6HWGZ","short_pith_number":"pith:P6GMAID7","canonical_record":{"source":{"id":"1908.04522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-13T07:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"689fcb785ab768a24e11952e5a19d30b96daa5a14ee0b88074999a5de30612ae","abstract_canon_sha256":"c098988fb20b389d0024470aee0a761fea0f8f4b1637a2d2c65f4267d8ed632e"},"schema_version":"1.0"},"canonical_sha256":"7f8cc0207fd015bd1115c35194f8f63674106df8ad6ba6678c2c267297d7ee49","source":{"kind":"arxiv","id":"1908.04522","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04522","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04522v1","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04522","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"P6GMAID72AK3","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_16","alias_value":"P6GMAID72AK32EIV","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_8","alias_value":"P6GMAID7","created_at":"2026-07-04T23:55:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P6GMAID72AK32EIVYNIZJ6HWGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-13T07:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"689fcb785ab768a24e11952e5a19d30b96daa5a14ee0b88074999a5de30612ae","abstract_canon_sha256":"c098988fb20b389d0024470aee0a761fea0f8f4b1637a2d2c65f4267d8ed632e"},"schema_version":"1.0"},"canonical_sha256":"7f8cc0207fd015bd1115c35194f8f63674106df8ad6ba6678c2c267297d7ee49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:55:14.503783Z","signature_b64":"8GT7hVkIBhLUZBACP8ngvOqObH1Z0fOo1BYZcY96bkqe3SMYpOkdRaEGnrWoXlN2ViecVgzRwdJmN4IvNYe1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f8cc0207fd015bd1115c35194f8f63674106df8ad6ba6678c2c267297d7ee49","last_reissued_at":"2026-07-04T23:55:14.503379Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:55:14.503379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04522","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":"2026-07-04T23:55:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QnF2zupz+ujCE3jNwYFwpDR652KE6FG8nsCEPEaIXvauKWsgvQGJitHpeG0x6gvEuvUf4p/5mHC6F4IJoiovCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:04:28.999757Z"},"content_sha256":"a31b8a48da60908afbdb70f55a2e29107e95dba594bcd38d8257c4c79c1694ae","schema_version":"1.0","event_id":"sha256:a31b8a48da60908afbdb70f55a2e29107e95dba594bcd38d8257c4c79c1694ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P6GMAID72AK32EIVYNIZJ6HWGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proximal DC approach for quadratic assignment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chao Ding, Xinyuan Zhao, Zhuoxuan Jiang","submitted_at":"2019-08-13T07:34:57Z","abstract_excerpt":"In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under the framework of the difference of convex functions (DC) approach, a semi-proximal DC algorithm (DCA) is proposed for solving the relaxation of the rank constrained DNN problem whose subproblems can be solved by the semi-proximal augmented Lagrangian method (sPALM). We show that the generated sequence converges to a stationary point of the corresponding DC problem, which is feasible to the rank constrained DNN problem. Moreover, numeri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04522","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04522/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:55:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s/KN2JLVJkeeKV9aq7V7tkw+6roMCUC6TKSXs6zXo6N7A7El2eF37iPvrOXyBEGg+j/CFFco0qV9e7Y0cIw6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:04:29.000246Z"},"content_sha256":"d2c00b1b469c22ad1a9df9609daa57cb9bd5d1214b7645e078238973207cf766","schema_version":"1.0","event_id":"sha256:d2c00b1b469c22ad1a9df9609daa57cb9bd5d1214b7645e078238973207cf766"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/bundle.json","state_url":"https://pith.science/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/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":"2026-08-16T12:04:29Z","links":{"resolver":"https://pith.science/pith/P6GMAID72AK32EIVYNIZJ6HWGZ","bundle":"https://pith.science/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/bundle.json","state":"https://pith.science/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6GMAID72AK32EIVYNIZJ6HWGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P6GMAID72AK32EIVYNIZJ6HWGZ","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":"c098988fb20b389d0024470aee0a761fea0f8f4b1637a2d2c65f4267d8ed632e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-13T07:34:57Z","title_canon_sha256":"689fcb785ab768a24e11952e5a19d30b96daa5a14ee0b88074999a5de30612ae"},"schema_version":"1.0","source":{"id":"1908.04522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04522","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04522v1","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04522","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"P6GMAID72AK3","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_16","alias_value":"P6GMAID72AK32EIV","created_at":"2026-07-04T23:55:14Z"},{"alias_kind":"pith_short_8","alias_value":"P6GMAID7","created_at":"2026-07-04T23:55:14Z"}],"graph_snapshots":[{"event_id":"sha256:d2c00b1b469c22ad1a9df9609daa57cb9bd5d1214b7645e078238973207cf766","target":"graph","created_at":"2026-07-04T23:55:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under the framework of the difference of convex functions (DC) approach, a semi-proximal DC algorithm (DCA) is proposed for solving the relaxation of the rank constrained DNN problem whose subproblems can be solved by the semi-proximal augmented Lagrangian method (sPALM). We show that the generated sequence converges to a stationary point of the corresponding DC problem, which is feasible to the rank constrained DNN problem. Moreover, numeri","authors_text":"Chao Ding, Xinyuan Zhao, Zhuoxuan Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-13T07:34:57Z","title":"A proximal DC approach for quadratic assignment problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04522","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:a31b8a48da60908afbdb70f55a2e29107e95dba594bcd38d8257c4c79c1694ae","target":"record","created_at":"2026-07-04T23:55:14Z","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":"c098988fb20b389d0024470aee0a761fea0f8f4b1637a2d2c65f4267d8ed632e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-13T07:34:57Z","title_canon_sha256":"689fcb785ab768a24e11952e5a19d30b96daa5a14ee0b88074999a5de30612ae"},"schema_version":"1.0","source":{"id":"1908.04522","kind":"arxiv","version":1}},"canonical_sha256":"7f8cc0207fd015bd1115c35194f8f63674106df8ad6ba6678c2c267297d7ee49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f8cc0207fd015bd1115c35194f8f63674106df8ad6ba6678c2c267297d7ee49","first_computed_at":"2026-07-04T23:55:14.503379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:14.503379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8GT7hVkIBhLUZBACP8ngvOqObH1Z0fOo1BYZcY96bkqe3SMYpOkdRaEGnrWoXlN2ViecVgzRwdJmN4IvNYe1CA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:14.503783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a31b8a48da60908afbdb70f55a2e29107e95dba594bcd38d8257c4c79c1694ae","sha256:d2c00b1b469c22ad1a9df9609daa57cb9bd5d1214b7645e078238973207cf766"],"state_sha256":"8e7658f14f2d829959cc3ba4add5f64c03dc65c1a4a94df0a9c05969bf68aff2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmyY4uKLmXRoZ2y6Thr7/S84SU7xKxQS3Wqqw+HLE/w2OfomFjnNMaq1gweX3HwJfOoRQtE67zfnXpEmPRr6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:04:29.003458Z","bundle_sha256":"f26402964d31f2ead085523ec6454eef511bf32eef10791b36231bab2670adc3"}}