{"as_of":"2026-08-17T23:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fb3c0322a27a6fbc784c9a41ab6def1ebcf6318d9a51b56f61f1075bf797d407","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T18:42:33.351242Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.07634/citation-record","integrity":"/paper/2412.07634/integrity","json":"/paper/2412.07634/citation-record.json","paper":"/paper/2412.07634"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1186/s42492-018-0004-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.707398Z","title":"A review of the design methods of complex topology structures for 3D printing","venue":null,"work_id":"e2a944bf-a4f6-4df7-8f1e-cc7caba2aabe","year":2018},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.161272Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:1f9c666491a2ab5d7b28280a6f2f38e5610de53f7a87dc6d14b4bd4e5336cb27","observation_id":"d3910d62-fa94-4bd4-b717-8e91dea350e2","resolution":{"observed_at":"2026-08-11T18:42:33.711804Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1115/1.1388075","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.692853Z","title":"Topology Optimization of Continuum Structures: A Review.Applied Mechanics Reviews","venue":null,"work_id":"17cca93e-6ff2-4aef-a647-bd5248130609","year":2001},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.166080Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:9aa5679caeafd7ac13914c2df919a377c253455bb32de61042dfe512817eedb1","observation_id":"41068731-854b-474d-9656-82d76e76757e","resolution":{"observed_at":"2026-08-11T18:42:33.697798Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.applthermaleng.2016.10.134","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.679053Z","title":"A review about the engineering design of optimal heat transfer systems using topology optimization","venue":null,"work_id":"1ec32514-7bd8-4e8f-a2b8-1a9a5eeb48d1","year":2017},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.170250Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:a34c74f484b857d405ee5919b061341d64071d3fe1d6a1eada48f16c7366d700","observation_id":"6f0530fd-8dfc-4261-9d81-77f2b53d6d06","resolution":{"observed_at":"2026-08-11T18:42:33.683491Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.174816Z","title":"A Review of Topology Optimisation for Fluid-Based Problems.Fluids","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.174816Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:14c96b87cb923ad384c105f75204e79e8b9e59017fafbca9fc2b1852e2f57408","observation_id":"a6ee5ef4-7964-41ce-82e9-f76023b52236","resolution":{"observed_at":"2026-08-11T18:42:33.174816Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.179748Z","title":"The method of moving asymptotes—a new method for structural optimization","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.179748Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:6743f1ff8c2f8d2ff098d12494d0d37552ffd87ea8cceb03d794803a552f251a","observation_id":"1db850f4-0c55-4bf2-98b7-7046981e7eb0","resolution":{"observed_at":"2026-08-11T18:42:33.179748Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1590/s1807-03022011000100003","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.646421Z","title":"An SLP algorithm and its application to topology optimization","venue":null,"work_id":"fb10681c-6534-40bf-b0d0-79bb621afe93","year":2011},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.184272Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:8983ad34642bad251cfb995b2f4627be39ab379427cf44ea3d4f7b5cae6c828f","observation_id":"63d168c6-5bba-4210-b8cb-f92c21016e71","resolution":{"observed_at":"2026-08-11T18:42:33.650997Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00158-016-1471-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.632336Z","title":"An efficient second-order SQP method for structural topology optimization","venue":null,"work_id":"9a095a81-071c-451f-8a72-df2e7d802805","year":2016},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.189161Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:a9fec86872413750bd1ce93ebff78f91132f7386d38913f532512f0421ae28ce","observation_id":"59d612a5-1ed6-4988-8b01-49b1704c90df","resolution":{"observed_at":"2026-08-11T18:42:33.636914Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0045-7949(98)00131-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.618174Z","title":"A review of homogenization and topology optimization III—topology optimization using optimality criteria","venue":null,"work_id":"9528aa14-c2fe-44ee-afdc-2cf70fb7a705","year":1998},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.193391Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:465fbc7ca111f9f495302a325dc0923e4016a0336612827a9d58b2dc93f1007e","observation_id":"0edfec84-c4a5-4b91-93d9-dbd603d0f95f","resolution":{"observed_at":"2026-08-11T18:42:33.622905Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1014072503048","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.604224Z","title":"Primal-dual Newton-type interior-point method for topology optimization.Journal of Optimization Theory and Applications","venue":null,"work_id":"12865617-85f5-43ad-bbee-bbdf82d2b472","year":2002},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.197584Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:4f7fcfb1d4375cbd2d4cafb0c2de6d1ca477d85ce5ff56013891f133d0f33bb9","observation_id":"f6cbaed7-2c4e-4a77-80cd-2e4119533c62","resolution":{"observed_at":"2026-08-11T18:42:33.608976Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cma.2014.04.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.590044Z","title":"Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method","venue":null,"work_id":"ac05e6d5-2cf6-437b-9388-5047bdc131b1","year":2014},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.201992Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:c79d9457c1cd6aba5bec091bf4969cad7b108156dc03ffbf2421b3085f0d98b0","observation_id":"d69921ac-c9c1-4696-a591-570cfad22388","resolution":{"observed_at":"2026-08-11T18:42:33.594915Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s13160-023-00563-0","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.576446Z","title":"Inertial projected gradient method for large-scale topology optimization.Japan Journal of Industrial and Applied Mathematics","venue":null,"work_id":"716018c0-615f-41ad-a7e8-e1c6e6575fee","year":2023},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.206369Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:3454526b11f1b28d8c547dc4551a1a5bbb02dd4c6b1cf9dbfeba39945d1533ff","observation_id":"f0e8bd0e-3bd7-404d-990f-cd570062363f","resolution":{"observed_at":"2026-08-11T18:42:33.581023Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2305.19605","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.916045Z","title":"Parameter-free projected gradient descent","venue":null,"work_id":"f175885a-70da-40a3-9857-5765d24ff21c","year":2023},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.210766Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:c4de7d52bc684eb5f07f4becd39857d2934387903b27a83e9277a7e88f3a42ae","observation_id":"7f7c4f4a-c741-4faa-a33c-1a59f4c1d363","resolution":{"observed_at":"2026-08-11T18:42:33.923652Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.149012Z","title":"Boosting the robustness of neural networks with M-PGD","venue":null,"work_id":"1a98ac6c-b9cd-40ee-a2fd-1be3980fef62","year":2022},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.215179Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:9b294616c2191756b0560b322f52a3efc3b3fb937ba1098592b0d074d2e2252b","observation_id":"a986ceac-3caa-4250-987c-ccc00ccd2266","resolution":{"observed_at":"2026-08-11T18:42:34.153675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/mcom/3647","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.562486Z","title":"A random active set method for strictly convex quadratic problem with simple bounds.Mathematics of Computation","venue":null,"work_id":"6e1c57a2-82ac-4f58-9ab7-febc41ada22b","year":2024},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.219398Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:10d5a399b471e8e4b6c8e00ae46efc000668a364e6c9bc3f5318e7e26b9d2a34","observation_id":"cdfae51e-9917-442d-ada6-0472bf77b66f","resolution":{"observed_at":"2026-08-11T18:42:33.567182Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10589-005-4584-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.548349Z","title":"Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination.Computational Optimization and Applications","venue":null,"work_id":"c56f1a4d-9a40-4ce9-ac4f-5c0cb0f25adb","year":2005},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.223722Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:fe750482ba04c43cae85fdd2888c85b06ea6c740692c12f58c5bd425ee9c35d5","observation_id":"6dfc5eb1-4147-4ca0-b1a6-4445f27dd046","resolution":{"observed_at":"2026-08-11T18:42:33.553073Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s1052623401382206","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.534288Z","title":"An infeasible active set method for quadratic problems with simple bounds.SIAM Journal on Optimization","venue":null,"work_id":"5659ec61-8339-486f-b2f4-e6a9f8e54991","year":2003},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.228249Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:d0712fda6ba49ad260e3a3141df5bde1215d7c7b392e3dffb7be86efd359d07c","observation_id":"bdbf7fe8-b4cf-434d-b9a4-18d7f885cddf","resolution":{"observed_at":"2026-08-11T18:42:33.539005Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/140961676","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.521155Z","title":"A feasible active set method for strictly convex quadratic problems with simple bounds.SIAM Journal on Optimization","venue":null,"work_id":"6ffcf5e3-c6e7-4796-94b7-ebecb6377053","year":2015},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.232729Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:8025e281c7811f6cca430135f1a82656e7cd40cb5f15fb03b2d1164b37bb2846","observation_id":"33e19ca0-0acc-43d4-9589-8c1aba535df2","resolution":{"observed_at":"2026-08-11T18:42:33.525182Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.134998Z","title":"Primal and dual active-set methods for convex quadratic programming.Mathematical Programming.2016;159(1):469–","venue":null,"work_id":"70e08f61-b969-46ee-9db3-7a257075ab5c","year":2016},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.237060Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:d8808448927656adb5eaf51ca4cb1fae5d3d61457945ef5b5d754ef8404016e5","observation_id":"36f7221d-cfee-4de1-8d6d-4a1b9f3012e4","resolution":{"observed_at":"2026-08-11T18:42:34.139547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.apnum.2009.07.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.494051Z","title":"An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints","venue":null,"work_id":"d3800e2d-3b1f-474d-98ce-1454ddb83da3","year":2009},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.245738Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:707e37e56f58e2263b20ef68b0f9960bb1105cebe6a20ca9f7382cd3c264efbf","observation_id":"89a66d8a-589c-449f-b7e0-428824e7bba4","resolution":{"observed_at":"2026-08-11T18:42:33.498879Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10957-016-1024-9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.479267Z","title":"A two-stage active-set algorithm for bound-constrained optimization","venue":null,"work_id":"b2108d1a-f959-416b-b64a-088e9ef977b7","year":2017},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.250250Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:aca8edf0b00be17d7716989c61c081cf6496ecea538e2697c129acfeeb9ef5e4","observation_id":"45f8291a-f150-4855-b9fc-cea01685f09d","resolution":{"observed_at":"2026-08-11T18:42:33.483949Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.120550Z","title":"Topology optimization for additive manufacturing: considering maximum overhang constraint","venue":null,"work_id":"941a8397-ec69-4aa7-a025-74623eb704f1","year":2014},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.254873Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:d88ddca594ee82a0f6d6565304c214307ea98cc82e43beb8115b9d58899b7a8b","observation_id":"62b3f21e-1cbb-4250-8cca-e5e1c2dd0f94","resolution":{"observed_at":"2026-08-11T18:42:34.125332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/nme.5461","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Undercut and overhang angle control in topology optimization: A density gradient based integral approach","venue":"International Journal for Numerical Methods in Engineering","work_id":"c6ee9eab-efc0-41a2-8a65-d76bc36d59a4","year":2017},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.259042Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:4b5aa0bf68994957cf80ede69873ca9ac25d7148472a3dfcd4514c9d86de40f7","observation_id":"09b2309f-0a3c-4590-8e4e-2523db215590","resolution":{"observed_at":"2026-08-11T18:42:33.469906Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00158-024-03846-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.451104Z","title":"Additively manufactured conformal cooling channels through topology optimization","venue":null,"work_id":"fe80f6be-8e0f-4e0e-8dfb-58e7badad947","year":2024},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.263544Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:8142d47f58e643e94f758e6324a4c9e7014d70314d4740a5c7cecdbc0386dcda","observation_id":"2d287ef2-a86a-4502-9d54-9de569630ef9","resolution":{"observed_at":"2026-08-11T18:42:33.455770Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00158-016-1551-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.106816Z","title":"Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design","venue":null,"work_id":"d06b8266-ebdf-4c7a-9f17-2f05b701a6f4","year":2016},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.267408Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:75eafb7274d37f127c0647298b04789e0a7f411c90873a36316b26b448f0372c","observation_id":"ac5c4e04-01fd-4185-94a9-20cbf8e2ee87","resolution":{"observed_at":"2026-08-11T18:42:34.111509Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.092933Z","title":"First-order methods in optimization","venue":null,"work_id":"0fdd05ba-4035-456c-8d6f-8ff3a01389bd","year":2017},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.271444Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:aa9747873305480d27e44912515d30a880ed0a363a6112ca6ea6f51a9c8b0a05","observation_id":"710138aa-0151-4c37-8751-a6550dd5f187","resolution":{"observed_at":"2026-08-11T18:42:34.097446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.078704Z","title":"Improved analysis of clipping algorithms for non-convex optimization.Advances in Neural Information Processing Systems","venue":null,"work_id":"d2965e1b-f8aa-49d8-b083-5b4c0d0df40a","year":2020},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.275375Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:af3cee79bebabfa59a8f113ccf4f49e2f5ea6475c3d08c4079dea755f1a35efb","observation_id":"f7b818b4-fde8-43cf-a90f-cc0afb330dc1","resolution":{"observed_at":"2026-08-11T18:42:34.083328Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11081-006-6588-z","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.436334Z","title":"QPSchur: a dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming","venue":null,"work_id":"2e7cad3f-f825-4070-87d9-dd9870631cf6","year":2006},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.278998Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:06f9ecb8d7fd048905e7d0d5c0fc485b42d8349aa3c0cca38655a5e87ebb305a","observation_id":"889a1214-7d9a-49c0-a055-de95742c370b","resolution":{"observed_at":"2026-08-11T18:42:33.440926Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.064406Z","title":"Active-set methods for quadratic programming","venue":null,"work_id":"a2e2a8c1-c2b6-4a31-a80d-f8d9a717d940","year":2011},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.283288Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:0738f9ff05091da1b306de41cdd37b102e7534f5465c16f7876fb9410c87f124","observation_id":"2b253cb5-6423-4e0f-9aab-f7afdaed7331","resolution":{"observed_at":"2026-08-11T18:42:34.069161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.050307Z","title":"DFEMwork: A Parallel Computing Framework for Material Processing","venue":null,"work_id":"193f0ff4-e9e3-4c71-a1f1-d5efb41d8f7a","year":2008},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.287387Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:55004d2f84b8678236a40c295180a28b7272423eaa65bbdd140d0b7d37284d96","observation_id":"c47c4d9d-27c2-48d4-ac1a-0b7a174ed82f","resolution":{"observed_at":"2026-08-11T18:42:34.054862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.035298Z","title":"Development of a Topology Optimization Framework For Cooling Channel Design in Die Casting Molds","venue":null,"work_id":"7a483992-d883-4491-89a4-d180e90185b3","year":2021},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.291380Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:ae11dbafc6f3f92c2e5d6164c3b1cd0e7aa282d34eac698f5e50cdd234846d17","observation_id":"018a98cc-563f-4b83-a5bf-713b9f8c59e6","resolution":{"observed_at":"2026-08-11T18:42:34.040170Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/16m1098103","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.420110Z","title":"A Projected Gradient and Constraint Linearization Method for Nonlinear Model Predictive Control","venue":null,"work_id":"77a1386c-6d3b-4d4e-a576-ee2bc73de8f4","year":2018},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.295265Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:9419d58f1232ae584f16e1602905a7adf22ca34ab92fadc8741ba7b524b22ac1","observation_id":"672d5038-f24e-4d30-813d-2a57c925b19c","resolution":{"observed_at":"2026-08-11T18:42:33.426520Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.020898Z","title":"Constrained optimization and Lagrange multiplier methods","venue":null,"work_id":"fcc8824a-40a5-4040-a185-20f0b53da0d5","year":2014},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.299813Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:3a51cf206e15432f005b467a4277d7a1f545f45ee5aafcb03641f04f8eba3554","observation_id":"7097c25e-3c9a-4667-85ef-ee645f877f59","resolution":{"observed_at":"2026-08-11T18:42:34.025511Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:34.006892Z","title":"Numerical optimization","venue":null,"work_id":"28097e89-4229-4144-9662-3e1eedc6201e","year":1999},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.304271Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:21964b73cc87e4313d9673882c9aa47eedf04c9d245bda9e35054c22f2ccd8d4","observation_id":"d1844a92-b777-428a-a43f-f6a66604a78a","resolution":{"observed_at":"2026-08-11T18:42:34.011450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.992557Z","title":"Linear Algebra and Its Applications","venue":null,"work_id":"0fee46fe-b121-4e64-9bfe-4298da315a01","year":2012},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.308477Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:07241729bf763aa58aac73072986c404e2aa491e8bcca2a8660068b4a1bc6847","observation_id":"8fb4fa8f-a852-44d6-9a4e-a0d13db169c7","resolution":{"observed_at":"2026-08-11T18:42:33.996988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.977561Z","title":"Convex Optimization","venue":null,"work_id":"6db186c2-bdaa-482e-94c2-555dcbe7a652","year":2004},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.312618Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:26d56b72945f240e45f1e06facbf24bd638f820d83fce15f38c7ad2d8e59304f","observation_id":"4f457f30-b8e8-4d4c-9324-8472b85836cd","resolution":{"observed_at":"2026-08-11T18:42:33.982431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.317145Z","title":"dSJ, et al","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.317145Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:ffe838bb2191888bbf7879fb7a78bba8cc0aa22d81fa1276f349a44bda20e3ed","observation_id":"238a21f3-d1e1-4643-a554-6e35ac3603ac","resolution":{"observed_at":"2026-08-11T18:42:33.317145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2023.12131","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.832973Z","title":"Thermofluid Topology Optimization for Cooling Channel Design","venue":null,"work_id":"4b96cd1f-63b4-4aca-aac2-e8dc4d1cbb7f","year":2024},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.321443Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:184dff1a0932dab5f66bc7c5f2a081ec8eaf54c490063c63e24a91c24bf5a3e8","observation_id":"54656c31-cb29-4710-9830-00ac1e5e8031","resolution":{"observed_at":"2026-08-11T18:42:33.840448Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.325581Z","title":"Filters in Topology Optimization Based on Helmholtz-type Differential Equations.International Journal for Numerical Methods in Engineering","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.325581Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:7c42e4b1d754317a40af09867f4c5bc71537f9578bfb7019a132b272447a64e4","observation_id":"4a45d354-9f98-4ea4-b448-c4d9e317431d","resolution":{"observed_at":"2026-08-11T18:42:33.325581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.329750Z","title":"On projection methods, convergence and robust formulations in topology optimization","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.329750Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:ec61d4297c85bab1fd4f2c33383d0db6777cc6e04c75ff378a509d00154bffc9","observation_id":"2f29087a-196b-48e2-a06b-7717bc242930","resolution":{"observed_at":"2026-08-11T18:42:33.329750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.333955Z","title":"Generating optimal topologies in structural design using a homogenization method","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.333955Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:73e64644a48fc270a6ac5be84dbdfd1cdfb0555150aa66a19fb1a75679c31d25","observation_id":"780ca96e-d0fc-4bad-99f8-b09d45eec589","resolution":{"observed_at":"2026-08-11T18:42:33.333955Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.962776Z","title":"Volume 11: Heat Transfer and Thermal Engineering of ASME International Mechanical Engineering Congress and Exposition; : 2021","venue":null,"work_id":"ab11f6c5-2062-45da-b613-094b2e3efec4","year":2021},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.338389Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:8fd49dc82a71aa6185cd75507cb29469874c5aa5309416e5d17cc9032ee05c59","observation_id":"2f043a27-f7c5-4df9-82ac-73cec94e5093","resolution":{"observed_at":"2026-08-11T18:42:33.967424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.948944Z","title":"Gmsh.; 2020","venue":null,"work_id":"05b6bc1c-dc06-4d21-9c1b-1408c9ebb6cc","year":2020},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.342691Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:4cafe0f4127f6652fb1917dbe3f9e5a31f2d30faad1521a2283369209839a8ad","observation_id":"4141ba06-c179-4706-8624-8001bd22b804","resolution":{"observed_at":"2026-08-11T18:42:33.953355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.934367Z","title":"The NLopt Nonlinear-Optimization Package","venue":null,"work_id":"cc051a13-308a-4dad-a27d-33705cf958bd","year":2007},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.346974Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:60159b4a893aa53940a9562c661ab15a6f52411e8626102c664b3e89b2924bef","observation_id":"47942c8a-e2ab-46cc-b7da-d7e7df00df0e","resolution":{"observed_at":"2026-08-11T18:42:33.939429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.09154","last_updated":"2025-03-03T09:37:27Z","snapshot_observed_at":"2026-08-16T14:18:39.959590Z","submitted_at":"2024-02-14T13:13:26Z","title":"Attacking Large Language Models with Projected Gradient Descent","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.09154","snapshot_observed_at":"2026-08-11T18:42:33.351242Z","title":"Attacking Large Language Models with Projected Gradient Descent.arXiv preprint arXiv:2402.09154","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.351242Z"},"links":{"cited_paper":"/paper/2402.09154","citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:d43373aeba40af71af44afd4910f80ef9426fd8271ad5034d3611a48afa57241","observation_id":"bfd9486a-9c6d-471f-9738-f76846e34efa","resolution":{"observed_at":"2026-08-11T18:42:33.351242Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10107-015-0966-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T18:42:33.508251Z","title":null,"venue":null,"work_id":"8e3fc7ef-1a92-4e44-b25e-a51859fe0774","year":null},"citing_paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","version":1},"reference_index":508,"source":"pdf_text","source_observed_at":"2026-08-11T18:42:33.241359Z"},"links":{"citing_paper":"/paper/2412.07634"},"observation_digest":"sha256:1bcb0a4a3262aa821ece505ff6b8466c1978a34736493f8ec0560995ce5036fc","observation_id":"7039877c-3956-4aa5-bb33-18ec40bac84d","resolution":{"observed_at":"2026-08-11T18:42:33.512262Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.07634","last_updated":"2024-12-10T16:13:59Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-12T05:35:35.248416Z","submitted_at":"2024-12-10T16:13:59Z","title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":7,"verified_exact":22,"verified_fuzzy":15},"total_outbound_references":45},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2412.07634."}