{"as_of":"2026-08-09T06:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a78ea7906a48380c37e4bd606f5d5e9cb3fa4c00cb9656f2f425786d90bf4056","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:21:12.924418Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2607.25192/citation-record","integrity":"/paper/2607.25192/integrity","json":"/paper/2607.25192/citation-record.json","paper":"/paper/2607.25192"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:21:10.720398Z","title":"Hirani.Discrete Exterior Calculus","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:10.720398Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:3157d8c563847a5f3f8fcdaabfb07775a5ce29b215fe63eaf0af74250e5e0185","observation_id":"dece58a2-72d1-46a3-8a6f-a13f1c4c1de4","resolution":{"observed_at":"2026-08-01T03:21:10.720398Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0508341","last_updated":"2005-08-18T22:27:29Z","snapshot_observed_at":"2026-07-07T05:50:41.355296Z","submitted_at":"2005-08-18T14:13:14Z","title":"Discrete Exterior Calculus","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0508341","snapshot_observed_at":"2026-08-01T03:21:10.854988Z","title":"Hirani, Melvin Leok, and Jerrold E","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:10.854988Z"},"links":{"cited_paper":"/paper/math/0508341","citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:7e5b92e99069c4158393439849075c43627d6f35142f5f11845dd047ebe978e4","observation_id":"c4da9ec9-99e5-4603-b8c3-f39ab6c29a3a","resolution":{"observed_at":"2026-08-01T03:21:10.854988Z","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":"10.1016/b978-0-12-118740-8.x5000-8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:24:17.965526Z","title":"Academic Press, 1998","venue":null,"work_id":"9eb395db-8098-4b1f-ad96-934ba576e468","year":1998},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:10.978589Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:489b35ae4b916e14db290b3a719ff8ceeff9d8328d57170833ebee50e40686c6","observation_id":"337f2c6e-5ace-4451-943a-e858fa67f66b","resolution":{"observed_at":"2026-08-01T03:24:18.034965Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:11.094689Z","title":"Digital geometry processing with discrete exterior calculus","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.094689Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:2795ca07bf800a93832b3ac4c214d51a4a88f1d6997e451cdd65265df408085e","observation_id":"81d1e138-e95a-4b78-b40c-fc4a1ee47d6f","resolution":{"observed_at":"2026-08-01T03:21:11.094689Z","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":"2026-08-01T03:21:11.181400Z","title":"Stable, circulation-preserving, simplicial fluids.ACM Transactions on Graphics, 26(1):4, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.181400Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:0d92d52d7789e9ebffd7b8913b092a79851083e30ad89c33b769df4dee2761c9","observation_id":"88c4bae9-7824-45b5-8b88-11cacb67033a","resolution":{"observed_at":"2026-08-01T03:21:11.181400Z","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":"2026-08-01T03:21:11.261519Z","title":"Mohamed, Anil N","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.261519Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:913a68ce12692b782f5e66ee90089491cfed975f298f2271e56e7e430de3845f","observation_id":"9c9bc2d0-3a8e-4572-a4d1-6a467cec3201","resolution":{"observed_at":"2026-08-01T03:21:11.261519Z","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":"10.1063/5.0035981","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Mohamed, and Ravi Samtaney","venue":"Physics of Fluids","work_id":"9798353d-a71e-4108-ae95-db98e4d538e8","year":2021},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.406193Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:7669a157d3a2692cb66a156127c4ff4739d1575ffe08d0cd4fc4ca9d205dbe00","observation_id":"a7d6acf2-2c7c-4285-b699-b337e90c3d14","resolution":{"observed_at":"2026-08-01T03:24:17.932452Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-319-56602-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Discrete exterior calculus (DEC) for the surface Navier–Stokes equation","venue":"Advances in mathematical fluid mechanics","work_id":"ccb3913e-d2f5-4c04-b178-a6cd0934c04a","year":2017},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.545359Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:9e53d5c87bf50282f7b722771f1afd05bd595a8f296cc175d0c46b5ae62b3792","observation_id":"e60d34ea-f786-4e7b-bfa2-73202b482245","resolution":{"observed_at":"2026-08-01T03:24:17.857766Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:11.690648Z","title":"Mohamed, Anil N","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.690648Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:ee3eb7353ff3f683fc5624a499da2c0cb245577d0b7288b69e229400c5661aa9","observation_id":"1a609798-f1a4-4b53-8a8d-67fe55010b7a","resolution":{"observed_at":"2026-08-01T03:21:11.690648Z","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":"10.1090/lam/029","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:24:17.684164Z","title":"Allgower, K","venue":null,"work_id":"08b369b5-86c1-48d7-a5be-a75bbb0f9b33","year":1997},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.856460Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:4f8d2ead4f911e3a41800bcd8df97b6d4dfc8a78916b3d57d828e2e017ed35da","observation_id":"62db818f-4b6a-44db-8aa1-e56c8e3c7ac2","resolution":{"observed_at":"2026-08-01T03:24:17.774042Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-1-4612-2824-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Birkh¨ auser, 1992","venue":null,"work_id":"c749c7c0-9e00-4c2c-9b88-a9c0b1e32d86","year":1992},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:11.972102Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:9519b6d09307c30332ac2716232db1340bf93e143b7014f3ea56806203451706","observation_id":"f7309f98-0eda-4709-96c7-b6a73e87fdf4","resolution":{"observed_at":"2026-08-01T03:24:17.674405Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0045-7825(86)90119-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Symmetry, groups, and boundary value problems","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"42244ca0-a2d3-40f9-8d48-57d40796739e","year":1986},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.076271Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:c248fb9ad4e391f7fb576fd6b9df4bff26709684cb36e088ab7bb8b5c7ff9a33","observation_id":"79f04cd6-24c8-429c-960b-f747fed75038","resolution":{"observed_at":"2026-08-01T03:24:17.571147Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10543-005-0030-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Munthe-Kaas","venue":"BIT Numerical Mathematics","work_id":"dd904531-d822-4238-86f1-c8f3cd6a9933","year":2005},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.121022Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:0a93c010fdd87d07fb796cef694c20a8b2012c7902d582a18f18e6038646ae8e","observation_id":"ac1d4742-051e-41ae-9c98-575a8fe1f955","resolution":{"observed_at":"2026-08-01T03:24:17.492983Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:12.246416Z","title":"Parallelisation of partial differential equations via representation the- ory.SIAM Review (to appear), 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.246416Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:dde4daaf8b96d96f683f7d1dd8bce5e97ab5b9f13677ee706a9c1ceca90dd076","observation_id":"833bfee4-0de3-4da2-8ae6-fa8993b07e25","resolution":{"observed_at":"2026-08-01T03:21:12.246416Z","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":"2026-08-01T03:21:12.418499Z","title":"Arnold, Richard S","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.418499Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:4d7dd454c94f45e592c9967b5a54cb5a09e1669d1a3cc916433f4b1e2dd62e58","observation_id":"baf8877c-e484-470a-b450-b4c5f3390f4e","resolution":{"observed_at":"2026-08-01T03:21:12.418499Z","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":"2026-08-01T03:21:12.531881Z","title":"Arnold, Richard S","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.531881Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:5d7024d36ca33bf15962959d78484bc56d9f76071d98a011ab17ae77828f62a9","observation_id":"62e79f78-f797-4937-ad3b-beaac49d8cea","resolution":{"observed_at":"2026-08-01T03:21:12.531881Z","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/s10208-024-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:24:17.226326Z","title":null,"venue":null,"work_id":"9abdd991-a24d-483e-8bd3-38e7c49a6aea","year":2024},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.786888Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:2bc291daf0dc551f0095b31ec4fd1b948f1ffbd43dd0dc8db2bb5db5b7cfb443","observation_id":"a196b139-f2ad-447a-b83f-62966ffbba69","resolution":{"observed_at":"2026-08-01T03:24:17.284331Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s096249290100003x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:24:17.117849Z","title":"Marsden and Matthew West","venue":null,"work_id":"1c0572e7-b495-4129-b279-b71d3524c7a4","year":2001},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.852114Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:ca22dcea7ccfdf916eb07fc8881dbba4f36315a33e6b30b5af6aef8e8ec00bcf","observation_id":"576cc2c1-fd6a-45ed-955e-d493ab1bdcd2","resolution":{"observed_at":"2026-08-01T03:24:17.210731Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13478","last_updated":"2021-05-02T16:16:03Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-04-27T21:09:51Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13478","snapshot_observed_at":"2026-08-01T03:21:12.856346Z","title":"Bronstein, Joan Bruna, Taco Cohen, and Petar Veliˇ ckovi´ c","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.856346Z"},"links":{"cited_paper":"/paper/2104.13478","citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:73ff9bf1c5ff43eac3bf381a480b99e3215e148ee2d66a825e5e23e692ebff3a","observation_id":"736f8bbc-0ac0-4295-a332-b27e193fc35f","resolution":{"observed_at":"2026-08-01T03:21:12.856346Z","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":"2026-08-01T03:21:12.864964Z","title":"Group equivariant convolutional networks","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.864964Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:94ec972ad78e3d910b7d2988deae49b0ec3e588eaeba37a05c2a0fb05d46b199","observation_id":"14bc48c3-c998-4873-bff5-1aa2fcfb731b","resolution":{"observed_at":"2026-08-01T03:21:12.864964Z","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":"2026-08-01T03:21:12.869096Z","title":"Boom, Ashley Seepujak, Odysseas Kosmas, Lee Margetts, and Andrey Jivkov","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.869096Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:d0e4edb110f1f106e8389b0eb2a957d96f4047e619f46a73402fbf6cac676227","observation_id":"331ff9fc-2b98-4270-9f1a-b2a81de29a74","resolution":{"observed_at":"2026-08-01T03:21:12.869096Z","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":"2026-08-01T03:21:12.872714Z","title":"Springer-Verlag, 1977","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.872714Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:dc477926c0e135e640dd8edd678d968a995119005cc1f4ef6f9acd7f76abacb7","observation_id":"b9bb5d40-91ec-4169-9fd9-0613811cd976","resolution":{"observed_at":"2026-08-01T03:21:12.872714Z","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/s00454-007-1339-4","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:24:16.795314Z","title":"Bobenko and Boris A","venue":null,"work_id":"6d90574d-855f-483f-9e50-d2ba0ef8bfa7","year":2007},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.876535Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:6bbb49dbb4fa188cff120c5cbacd832763c61a51d3a683dedb590cad31882c7d","observation_id":"885924e3-2ed2-4b50-8c3d-d8aced57254e","resolution":{"observed_at":"2026-08-01T03:24:16.853733Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:12.880371Z","title":"Hirani, Damrong Guoy, and Edgar A","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.880371Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:cb263736ab7c3822221c3c9ad58c2dd4660cd668688fa20ae3a4f70877563352","observation_id":"2c60155c-3ebb-4529-8745-c1f64caa41e8","resolution":{"observed_at":"2026-08-01T03:21:12.880371Z","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":"2026-08-01T03:21:12.884939Z","title":"Hirani, Kalyana B","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.884939Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:2514b27eccb05d278a8ddd5ed2467c4d5dc39d572802df6618a7a088c26d5fae","observation_id":"0c12e711-2e38-48ae-9b01-394f6d97bb5e","resolution":{"observed_at":"2026-08-01T03:21:12.884939Z","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":"10.1137/0153064","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Bossavit","venue":"SIAM Journal on Applied Mathematics","work_id":"093cb3d9-0486-4835-b055-8719b8e0a45a","year":1993},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.888814Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:29d010416305e8d27b39e2beb09f1a67f56dff9f8b49e4a24f5953a564fe3e50","observation_id":"9648c16c-4f2a-48d3-b71b-d8174bc0216c","resolution":{"observed_at":"2026-08-01T03:24:16.754130Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:12.892921Z","title":"Guermond, P","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.892921Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:1fbb5dec507d35140c4fa0e3c4cb20319faf0c898dedaab0b0e723d8243b70df","observation_id":"8ac870cc-cc4d-4c46-ad5c-2b4ae27a0db4","resolution":{"observed_at":"2026-08-01T03:21:12.892921Z","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":"2026-08-01T03:21:12.896769Z","title":"da Silva and Marcelo P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.896769Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:98f77707a5726d3049d7572ad5caa8909fd3a6e7bbf80cd5f89dca3c064e4b35","observation_id":"4ab67d35-a585-46f5-9107-08606a63a1f2","resolution":{"observed_at":"2026-08-01T03:21:12.896769Z","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":"2026-08-01T03:21:12.904608Z","title":"do Carmo.Differential Geometry of Curves and Surfaces","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.904608Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:ed94eae52b957326b7a44015ba26f64f446c7b56946a19bc110f367916fda02b","observation_id":"c4e14e14-028f-4be8-8437-ac8fed341e8f","resolution":{"observed_at":"2026-08-01T03:21:12.904608Z","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":"10.2312/sgp/sgp07/033-037","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Discrete Laplace operators: No free lunch","venue":"Eurographics","work_id":"bb8ac4ef-1301-4dba-b097-9e123d06220a","year":2007},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.908251Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:f7371fe69fb918c2ece0551f1edac42163c2745dc3d8103344a6c88cbbfce53c","observation_id":"65adf746-5434-4b09-95b5-648632cc1779","resolution":{"observed_at":"2026-08-01T03:24:16.431692Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:12.911808Z","title":"Dresselhaus, Gene Dresselhaus, and Ado Jorio.Group Theory: Application to the Physics of Condensed Matter","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.911808Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:d1bc558905cbc6029801ffe1c8c04abe59288b9fd209fa619d98b376220f8910","observation_id":"583f5994-c2ec-48f2-a8fd-974ac1694456","resolution":{"observed_at":"2026-08-01T03:21:12.911808Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0305004100033156","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Mathematical Proceedings of the Cambridge Philosophical Society","work_id":"8562a5c1-988c-4d60-a2de-7aac58af0b6d","year":1958},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.916019Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:6bc04b45061da8db939596d228b61483514cdeba1f192cc91a77ee5410365a34","observation_id":"c7ed3a0c-e154-4792-8063-6370551d2514","resolution":{"observed_at":"2026-08-01T03:24:16.301299Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-01T03:21:12.920519Z","title":"Convergence of discrete exterior calculus approx- imations for poisson problems.Discrete & Computational Geometry, 63(2):346–376, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.920519Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:053c9daffe452bcd057fc277911f2e26091e0c5877205ff785a1000d718aba0c","observation_id":"ddb0ea13-bf1f-4366-a4fb-32892d9e183c","resolution":{"observed_at":"2026-08-01T03:21:12.920519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.08934","last_updated":"2026-04-30T20:12:43Z","snapshot_observed_at":"2026-07-06T21:23:28.579575Z","submitted_at":"2025-05-13T20:01:33Z","title":"A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.08934","snapshot_observed_at":"2026-08-01T03:21:12.924418Z","title":"A framework for analysis of DEC approximations to Hodge-Laplacian problems using generalized Whitney forms, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.924418Z"},"links":{"cited_paper":"/paper/2505.08934","citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:c227ddf3ac5ec685dbda8b19dae67f1b87a01a8e316665bbd86234e6fde7c10c","observation_id":"d778bebd-db16-49dd-8397-fa4b33d7f4e4","resolution":{"observed_at":"2026-08-01T03:21:12.924418Z","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":"2026-08-01T03:21:10.781053Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:10.781053Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:4fceb0f7ac8e0fd99157e27b7b83e742655c7a118a008b432f357485d41f7f02","observation_id":"564d9612-1038-44f5-abf2-4efeb07b03fa","resolution":{"observed_at":"2026-08-01T03:21:10.781053Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13478","last_updated":"2021-05-02T16:16:03Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-04-27T21:09:51Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13478","snapshot_observed_at":"2026-08-01T03:21:12.860803Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.860803Z"},"links":{"cited_paper":"/paper/2104.13478","citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:8ab5fbb9b3fc627c05816515a1bc867cf4add18d958aff013655fc25dfe59fe7","observation_id":"00f63f70-af68-4f0c-a3e3-0ae2f27399d3","resolution":{"observed_at":"2026-08-01T03:21:12.860803Z","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":"2509.19479","doi":"10.48550/arxiv.2509.19479","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"URLhttps://doi.org/10.48550/arXiv.2509","venue":"arXiv (Cornell University)","work_id":"fa0fbe7d-0c60-4143-bef0-e8d97f37cee3","year":null},"citing_paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-01T03:21:12.900533Z"},"links":{"citing_paper":"/paper/2607.25192"},"observation_digest":"sha256:9384456e0201414c5d731925de52f6e87c51b926e4c6521d25641dd0faca86fd","observation_id":"d122c28a-cff5-4972-8bd9-9c7ca5ef9608","resolution":{"observed_at":"2026-08-01T03:24:16.591084Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.25192","last_updated":"2026-07-28T01:46:13Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T09:35:51.162123Z","submitted_at":"2026-07-28T01:46:13Z","title":"Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":13,"verified_fuzzy":0},"total_outbound_references":37},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.25192."}