{"as_of":"2026-08-22T03:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4c39970f2efbc4d0fd854e4b6a878e8fb2b084901d19d898b19e18248d77bc27","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T16:10:56.984191Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2509.08772/citation-record","integrity":"/paper/2509.08772/integrity","json":"/paper/2509.08772/citation-record.json","paper":"/paper/2509.08772"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:10:58.614645Z","title":"Evolutionary dynamics of higher-order interactions in social networks","venue":null,"work_id":"dd14c7e8-315f-48d7-bd73-6a8b0d1eee01","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.495347Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:0b88c5850de5bdfb432e2aa6a4b6e29b3c09bc2dea76e861d027b7b506ef295f","observation_id":"95cf5469-f8b0-404b-829f-2f93cb22dad1","resolution":{"observed_at":"2026-08-15T16:10:58.624321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.502785Z","title":"A Survey on Hypergraph Representation Learning","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.502785Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:b1734f2adb279eb7162475afaa189446f4cfd5fe5d107b7948ebafcf8ef068e1","observation_id":"b4d1e7dd-a1ac-48ed-b518-01b0ed85ceee","resolution":{"observed_at":"2026-08-15T16:10:56.502785Z","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":"2026-08-15T16:10:58.588184Z","title":"Minimization of functions having Lipschitz continuous first partial derivatives","venue":null,"work_id":"13505fcb-fb1e-4a98-988a-f3029759cb83","year":1966},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.519440Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:717b3ddabfbdd4aa4fc6e433b2882090cc50dbaf60e5f3d0d2beafe90cae6dcd","observation_id":"cde99f0d-690e-429f-8fd4-989bc8a421f9","resolution":{"observed_at":"2026-08-15T16:10:58.594222Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.556392Z","title":"Class of models for random hypergraphs","venue":null,"work_id":"675b3808-d923-401f-8968-bebbb95bebe3","year":2022},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.531010Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:1f935eb5768545bd1a7c92f73599dcc9c0773d2359ae9d4eff27f80f361d5e46","observation_id":"ad56ac9c-01ba-4491-9f4c-99b37165b4ae","resolution":{"observed_at":"2026-08-15T16:10:58.571553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.523199Z","title":"The physics of higher-order interactions in complex systems","venue":null,"work_id":"25b70097-2ec5-4742-85d8-d6657e00c55c","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.543688Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:23b6f08a331aa741c38fb19ed95ed4636a94cf4babd67c45c96782ee01d69365","observation_id":"50f7bc28-e00a-44b1-abdb-00304019b866","resolution":{"observed_at":"2026-08-15T16:10:58.535603Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.493014Z","title":"Networks beyond pairwise interactions: Structure and dynamics","venue":null,"work_id":"b78b762b-b2c2-4338-a9f0-fa3e2bb1e294","year":2020},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.555705Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:6c68515083f2c00e094f79fb67ee9fc618b1e1ab2e1dfe417468b4a173d9a440","observation_id":"1d56a1cd-47e3-4d1a-9eb0-2f1be29b9e3b","resolution":{"observed_at":"2026-08-15T16:10:58.508322Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.457327Z","title":"Towards a theoretical foundation for Laplacian- based manifold methods","venue":null,"work_id":"01638db4-9b7f-4284-820f-e5e90c701240","year":2008},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.579817Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:acbbe73a291d10c294aa8aa80e313bcde04e8ef72f50b16f19470fa842ee7e0c","observation_id":"56bbcf01-b204-429f-829c-0b5b7e5add96","resolution":{"observed_at":"2026-08-15T16:10:58.470201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.427307Z","title":"Higher-order organization of complex networks","venue":null,"work_id":"6f086f01-5ea2-460a-9aa7-84c3b29483f0","year":2016},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.606861Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:bcc963b208e9654d71fce9ac745839ea378edfd584f64f77f2c74bd77313e685","observation_id":"fa306ee8-7812-4699-a480-aa2bf7338f23","resolution":{"observed_at":"2026-08-15T16:10:58.435910Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.628674Z","title":"Three Hypergraph Eigenvector Centralities","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.628674Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:1fea8755af582e9788222b9589a3e84b92f9c14247c365f7849d0885b5b80e38","observation_id":"a390d1c1-737a-437e-bd89-fb0be769b5d8","resolution":{"observed_at":"2026-08-15T16:10:56.628674Z","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":"2026-08-15T16:10:58.379296Z","title":"What Are Higher- Order Networks?","venue":null,"work_id":"b3e8639f-3102-4c94-b0b7-72227cd46b50","year":2023},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.667523Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:99044bbe5465bc1cb1082de19ce4a925ed4a8a3dee24ed88c5ac6d5e93be9367","observation_id":"677f2408-d0e6-4002-85cb-fdcc4cf4c8c8","resolution":{"observed_at":"2026-08-15T16:10:58.388795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.351165Z","title":"The use of the area under the ROC curve in the evaluation of machine learning algorithms","venue":null,"work_id":"ff42e549-c832-4398-b6ab-50141fefc8fc","year":1997},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.682044Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:cf19984d32d14a340c1807666f69c75c01846b5460a05d6dac4ef75f30c7b83e","observation_id":"dfae5ace-fd5d-40bd-aa7b-538f4daab58b","resolution":{"observed_at":"2026-08-15T16:10:58.358868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.323940Z","title":"Hypergraph clustering: from blockmodels to modularity","venue":null,"work_id":"195cc3db-8dc6-47e3-9175-0aa58521aded","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.694826Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:91a5af0c129b0a25ff9d98d96fa93c1638af6c1877fab5291b8f9519499f2e4f","observation_id":"d7c50260-ea82-4f8d-8db5-3d8403764ea2","resolution":{"observed_at":"2026-08-15T16:10:58.332354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.281590Z","title":"A spatial hypergraph model where epidemic spread demonstrates clear higher-order effects","venue":null,"work_id":"1967e65d-af42-437e-a2e7-8dd6d522e4a1","year":2024},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.703162Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:5c310537a9cee158ff2db553aa4bb089466595945be7ff3440a67b448a79e052","observation_id":"dc24205d-7cdd-4ff2-9e22-1a6f57375cde","resolution":{"observed_at":"2026-08-15T16:10:58.290692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.246789Z","title":"Estimating the intrinsic dimension of datasets by a minimal neighbourhood information","venue":null,"work_id":"4b5c3ce0-6fb0-4037-85b1-d3fe98f66e34","year":2017},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.713817Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:0b3ee9314aaa01b2df43dd58a0ab1eeb21b2e1d504c5de290e0f2201c2c05d6b","observation_id":"0f78ed75-0493-4d6d-b49b-bcdfa01c8acd","resolution":{"observed_at":"2026-08-15T16:10:58.253803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.218666Z","title":"A Representation of Hypergraphs in the Euclidean Space","venue":null,"work_id":"440fe71d-1eab-499b-bc34-e23aafd12d35","year":1984},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.724975Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:6818f99bb8dd9c965ccd54c587ae80e19a7b4fa159c9a2ce49dbf84ce36a8bbd","observation_id":"41b30280-4b94-4abb-b17c-d5420a2590b9","resolution":{"observed_at":"2026-08-15T16:10:58.227916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.178388Z","title":"Random plane networks","venue":null,"work_id":"18381088-d184-4771-a918-8bfffcd7d6e0","year":1961},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.735642Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:297fd48f1755d1c99f7b9f87d377114f8fc16e4cdf786393e5c61404ffab8605","observation_id":"070c8f69-b624-48a4-9661-0e73c9745009","resolution":{"observed_at":"2026-08-15T16:10:58.186097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.749215Z","title":"Generative hypergraph models and spectral embedding","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.749215Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:094dc38d558104dbb93374f886f72e9069e6c03e31ba4e5f8c2b29cbf089fd81","observation_id":"dd8ae1d3-6e87-47c7-8d75-fb1f0870166b","resolution":{"observed_at":"2026-08-15T16:10:56.749215Z","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":"2026-08-15T16:10:58.139084Z","title":"Estimating network dimension when the spectrum struggles","venue":null,"work_id":"acfdf3b8-bbbe-4a9b-aa5c-f9c613f41758","year":2024},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.775905Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:bf474d9a3cf962c9efc0268c66626b411777b02c84545749428b0820cb340bf9","observation_id":"ca497cd4-e733-4b6d-b39b-7523374afe25","resolution":{"observed_at":"2026-08-15T16:10:58.149918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.101570Z","title":"Periodic reordering","venue":null,"work_id":"2a4ccd81-1095-4662-85b8-f0ebbd458bca","year":2010},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.783071Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:0b3851ef18103c56f11affcf80f3a44d0e06fe1aef5ee2577e0d1e333120025b","observation_id":"8f48ec5c-201c-47ad-907e-21a675a32abd","resolution":{"observed_at":"2026-08-15T16:10:58.112363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.060548Z","title":"Epidemics on hypergraphs: Spectral thresholds for extinction","venue":null,"work_id":"6eb3a998-b61b-4e23-9e73-d5c8a8e913c4","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.790540Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:5cee8a21d1241953765e7bfdc6f5822d699a6393615c8b7fe29f3b9e3b4d484e","observation_id":"0a7f3fbf-ee61-4db3-9d6e-6804912af527","resolution":{"observed_at":"2026-08-15T16:10:58.065974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:58.012078Z","title":"Spectral clustering and its use in bioinformatics","venue":null,"work_id":"ee0b0924-36bc-4e23-850d-c52db0af41e0","year":2007},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.805266Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:513d998041e5472d94e11a19b9725a1929136aeaa593d7f802cc3a95373ee10f","observation_id":"11d58a7e-09f5-4a26-901a-033724f3194f","resolution":{"observed_at":"2026-08-15T16:10:58.024166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.979223Z","title":"Comparing partitions","venue":null,"work_id":"a3b4b14d-907b-4f99-bcf1-3e4a36dbc0c8","year":1985},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.814804Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:646711d266abc1084b6dc05284eb260a6b58eb01a15928954b56acbe5694b4e3","observation_id":"db37dbb8-287d-4a32-9657-608c8b60558d","resolution":{"observed_at":"2026-08-15T16:10:57.986728Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.778015Z","title":"Connectivity of Random Geometric Hypergraphs","venue":null,"work_id":"48ecd2d3-9f06-4cd3-a73c-1cb3b90fb824","year":2023},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.826225Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:52827379b0a376dba020a7088d4fc67de6835d3c1c2bcb87f42fe5aa115df14c","observation_id":"4c2c13f6-50be-4912-8904-896dcce7bdf4","resolution":{"observed_at":"2026-08-15T16:10:57.793925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1701.01394","last_updated":"2018-03-30T00:51:22Z","snapshot_observed_at":"2026-08-14T21:22:24.946329Z","submitted_at":"2017-01-05T17:31:16Z","title":"On spectral partitioning of signed graphs","version":2},"cited_work":{"arxiv_id":"1701.01394","doi":null,"metadata_source":"pith","pith_arxiv_id":"1701.01394","snapshot_observed_at":"2026-08-15T16:10:57.429385Z","title":"On spectral partitioning of signed graphs","venue":"cs.DS","work_id":"7856bef2-a2d6-4b98-8493-aeb83cff3dbc","year":2017},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.833238Z"},"links":{"cited_paper":"/paper/1701.01394","citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:84bb659f080c8c496c63e5db9059461913b751662bd49b3d08529f99a6b54b79","observation_id":"28067804-8aa2-4b48-adae-af3b556aa04b","resolution":{"observed_at":"2026-08-15T16:10:57.438398Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.740562Z","title":"The effect of heterogeneity on hypergraph contagion models","venue":null,"work_id":"0a7737f7-d612-4575-a9e2-83e9e7fb437d","year":2020},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.839768Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:4be8ecb88319d1c1c6e8bd634a1838128e7afeb36854ea75f23a2ea5596264ee","observation_id":"835e4b78-f52f-4e58-b837-8b4af78ba745","resolution":{"observed_at":"2026-08-15T16:10:57.753551Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.702699Z","title":"Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualiza- tion","venue":null,"work_id":"6ba61386-d2df-4a3d-a7cc-0f0bd7e6d7bb","year":2010},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.847148Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:6cba12b0871406f96932d30c3451aed5bab7f1e2ed9a37caf178e9038a74ada2","observation_id":"976bd0d6-b944-491a-b2fc-ceda8662c19b","resolution":{"observed_at":"2026-08-15T16:10:57.713252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.661879Z","title":"A tutorial on spectral clustering","venue":null,"work_id":"21bf242d-edec-40ab-867a-ebaab5c89025","year":2007},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.860406Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:535f6030a30684064435324acc9370ba74fe3f4aebe8604d9841f78ed80ec9ec","observation_id":"fbe0bf68-82d0-4754-921d-e3355fbea34e","resolution":{"observed_at":"2026-08-15T16:10:57.675641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.875959Z","title":"Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.875959Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:818ee6d956b18a3935aa6e7b6912925fcac7bbfe2f2b3ee9ce2a693608d5d471","observation_id":"02f1ac98-7520-4b44-b85c-2302c60574c9","resolution":{"observed_at":"2026-08-15T16:10:56.875959Z","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":"10.1137/0725041","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:10:57.117379Z","title":"Derivatives and Perturbations of Eigen- vectors","venue":null,"work_id":"25979ffc-7fe2-4d6c-a453-f65d25505381","year":1988},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.889708Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:c5241b30bf95bcef1cec4936e620e1349f7b8b08d7f97a2dcaafbccd0954a8c3","observation_id":"58a83da5-44e2-4ac3-bffd-8ce6187f315a","resolution":{"observed_at":"2026-08-15T16:10:57.129457Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.615076Z","title":"Learning the effective order of a hypergraph dynamical system","venue":null,"work_id":"aac70208-6a47-427a-9440-94e3bf19ba94","year":2024},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.899797Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:afc16b7496e72fa1031dc2ff2f4809303099710332708f6f55a693d176fb686f","observation_id":"d1cf8f3f-049a-444c-bac7-be3629feb290","resolution":{"observed_at":"2026-08-15T16:10:57.628961Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.910431Z","title":"High-Resolution Measurements of Face-to-Face Contact Patterns in a Primary School","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.910431Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:a570eec4029274c0247318b8ab7640aa6a8b2fecc9167d5bbadfbd451cf5fee7","observation_id":"676cd3d5-b436-42b7-b16c-04be175c10fe","resolution":{"observed_at":"2026-08-15T16:10:56.910431Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.10953","last_updated":"2020-07-23T03:53:45Z","snapshot_observed_at":"2026-08-20T00:01:59.529359Z","submitted_at":"2019-05-27T03:12:52Z","title":"FOBE and HOBE: First- and High-Order Bipartite Embeddings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.10953","snapshot_observed_at":"2026-08-15T16:10:56.918717Z","title":"First- and High-Order Bipartite Embeddings","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.918717Z"},"links":{"cited_paper":"/paper/1905.10953","citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:28c83d62ba8a1697e8a15d996949aca28ed41df0e616867e4473dcb7ec06bb75","observation_id":"a6c90566-d52a-4ed3-9fb2-78d62e97d7c5","resolution":{"observed_at":"2026-08-15T16:10:56.918717Z","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":"2026-08-15T16:10:57.573052Z","title":"The why, how, and when of representations for complex systems","venue":null,"work_id":"ed95672a-e771-49b1-92d5-caeefb05059b","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.927314Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:0355d70a71bcfc44d0d6be56a912b24e0f87fa346119d48cb960077709ba5dc3","observation_id":"065de508-f2ea-45fa-99e6-68d8a10b8a32","resolution":{"observed_at":"2026-08-15T16:10:57.589640Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.529560Z","title":"Wilkinson and J","venue":null,"work_id":"7ec2a084-247d-41ef-bf98-8c5a9a27d281","year":1988},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.935979Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:4d8a3aefa821356222ca2b6de6634e99116eac0353da4972666114780a704032","observation_id":"8f674b91-adf3-4059-9010-17361bad5383","resolution":{"observed_at":"2026-08-15T16:10:57.542489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.491871Z","title":"A novel hypergraph convolution network-based approach for predicting the material removal rate in chemi- cal mechanical planarization","venue":null,"work_id":"51eab01d-bb4a-4319-82e1-a9a037ebdee9","year":2022},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.945898Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:7c8201b6a1147649fb38cacf093647089157c1bd2d484228b3d55b065c861bf6","observation_id":"3186b895-1a4e-4aff-a823-f0f8a21264ab","resolution":{"observed_at":"2026-08-15T16:10:57.508012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:56.957105Z","title":"Hypergraph Convolutional Recurrent Neural Network","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.957105Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:f29a59eb7cb7d6da434954655d768fe924b9d34ab5d339a1bfad17d101c87f05","observation_id":"3b48e732-59a3-40f1-869d-83e13c05288b","resolution":{"observed_at":"2026-08-15T16:10:56.957105Z","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/s13278-020-00718-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-20T11:03:42.707129Z","title":"Modeling signed social networks using spectral embedding","venue":"Social Network Analysis and Mining","work_id":"ccf182c9-3081-4761-b365-06348be90e97","year":2021},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.968257Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:f9f62d7f107cb5a033e30b38bbaf1d4732c4fe4e00bc739fd72308055022287d","observation_id":"8114fa04-e87b-483d-b755-674f20da3f82","resolution":{"observed_at":"2026-08-15T16:10:57.068945Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T16:10:57.455592Z","title":"Heterogeneous hypergraph embedding for document recommendation","venue":null,"work_id":"dae35877-9019-4414-ace6-c49e6a789ea0","year":2016},"citing_paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T16:10:56.984191Z"},"links":{"citing_paper":"/paper/2509.08772"},"observation_digest":"sha256:3d6a05672fdc52e02f9b14950993f81c130911a0c7be5d8ce903da3d7a58852f","observation_id":"0eda51c3-f8ca-4e0f-9e79-999259ebd853","resolution":{"observed_at":"2026-08-15T16:10:57.464825Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.08772","last_updated":"2025-09-10T17:02:30Z","latest_version":1,"primary_category":"cs.SI","snapshot_observed_at":"2026-08-21T16:59:58.921990Z","submitted_at":"2025-09-10T17:02:30Z","title":"Optimization of geometric hypergraph embedding"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":3,"verified_fuzzy":26},"total_outbound_references":38},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2509.08772."}