{"as_of":"2026-08-22T10:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:753509c7ff3ee91c9a18435103137482394ce42a4e4513dce2c5c21cc2fc5e1e","coverage":[{"denominator":61,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":61,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T12:46:21.062391Z","state":"measured"},{"denominator":61,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":61,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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/2509.01443/citation-record","integrity":"/paper/2509.01443/integrity","json":"/paper/2509.01443/citation-record.json","paper":"/paper/2509.01443"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:20.617389Z","title":"Dobkin, Deborah Joseph, and Jos \\' e Soares","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.617389Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:e19e12306d81111219b224cc7b295b8e4ed9f186246574577ebd330683cc809c","observation_id":"5dac65c1-ac97-4305-8159-9d7fcb576b14","resolution":{"observed_at":"2026-08-05T12:46:20.617389Z","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":"5058.22519","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:24.184908Z","title":"Mount, Jeffrey S","venue":null,"work_id":"1c1a1dd0-685f-48e1-abd0-49a7b09de093","year":1995},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.626327Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:88ea52a19ce290276bf8f14d0d684ee41b0573f861768052f5411a9e2fd75009","observation_id":"0f583975-2541-4532-947b-eaa82198fc12","resolution":{"observed_at":"2026-08-05T12:46:24.193618Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.633288Z","title":"Hyperbolic D elaunay complexes and V oronoi diagrams made practical","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.633288Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:37a3d0868f1809953949c4d3c37f653e8b48d01e2b0f9e581ef1bc8397ef27ff","observation_id":"dedffbc6-a36b-4280-a9d0-9c19122ea04f","resolution":{"observed_at":"2026-08-05T12:46:20.633288Z","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":"7216.20272","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:24.061334Z","title":"Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth","venue":null,"work_id":"b72202b6-ab2f-499f-be0a-6620a608ebfa","year":2011},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.639519Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:f493e07e582afb012be1e0c02a709ef91a01ed6505563bfee02a734ac97765d8","observation_id":"cf50ccc1-1a40-4309-8447-344bba34b523","resolution":{"observed_at":"2026-08-05T12:46:24.073097Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9781611978322.145","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"o m \\\" o t \\","venue":"Society for Industrial and Applied Mathematics eBooks","work_id":"a9f8e09f-5b98-4025-b09e-b00c4338b7b5","year":2025},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.644789Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:4a6e6cd274b0657db2ce2bbfda7c5d6eb6934de76ef13e35935c9994e0b157c5","observation_id":"dee9127a-7c83-4cf4-8869-fa3ee6e04041","resolution":{"observed_at":"2026-08-05T12:46:21.903755Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.650440Z","title":"Embedding of hyperbolic spaces in the product of trees","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.650440Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:9bfaaec101ab4942845521ac58d22ea1d4367c8ca986920ff69248315c9315b1","observation_id":"88dddad6-9c6e-4c0c-b003-f28fa31756c0","resolution":{"observed_at":"2026-08-05T12:46:20.650440Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0509355","last_updated":"2005-09-15T16:25:14Z","snapshot_observed_at":"2026-08-04T22:32:09.139258Z","submitted_at":"2005-09-15T16:25:14Z","title":"A product of trees as universal space for hyperbolic groups","version":1},"cited_work":{"arxiv_id":"math/0509355","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0509355","snapshot_observed_at":"2026-08-05T12:46:23.960245Z","title":"A product of trees as universal space for hyperbolic groups","venue":"math.GR","work_id":"a249d707-1355-48f9-ae0b-b8f6db049579","year":2005},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.657585Z"},"links":{"cited_paper":"/paper/math/0509355","citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:61e9acd9b4ee9aa8f5681c5f52f921546460a67947c4f180bf7cf50ee049d4c5","observation_id":"df6ac4af-a65d-45e6-b519-94ce8fde5aa7","resolution":{"observed_at":"2026-08-05T12:46:23.966105Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.663094Z","title":"T \\' o th","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.663094Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:47d9d41a6df3fbe41df878ecbf7f0869d48c3b3cfc1461cc170ef811b692534f","observation_id":"c0ebaee8-f21c-4dc4-a5f3-3b78575bf9f7","resolution":{"observed_at":"2026-08-05T12:46:20.663094Z","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":"2026-08-05T12:46:20.668103Z","title":"Structure and independence in hyperbolic uniform disk graphs","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.668103Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:e8a8bc80c4250c086f0f3b00406ad0f140d03af9a0c3840e4c349533e8d0b2bd","observation_id":"63e32185-eebb-4853-a271-cc6bfbd233b6","resolution":{"observed_at":"2026-08-05T12:46:20.668103Z","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":"2026-08-05T12:46:20.673553Z","title":"Covering planar metrics (and beyond): O(1) trees suffice","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.673553Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:7573245c16a3ce3765a94ab9305ec3af5b26f9eebb78c57ce6729d5626ce76aa","observation_id":"5842d83f-6c3a-41cf-a0cd-fe0b0c457e9e","resolution":{"observed_at":"2026-08-05T12:46:20.673553Z","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":"2026-08-05T12:46:20.683946Z","title":"Optimal E uclidean tree covers","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.683946Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:dc1258b0cf2ef85e6b13496c141c5af6322695aac9fff89af4fceabc31f204d2","observation_id":"8a277c85-ac9d-4df6-b06f-78092e2cabf6","resolution":{"observed_at":"2026-08-05T12:46:20.683946Z","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":"2026-08-05T12:46:20.690104Z","title":"Tightening curves on surfaces monotonically with applications","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.690104Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:5b3c09accc4b9eb892ad3d636829e7bfa41a5cc5e794a83eb8b1e576217ee2cd","observation_id":"686c2f33-916f-4b58-95c3-467d957b4299","resolution":{"observed_at":"2026-08-05T12:46:20.690104Z","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/s00454-008-9115-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Discrete & Computational Geometry","work_id":"c52db9c4-0935-446a-9bdb-582c502bda84","year":2009},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.697917Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:87b3734b9a89963548ab1bb61e49ca2a9ccedfbf91810f4217d54c062ab89600","observation_id":"a2078150-58ac-4655-8003-84d82890b7d7","resolution":{"observed_at":"2026-08-05T12:46:21.806127Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/pl00009390","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Discrete & Computational Geometry","work_id":"005a2ac7-fcbf-4497-b28c-ff15e7bd5414","year":1998},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.704493Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:8a5f99268db83900385cb9e61772a022c134729cc073860625473c1b2e62b791","observation_id":"ce1f7ae4-fa4c-4db1-a8f6-b68c257c0555","resolution":{"observed_at":"2026-08-05T12:46:21.786474Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.710729Z","title":"There is a planar graph almost as good as the complete graph","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.710729Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:fdc9b81b40b2c3cd5d1d5c45d4dbd2f6a27b4a6fd7396ceaf7edb98aa2bd94b2","observation_id":"8014a21d-9ecf-48f9-999e-9f97fcd09f29","resolution":{"observed_at":"2026-08-05T12:46:20.710729Z","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":"2026-08-05T12:46:20.716065Z","title":"Chan, Sariel Har-Peled, and Mitchell Jones","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.716065Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:2a4c94c7643c65e9cd24c2bd26338d49c202261172e57323514bf6c57caf4046","observation_id":"296224ea-d3e6-4682-8d12-8fa70a8a7eb6","resolution":{"observed_at":"2026-08-05T12:46:20.716065Z","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":"0836.20085","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:23.748436Z","title":"Callahan and S","venue":null,"work_id":"7cec6f85-3f73-4741-aca5-f0812a049d27","year":1995},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.722067Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:ff8b1766d3ef0f8a5b556f26a6705d5fbef760e447e41065ce56252b05322d40","observation_id":"1c4bc4cf-a9ab-464e-b88a-fdcb101d8411","resolution":{"observed_at":"2026-08-05T12:46:23.757824Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"8395.28402","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:23.641772Z","title":"Clarkson","venue":null,"work_id":"9541f6d6-fb90-4133-8efd-52c0d14d4ca0","year":1987},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.727356Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:e2493cdf3c8282c44e31e09c264448fcdcfea72e995a298d7ade7bed61102dd9","observation_id":"5e619c1f-857a-4fc7-b9e5-cc5b59c0abce","resolution":{"observed_at":"2026-08-05T12:46:23.650908Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/130930984","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"SIAM Journal on Computing","work_id":"e8dead7f-83c3-4ee0-b4aa-b168fc6ba6ac","year":2015},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.732141Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:40d6705c9c2f2363407303f0c3e54c539ae8a8edbd95b1bba9f7d41a72075f8f","observation_id":"433378d2-5287-4a6e-8ea4-18ebbab1152f","resolution":{"observed_at":"2026-08-05T12:46:21.745409Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"file/0415740","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:23.526493Z","title":"Hyperbolic graph convolutional neural networks","venue":null,"work_id":"a70ddbce-106e-409a-8b6f-09b138d5d0b0","year":2019},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.739065Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:08947198453b53ea3c05c508c8245d9d1f26342066508b938e079c1baf934cb8","observation_id":"13fcbf94-edb4-4925-9277-a92441d64de1","resolution":{"observed_at":"2026-08-05T12:46:23.537629Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.744829Z","title":"van Kreveld, and Mark H","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.744829Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:d2bd8b817273a9ef63126711caff3d5b191bdaac90bffd8403d44eda36c4d918","observation_id":"c6f8fd90-e266-4c8c-9f1f-2c2c3ddb51a0","resolution":{"observed_at":"2026-08-05T12:46:20.744829Z","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":"10.1023/a:1004272423695","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Dolbilin and Daniel H","venue":"Periodica Mathematica Hungarica","work_id":"ec8d2a8f-e988-4e08-8a04-6a6069f2ed0d","year":1997},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.754994Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:f36b2dc89bd13d7e7c0272e5941d115885279cfe9b3a6bec13f0322c1fa244bf","observation_id":"ccb2ea44-ca87-47bc-91e7-eebd1d8850f5","resolution":{"observed_at":"2026-08-05T12:46:21.692923Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00493-010-2341-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Demaine, MohammadTaghi Hajiaghayi, and Bojan Mohar","venue":"COMBINATORICA","work_id":"77520ecf-f1ac-41db-bd9e-28bcad34690e","year":2010},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.764014Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:346fa741b2282345209622140fcadf2166d270bbac6f1055781d513411c9eb7f","observation_id":"0fad73eb-e7c2-434d-9c6e-af101dab15b5","resolution":{"observed_at":"2026-08-05T12:46:21.672359Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00454-024-00653-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Representing infinite periodic hyperbolic D elaunay triangulations using finitely many D irichlet domains","venue":"Discrete & Computational Geometry","work_id":"f700a14c-5a65-4fde-a49b-29d30dbe34da","year":2024},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.771538Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:cc05b7c7c577c1ff7670239ce1127deff48fdd172b66244908ef4a9bb8d7f46e","observation_id":"6be09ccc-2485-46cd-95b2-97138313af29","resolution":{"observed_at":"2026-08-05T12:46:21.647848Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:24.275603Z","title":"The space of spheres, a geometric tool to unify duality results on Voronoi diagrams","venue":null,"work_id":"b805a060-f934-4932-a7e1-aebce69a243c","year":1992},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.779962Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:a67f11294e97f6faa199d5c55eb025773e80261151345c4d24979060481a728c","observation_id":"34f85b21-1752-47a0-9e01-eee0326f7609","resolution":{"observed_at":"2026-08-05T12:46:24.282554Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0218195997000193","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"A fast algorithm for constructing sparse E uclidean spanners","venue":"International Journal of Computational Geometry & Applications","work_id":"016dad81-ba22-4227-a3d5-38661002a95a","year":1997},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.789077Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:0a9796375cd1795bfdca561a860816c85b7daf1c5bc4b82d9d793037aa0f9f0e","observation_id":"b4b46aea-80c8-48bd-a009-5153996dff84","resolution":{"observed_at":"2026-08-05T12:46:21.622586Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9781611977912.175","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Untangling graphs on surfaces","venue":"Society for Industrial and Applied Mathematics eBooks","work_id":"736d660b-45b5-4ccb-af40-b6e62c1adc37","year":2024},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.796417Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:7fe722f2dfccf6292ddda3c795b7fb2bc85c0ec6453093f00655e7f065e4adaf","observation_id":"9d418f3f-b293-4dd1-805e-13ab0d95d490","resolution":{"observed_at":"2026-08-05T12:46:21.595732Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/090761653","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Tightening nonsimple paths and cycles on surfaces","venue":"SIAM Journal on Computing","work_id":"94569557-dc2a-4b30-a761-48adce494bde","year":2010},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.801894Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:d3399f0822c08892e3ea600c47a2610999a18e00b38f0c268db2f8fc439149ca","observation_id":"ef001cb9-4f86-4da2-b0c2-f40af245f928","resolution":{"observed_at":"2026-08-05T12:46:21.575615Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.807503Z","title":"Locality-sensitive orderings and applications to reliable spanners","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.807503Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:24a75db6507b7664276ffb90afe8a2b8964cc3f77fa790b40f3bfe8d5fd385f8","observation_id":"521b7b8a-582c-4c49-abb3-2749704b7f32","resolution":{"observed_at":"2026-08-05T12:46:20.807503Z","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":"8728.35874","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:23.326640Z","title":"An effective way to represent quadtrees","venue":null,"work_id":"0309d497-7aa2-4d85-b2c2-d8ddcedc635c","year":1982},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.815151Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:d5bbac285cb54fb83b8a6cc7b882d775d543cbd9f883cd1bbec480ab349c07a4","observation_id":"104283d7-c24a-441e-a37d-a0730c0e34a3","resolution":{"observed_at":"2026-08-05T12:46:23.338879Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:24.242614Z","title":"Hyperbolic neural networks","venue":null,"work_id":"beee060c-a342-4b84-b4f5-79f2298fc36a","year":2018},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.823619Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:b69dfb7eff20c2f32e7d99f62d5c4f715a7d1328738eed96052ef1f818c81edf","observation_id":"a9ac1d28-bf37-453f-8ed1-8fee3f7d6c93","resolution":{"observed_at":"2026-08-05T12:46:24.250990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.comgeo.2005.10.001","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Guibas, and An Thai Nguyen","venue":"Computational Geometry","work_id":"658e1bd0-1e07-48a5-9ebb-afa18ccb7a68","year":2006},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.835289Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:1c9e022659e77a23995d61f97422dfc3e5e2d907d15d88a152bfa5890c6338d7","observation_id":"2e6b6690-d855-49c8-b4d9-4126e92ad55a","resolution":{"observed_at":"2026-08-05T12:46:21.546510Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.socg.2024.60","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Near optimal locality sensitive orderings in E uclidean space","venue":"arXiv (Cornell University)","work_id":"041523c3-a799-45a4-90e3-7e3fcc932213","year":2024},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.842659Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:8ed40e7686d818cd8023e5f947ee2b9d60a0ccb7b9038d186b564c1c72d886ba","observation_id":"9e233c32-a399-4252-a2b4-353d01b9da52","resolution":{"observed_at":"2026-08-05T12:46:21.523610Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.848908Z","title":"Improved algorithms for fully dynamic geometric spanners and geometric routing","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.848908Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:bdbc353388fd298ac5964301c54dbcf78664b445fce78f98fbeda7c63d307731","observation_id":"ac56e693-05cc-45d2-bb29-afef2a50c8d2","resolution":{"observed_at":"2026-08-05T12:46:20.848908Z","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":"10.1007/978-3-540-87744-8_40","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"An optimal dynamic spanner for doubling metric spaces","venue":"Lecture notes in computer science","work_id":"8581f05e-5462-4a22-a824-b79300d65b0a","year":2008},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.857239Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:783a999c1ab528eb8b152fb1dfdaba202d938d9d501f4d3b7e138b98cf6336ad","observation_id":"9ad681ac-c526-4629-ae3c-07229aabcd0a","resolution":{"observed_at":"2026-08-05T12:46:21.492897Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.870173Z","title":"Fast construction of nets in low-dimensional metrics and their applications","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.870173Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:4e764110340d4ec9dcac3454d1e09aa54bbdc7b5a8b915eff3860c38f4847614","observation_id":"71eb21fe-792d-4c0f-adfa-ddc0d62fa68f","resolution":{"observed_at":"2026-08-05T12:46:20.870173Z","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":"2026-08-05T12:46:20.876916Z","title":"Geometric Approximation Algorithms","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.876916Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:d928b15abe2e6d0c68471913a76782dd16bbfbb4a767c1d6e4063bed3f27e146","observation_id":"4f9860e7-c600-450c-b998-4d5d03a031ff","resolution":{"observed_at":"2026-08-05T12:46:20.876916Z","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":"2026-08-05T12:46:20.884349Z","title":"A gap- ETH -tight approximation scheme for E uclidean TSP","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.884349Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:e1a24c79cb7269e86d7cdeb14f7fb1f660eb0546316123f7cedb9d7a8b36cb65","observation_id":"5bb5a2a6-0f1f-44fa-ba47-8666160fe8c2","resolution":{"observed_at":"2026-08-05T12:46:20.884349Z","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":"2026-08-05T12:46:20.892710Z","title":"Mark Keil","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.892710Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:e398ec8e08b63a8eb11b8912d2e4cc39e7b957d0f475b3d187c932682ba4ceee","observation_id":"279506d6-cf49-4a7a-a111-dce81dfefb82","resolution":{"observed_at":"2026-08-05T12:46:20.892710Z","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":"10.1137/1.9781611975994.100","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Hyperbolic intersection graphs and (quasi)-polynomial time","venue":"Society for Industrial and Applied Mathematics eBooks","work_id":"77ee6688-b9ae-4d25-b66e-d14f907705ab","year":2020},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.898545Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:49f6509c55daceadc14a5baada70880160e692904e3eac7c1b9e0ed4a9334793","observation_id":"54f7b982-2d31-4cee-b4b6-6b5cceadedc1","resolution":{"observed_at":"2026-08-05T12:46:21.408110Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.socg.2020.55","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"u rich, Switzerland , volume 164 of LIPIcs , pages 55:1--55:15. Schloss Dagstuhl - Leibniz-Zentrum f \\","venue":"arXiv (Cornell University)","work_id":"fe8164c3-b349-49af-9f92-cd89f96dbbcc","year":2020},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.905105Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:38b5d520215b83a39ba934f470ebda422cc38c21fd28ee561525458c0f646936","observation_id":"2c37d4b8-3ac0-425a-a790-78c9bfc40c38","resolution":{"observed_at":"2026-08-05T12:46:21.383994Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1109/focs.2006.9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":null,"work_id":"453f9f28-bfe8-4896-a9aa-2e7b235bfea0","year":2006},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.914846Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:9f0da54769330d0bd547272fb3866da7c2066cf89dce0c76f35705db225ad702","observation_id":"ed22cc1c-5935-4db0-95e5-6f314bbad26e","resolution":{"observed_at":"2026-08-05T12:46:21.349324Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2516.11326","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:22.977258Z","title":null,"venue":null,"work_id":"cb1d758c-4519-431c-a286-8a9aaa9559a9","year":2006},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.920239Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:f595c075a800a860c8c68a08014a94fa3c6f4e4ffa8c86738df90eb994f9f46f","observation_id":"d5c6c7df-27e9-42b5-99ea-da82e87d6379","resolution":{"observed_at":"2026-08-05T12:46:22.999004Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.925354Z","title":"Hyperbolic geometry of complex networks","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.925354Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:928f7de842f0115b0e82ea3adffc1db35c66d1ff7d9d376b0a66d6000806e5ad","observation_id":"0fee0413-5e33-4a88-a5ed-55f08ad0e1b1","resolution":{"observed_at":"2026-08-05T12:46:20.925354Z","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":"2026-08-05T12:46:20.930166Z","title":"A quadtree, a S teiner spanner, and approximate nearest neighbours in hyperbolic space","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.930166Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:829db8ae18af427e22e22058e4b2efe9704b92edc73b2b07e554755027896b89","observation_id":"8eccfc7a-a6a3-426a-a397-fb3c9d18a47f","resolution":{"observed_at":"2026-08-05T12:46:20.930166Z","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":"2026-08-05T12:46:20.936845Z","title":"Dynamic locality sensitive orderings in doubling metrics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.936845Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:9996ad36c0da056c2ea7f663be8f48fe667aa26800222ccc41eafc79bd882d06","observation_id":"717c6098-a1b7-4f31-b60f-c7b38c95ea10","resolution":{"observed_at":"2026-08-05T12:46:20.936845Z","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":"2026-08-05T12:46:20.943712Z","title":"A focus+context technique based on hyperbolic geometry for visualizing large hierarchies","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.943712Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:503d752c08b0f88cf5f8ae04d293232368cc9366ac19b30f747dc13ac29a3a8d","observation_id":"7d5378cb-a9d6-4483-9504-ccc2ee51c2f6","resolution":{"observed_at":"2026-08-05T12:46:20.943712Z","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":"2026-08-05T12:46:20.949455Z","title":"Truly optimal E uclidean spanners","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.949455Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:da4a64df26c926d58b88c86d6c38b5a6c55c86abb6bbc29b0a30e602500ff5c2","observation_id":"ac1a671f-f3b0-4f0f-b35c-5730149d7df2","resolution":{"observed_at":"2026-08-05T12:46:20.949455Z","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":"2026-08-05T12:46:24.209396Z","title":"Learning continuous hierarchies in the L orentz model of hyperbolic geometry","venue":null,"work_id":"e07a5f03-1738-4c05-bee1-d56214a59f2c","year":2018},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.955199Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:085ced82ec94d0308481ad6675c5285dc9ce97ac5bcea70a4115b7a0fb343e14","observation_id":"4b17b7a0-0b36-489e-8d30-0449f895a05a","resolution":{"observed_at":"2026-08-05T12:46:24.223516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:20.966184Z","title":"Voronoi diagrams on the sphere","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.966184Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:0ae7a9636e267466e0c4b38a2ee16d07212bca2030e7c50fa068cc1d8fceb697","observation_id":"0900d70c-35e7-4bc3-8852-4b9a1d0a3eec","resolution":{"observed_at":"2026-08-05T12:46:20.966184Z","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":"2026-08-05T12:46:20.972910Z","title":"Geometric spanner networks","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.972910Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:04cbe6ef5b038d66d59a36e93a9603a6d4402b87e616c09d398bb9a4cebd625c","observation_id":"1ce12a96-68b3-4c8a-a9d9-e5b40e4e0598","resolution":{"observed_at":"2026-08-05T12:46:20.972910Z","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":"2024.10215","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:22.655706Z","title":"Embeddings and near-neighbor searching with constant additive error for hyperbolic spaces","venue":null,"work_id":"e86c0f65-201b-4cb0-81e1-da8dbf41a694","year":2025},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.982110Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:431dee84df99a017ffbe939f5985f2bedc04d3898f3c60c812b386fe9d4bebfa","observation_id":"8027d025-9968-46e7-b64c-50404be6b8c6","resolution":{"observed_at":"2026-08-05T12:46:22.669254Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2021.31369","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:22.558861Z","title":"Hyperbolic deep neural networks: A survey","venue":null,"work_id":"3a61543a-81de-4c01-b247-760d598604cd","year":2022},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.989871Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:9fd3dad2b61672c629c514a84b04c2e2b47a19d0e8ee983790a9be5f4d34f11a","observation_id":"1fd322fb-4d77-403e-b814-73b725360bff","resolution":{"observed_at":"2026-08-05T12:46:22.568818Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-642-16367-8_10","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Transitive-closure spanners: A survey","venue":"Lecture notes in computer science","work_id":"4bd043d0-4de3-4dee-b95f-eb496bc97506","year":2010},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:20.995714Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:bd7a694cbe93c412baeef2fe92af64b921c61ab3dafd64db9e3be4f06b25f0cd","observation_id":"23b3484a-c8a1-49fe-857e-aef1e5459d1b","resolution":{"observed_at":"2026-08-05T12:46:21.201935Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00453-011-9504-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Fully dynamic geometric spanners","venue":"Algorithmica","work_id":"3bca50bf-d027-4f94-b0c6-84fd8f90b5b7","year":2012},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.001303Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:b8df9174006b07a4c5a1202ec380ec37a452a7b350ed47cdba74e2efd8e43d45","observation_id":"30d57bc0-f4e3-4480-affd-0ea66e0d621f","resolution":{"observed_at":"2026-08-05T12:46:21.173797Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"6698.27686","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:22.445810Z","title":"spanners","venue":null,"work_id":"25c7cbc0-cfd1-4ddc-aa24-02dee3ce6e90","year":1998},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.012966Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:bda07e273682e75d4e8e9203d4e539fa57ee9dc89005198c9c4e1bb8d1cb81d6","observation_id":"b263b729-796e-461b-988b-0d3da5d0f300","resolution":{"observed_at":"2026-08-05T12:46:22.457523Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-642-03456-5_19","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"The weak gap property in metric spaces of bounded doubling dimension","venue":"Lecture notes in computer science","work_id":"c82218f1-b65b-4826-bd46-0f043dd33315","year":2009},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.024733Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:b334bcc5e992ebc020deec9f1f90cffe12f4c44076b7e2f5c96762d786cc3831","observation_id":"7e11d016-276c-490f-9f75-9c67a84ceeee","resolution":{"observed_at":"2026-08-05T12:46:21.143312Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2004.13545","last_updated":"2020-04-28T14:16:49Z","snapshot_observed_at":"2026-08-09T04:09:57.799925Z","submitted_at":"2020-04-28T14:16:49Z","title":"The more you ask, the less you get: the negative impact of collaborative overload on performance","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.13545","snapshot_observed_at":"2026-08-05T12:46:21.034897Z","title":"Shavitt and T","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.034897Z"},"links":{"cited_paper":"/paper/2004.13545","citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:72773a5365cecb5fb6c0b6428d20628c08c0ad4b926d70e8b1f3abfbb31c296b","observation_id":"4fec8020-1899-4fac-be59-e3bfd41b091f","resolution":{"observed_at":"2026-08-05T12:46:21.034897Z","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":"2026-08-05T12:46:21.046031Z","title":"Bypassing the embedding: algorithms for low dimensional metrics","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.046031Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:9e769e29e5237cf4899c60ecd4a87eca7e39f33f205ead39ff9744a353f4cfd6","observation_id":"e51839a5-cf71-48d4-ba6a-7fc46de216df","resolution":{"observed_at":"2026-08-05T12:46:21.046031Z","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":"1996.0829","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:46:22.187903Z","title":"Parallel shortcutting of rooted trees","venue":null,"work_id":"c56cfc4d-2d50-48b2-a092-7e6e92ff035e","year":1997},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.054111Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:d021b863603034a94218667373295d8fcf5cf4e5c267ca9aec67a560d4d0d137","observation_id":"ba5f2eec-707e-4842-b8c8-83684a3d24e3","resolution":{"observed_at":"2026-08-05T12:46:22.220508Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-05T12:46:21.062391Z","title":"Metric embedding, hyperbolic space, and social networks","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-05T12:46:21.062391Z"},"links":{"citing_paper":"/paper/2509.01443"},"observation_digest":"sha256:98db4ad563df534d9b04da9a40738e77807a1a67b85b8f69f86586395bb427bd","observation_id":"8ec7a586-4b21-4ee6-8d05-04297d0b1132","resolution":{"observed_at":"2026-08-05T12:46:21.062391Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.01443","last_updated":"2025-09-01T12:58:16Z","latest_version":1,"primary_category":"cs.CG","snapshot_observed_at":"2026-08-14T01:11:33.866350Z","submitted_at":"2025-09-01T12:58:16Z","title":"Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces"},"reference_resolution":{"displayed":61,"state_counts":{"malformed_identifier":0,"metadata_mismatch":8,"parse_uncertain":0,"unresolved":27,"verified_exact":23,"verified_fuzzy":3},"total_outbound_references":61},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 0 inbound Pith citation observations for arXiv:2509.01443."}