{"as_of":"2026-08-09T23:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6a687c5cf4ce686fd48043fa331f72de84731d7612e195cdca68f5be221ef238","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:02:19.438055Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.01873/citation-record","integrity":"/paper/2507.01873/integrity","json":"/paper/2507.01873/citation-record.json","paper":"/paper/2507.01873"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.318049Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.318049Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:c6a7a9f33d5f35a17394ea4b3de3b3c5d68ee097018aa9e57845fb9e0735fb7d","observation_id":"293d446c-ed4b-49c3-b6c9-c12723541970","resolution":{"observed_at":"2026-08-06T21:02:19.318049Z","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":"2026-08-06T21:02:19.323508Z","title":"Better balance by being biased: A 0.8776-approximation for max bisection","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.323508Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:7610919eb4a212c2fe128faa4ee81cfbfb98e11039f74eeeb2029e8c8b62d212","observation_id":"bfa9b34a-c163-4aef-8b7b-235c5e5f285b","resolution":{"observed_at":"2026-08-06T21:02:19.323508Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.01798","last_updated":"2024-08-03T14:50:03Z","snapshot_observed_at":"2026-07-06T18:56:27.389917Z","submitted_at":"2024-08-03T14:50:03Z","title":"Differentially Private Gomory-Hu Trees","version":1},"cited_work":{"arxiv_id":"2408.01798","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.01798","snapshot_observed_at":"2026-08-06T21:02:19.526265Z","title":"Differentially Private Gomory-Hu Trees","venue":"cs.DS","work_id":"fb167d97-eb74-450b-aeb6-4432321a503e","year":2024},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.327178Z"},"links":{"cited_paper":"/paper/2408.01798","citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:370995563bc911ce4fae8d71fd6edf44c5c2a5bc13a9075153d70a77b0bdfaf5","observation_id":"bf4a0e40-4aac-4282-b573-a156fd635a48","resolution":{"observed_at":"2026-08-06T21:02:19.530289Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.883576Z","title":"Approximating the cut-norm via grothendieck's inequality","venue":null,"work_id":"c34fb192-97ec-4aab-be02-c5aacbd48483","year":2006},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.330820Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:7d85bba1e28916071e7fb25699800bb1d0e4202dd60578651a2f0c9b26b54135","observation_id":"6941a2a5-d995-4cad-9f7d-25305de7e123","resolution":{"observed_at":"2026-08-06T21:02:19.887238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.870683Z","title":"On differentially private graph sparsification and applications","venue":null,"work_id":"8ffc3c55-2834-4652-83a5-84df61b89d98","year":2019},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.334022Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:19c7daa922e3aad2f2871184c20892a13bdf94c33e36143f320cb787bff383af","observation_id":"cb5551a4-53d2-4c77-9b62-527c17158739","resolution":{"observed_at":"2026-08-06T21:02:19.875474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.857475Z","title":"Wherefore art thou R3579X? anonymized social networks, hidden patterns, and structural steganography","venue":null,"work_id":"7c5d638f-95d7-4289-934d-61eeecd018cc","year":2007},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.337650Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:0be90a95218fa9c6888a496589cb92354ab6d3309366e2ac4df7cd0e444f1cb7","observation_id":"deaedd8e-e78d-407e-a343-bcb9962f55cf","resolution":{"observed_at":"2026-08-06T21:02:19.861718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.844681Z","title":"Bencz\\' u r and David R","venue":null,"work_id":"39bec7e8-a1c4-4e4b-838f-6da38342ee44","year":1996},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.340980Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:f0a827e30c4feeb0e7003f40aa4ea35a50d66d61f492b22ccaf44c08905f8d7e","observation_id":"e9de831d-b789-4d36-8b2e-55d57bd20792","resolution":{"observed_at":"2026-08-06T21:02:19.848561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.06911","last_updated":"2024-12-03T17:25:05Z","snapshot_observed_at":"2026-08-09T19:32:53.939892Z","submitted_at":"2024-07-09T14:46:33Z","title":"Differentially Private Algorithms for Graph Cuts: A Shifting Mechanism Approach and More","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.06911","snapshot_observed_at":"2026-08-06T21:02:19.344955Z","title":"Differentially private multiway and k -cut","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.344955Z"},"links":{"cited_paper":"/paper/2407.06911","citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:e6a30b6ee0f9f7714299089966ea0237aef9f4e8231b8b94bf7d3d5fd6fb9ec1","observation_id":"99016054-cfa5-475d-a30d-fab0a926297f","resolution":{"observed_at":"2026-08-06T21:02:19.344955Z","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":"2026-08-06T21:02:19.831449Z","title":"A deterministic algorithm for balanced cut with applications to dynamic connectivity, flows, and beyond","venue":null,"work_id":"fe370400-50ea-4418-bbdf-be6841430694","year":2020},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.348437Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:566b266c5803bc70ccb3f6266ccecf34878666903fbedbf48a5bfa0ed1091d8c","observation_id":"bff4a0e2-3114-484e-83a4-e0fe5b504cef","resolution":{"observed_at":"2026-08-06T21:02:19.835276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.05004","last_updated":"2019-08-14T07:49:24Z","snapshot_observed_at":"2026-08-08T22:24:13.444591Z","submitted_at":"2019-08-14T07:49:24Z","title":"Stop the Open Data Bus, We Want to Get Off","version":1},"cited_work":{"arxiv_id":"1908.05004","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.05004","snapshot_observed_at":"2026-08-06T21:02:19.491434Z","title":"Stop the Open Data Bus, We Want to Get Off","venue":"cs.CR","work_id":"1018e41a-5f4b-4285-8afa-3281e86fb951","year":2019},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.351511Z"},"links":{"cited_paper":"/paper/1908.05004","citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:36a36f42451909e3bc85e1cb53165388ff923ac1680bb582705544dd1f580430","observation_id":"0ba2a0dc-37c8-48b0-b357-0952cc8dd158","resolution":{"observed_at":"2026-08-06T21:02:19.495560Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.818300Z","title":"On approximate graph colouring and max-k-cut algorithms based on the -function","venue":null,"work_id":"2e93fb66-f627-42e7-9f65-81b0e8e59c46","year":2004},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.355832Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:2a62b1a9122578ca7f6e808619b96ec2d09ebda33e12eba3ec5a0cff5b20fed9","observation_id":"c027b86a-c3c8-4ea5-bf81-4ac1b0993819","resolution":{"observed_at":"2026-08-06T21:02:19.822731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.805491Z","title":"Differential privacy and robust statistics","venue":null,"work_id":"529f8e53-822e-41b8-8e0e-715c514795be","year":2009},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.359177Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:d1857486ee2432a14e45f339a24c9f9920ff02a6da76958636b28e7ac6e4e0b8","observation_id":"ff0f9f69-e0f3-41d6-8868-e16bafbf4dbc","resolution":{"observed_at":"2026-08-06T21:02:19.809563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.793010Z","title":"Nearly tight bounds for differentially private multiway cut","venue":null,"work_id":"288f1a8b-b672-494a-8e46-583c4f113509","year":2023},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.362607Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:71bef389f8292ae1581493eb832e354bd769b60efd2deb1df51f77860b9c9065","observation_id":"c0db5ce0-4675-4e30-ad44-d9db86c812a0","resolution":{"observed_at":"2026-08-06T21:02:19.796807Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.781147Z","title":null,"venue":null,"work_id":"ff8fba68-f4b8-4afc-afd8-92339bcc413b","year":2006},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.365835Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:bb436d597a704051d6947cd1e1806ca5bf653e81c09ea9fc09089039cc57ac34","observation_id":"cb1a6d01-c285-4b2d-ad1f-027e3cef6c58","resolution":{"observed_at":"2026-08-06T21:02:19.784961Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.769494Z","title":"Differential privacy","venue":null,"work_id":"7736165b-d06e-4ee9-81c6-c5dfd0d44459","year":2006},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.368794Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:d156bd6173a375da882c6c22c69251fa8cde0d65dfc2bc993680d118c9c47cd9","observation_id":"2348fecb-45c1-45ed-bbac-84b2c78af77a","resolution":{"observed_at":"2026-08-06T21:02:19.773258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.757477Z","title":"Differentially private release of synthetic graphs","venue":null,"work_id":"f6903233-a320-4633-b948-02b7572abccb","year":2020},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.371768Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:5fb8b26cc8872d3938ca5c3723c537db9893295187eae6788b2f5ec485c84fc4","observation_id":"1350a6ee-db51-42dd-8109-c71e4301acdb","resolution":{"observed_at":"2026-08-06T21:02:19.761228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.374786Z","title":"Improved approximation algorithms for MAX k -CUT and MAX BISECTION","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.374786Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:c79781d5191d9c4ea1963f5eb67fca2c36cf10c4d56904b06a9ed3ac2469caf8","observation_id":"a6711943-6748-4baf-87ff-131898854f5f","resolution":{"observed_at":"2026-08-06T21:02:19.374786Z","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":"2026-08-06T21:02:19.735588Z","title":"On graph problems in a semi-streaming model","venue":null,"work_id":"3068deb3-f707-4b7c-ae80-b1c93a4c8d21","year":2005},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.377785Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:700072643ea52a151c4d8be29b5fee1afab0bdaabd4e47800a33a6f291b1d755","observation_id":"6d15bc03-3097-45d6-a6ae-dd530295f7fc","resolution":{"observed_at":"2026-08-06T21:02:19.739586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.380852Z","title":"Garey, David S","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.380852Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:1ed4ce64adbc54a97e6e38efa718d6d094b32ed65bab698a516b19900578c8d8","observation_id":"a36865e6-2e45-4e19-bc7b-ec287f0e136a","resolution":{"observed_at":"2026-08-06T21:02:19.380852Z","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":"2026-08-06T21:02:19.714374Z","title":"Differentially private combinatorial optimization","venue":null,"work_id":"8338b1cb-654c-4339-a52a-6e057c332e4a","year":2010},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.384718Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:48254bb6b486349a5563fcbba81cbb8dd5bed8983cdc1a6f9beca9bf2a7e36f6","observation_id":"c354f324-9936-45f1-be46-f4465df4040e","resolution":{"observed_at":"2026-08-06T21:02:19.718090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.701521Z","title":null,"venue":null,"work_id":"dba6da8b-4fc5-4a17-9dab-8da5a85a3971","year":2012},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.387799Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:8f1c67dd0f98f96e0913a2b78d930634eca5f0f812cbe8e4edab3956d8a9885f","observation_id":"d4123b6e-cb59-42ee-b222-63bdf2197014","resolution":{"observed_at":"2026-08-06T21:02:19.705363Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.688925Z","title":"Goemans and David P","venue":null,"work_id":"903f09a6-6c8f-4246-9dce-1ea3a14c6a8a","year":1995},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.391230Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:cbbdbe3c8114454c453142c46258fd9aa97bc82dd2151185de4769eda061a666","observation_id":"a649115e-8b32-4171-a3bd-f90af228715b","resolution":{"observed_at":"2026-08-06T21:02:19.692547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.676716Z","title":"Accurate estimation of the degree distribution of private networks","venue":null,"work_id":"4301a989-c6e3-46ee-ab85-7993daf92e4f","year":2009},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.394777Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:bd16f8fa43cbe70698df95b312ca1d9b343374997302b9e8b27fc5842d94b73f","observation_id":"b57cb1e2-76d6-403d-a57b-1a4933898e6d","resolution":{"observed_at":"2026-08-06T21:02:19.680769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.663687Z","title":"Random sampling in cut, flow, and network design problems","venue":null,"work_id":"8d6ca1d8-3270-4f9d-aafc-6fa6a2ae7e99","year":1994},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.398233Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:6f340e3e76139bd1adc87782d667d233142d8202bb47b70128eba531d59cee6d","observation_id":"69260466-129d-4743-9620-652403e35391","resolution":{"observed_at":"2026-08-06T21:02:19.667947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.649927Z","title":"Optimal inapproximability results for MAX-CUT and other 2-variable CSP s? SIAM Journal on Computing , 37(1):319--357, 2007","venue":null,"work_id":"78f54212-6372-4853-b7de-6b876344d032","year":2007},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.401479Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:ecba3ba769f7b33775775e5e490f2d1ba868f5b8d0509f039c3ae8bb3d7c684a","observation_id":"75f04974-6801-4ff6-adbf-0be4cc8efb1e","resolution":{"observed_at":"2026-08-06T21:02:19.653681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.637088Z","title":"Private graph data release: A survey","venue":null,"work_id":"21fc78ae-4bae-497a-8bc0-c1827c1ee086","year":2023},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.405068Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:2b8c95d2d9bf38cb8530e023d1d084109c3290f2c2fb0a718e77300dbf8537a7","observation_id":"f59c88c2-1f3a-4e16-87d7-59c9cfc17501","resolution":{"observed_at":"2026-08-06T21:02:19.641029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.01567","last_updated":"2021-06-03T03:24:36Z","snapshot_observed_at":"2026-07-06T11:15:26.915483Z","submitted_at":"2021-06-03T03:24:36Z","title":"Deterministic Weighted Expander Decomposition in Almost-linear Time","version":1},"cited_work":{"arxiv_id":"2106.01567","doi":null,"metadata_source":"pith","pith_arxiv_id":"2106.01567","snapshot_observed_at":"2026-08-06T21:02:19.471851Z","title":"Deterministic Weighted Expander Decomposition in Almost-linear Time","venue":"cs.DS","work_id":"89abfa39-7c06-40db-9370-d208316293d8","year":2021},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.409148Z"},"links":{"cited_paper":"/paper/2106.01567","citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:d38ff88d5e5cd77b8e43f9426c50bea0dc1a60807332427b8b47afeaa5d8137c","observation_id":"799f7b8f-7968-4927-829d-fd9012675fe5","resolution":{"observed_at":"2026-08-06T21:02:19.478057Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.624637Z","title":"Optimal bounds on private graph approximation","venue":null,"work_id":"67328017-c26a-4f17-b06b-e136fccf420b","year":2024},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.413361Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:0976e0b232da12963e8daf13918b1085f8f62e9d60da4796d149adca30331971","observation_id":"c05affc6-3385-46b5-a3b3-d365f23f7002","resolution":{"observed_at":"2026-08-06T21:02:19.628359Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.611843Z","title":"Robust de-anonymization of large sparse datasets","venue":null,"work_id":"d81bd98e-3eab-4ca2-9b95-15019eae1570","year":2008},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.417010Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:f479bc23e34e750a4914b62a99e84929f52ab5818fb5bfbbc47e2a25caa5c07f","observation_id":"212dd172-9530-4ba1-8bcc-2eb4525f8ba6","resolution":{"observed_at":"2026-08-06T21:02:19.615723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.598917Z","title":"Dynamic spanning forest with worst-case update time: adaptive, Las Vegas , and O(n\\( ^ 1/2 - \\( \\) \\)) -time","venue":null,"work_id":"4161f1bc-de85-4799-afb5-260091b43d37","year":2017},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.420515Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:daf962e5e2d926be60a30a15511afc5f0b6a0eefd692ab78296491ca87b45733","observation_id":"d9981575-4fa4-4154-ba59-17f630df5bcd","resolution":{"observed_at":"2026-08-06T21:02:19.602969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.424194Z","title":"Optimal hierarchical decompositions for congestion minimization in networks","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.424194Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:de58bfde6644a01a20ecdb37fc9460303d93ff6bf31f68d3510d25798d56769b","observation_id":"349a92a7-3b87-43f6-b1bb-13fabf7dcb50","resolution":{"observed_at":"2026-08-06T21:02:19.424194Z","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":"2026-08-06T21:02:19.576206Z","title":"Approximating CSP s with global cardinality constraints using SDP hierarchies","venue":null,"work_id":"a9a77410-4f69-4b41-ac64-9b33c7722106","year":2012},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.427925Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:68daa84d2e6421189f07203f24e1985ab389d3a1d90d3c9ce1f98b12089a3a6a","observation_id":"369f7d07-c541-416f-b5d8-0d0c84a7554a","resolution":{"observed_at":"2026-08-06T21:02:19.580208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.564051Z","title":"Expander decomposition and pruning: Faster, stronger, and simpler","venue":null,"work_id":"8effeaee-acb6-4aab-a0f2-e56e06c0c04a","year":2019},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.431381Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:ffc88b06cd18fa4986a98914870bba520dfcf8f3319d82feeabbc32c763e24b0","observation_id":"4899417c-6ea5-4514-ae9b-1922bba790ba","resolution":{"observed_at":"2026-08-06T21:02:19.567716Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.551820Z","title":"Differentially private analysis on graph streams","venue":null,"work_id":"2417e4be-d27f-4c16-becd-b826d933fa2a","year":2021},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.434660Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:5a54182c3b54cb4cd9203577383b8bc9671d56ae7e7d790a5666bb8f5af99518","observation_id":"93fbbd91-4f09-4ed5-a791-f8964d1cd19a","resolution":{"observed_at":"2026-08-06T21:02:19.555401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:02:19.538801Z","title":"Fully-dynamic minimum spanning forest with improved worst-case update time","venue":null,"work_id":"0eb7e4c3-d9d5-4324-b1c1-0f76c960bc9d","year":2017},"citing_paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T21:02:19.438055Z"},"links":{"citing_paper":"/paper/2507.01873"},"observation_digest":"sha256:23ab16e20a3a422e0c6d7fd5f73d3ab6c0f2b46b55fc0a4d3edc8e85aebfa4b9","observation_id":"f60a845a-a12a-444c-a9f3-93384c5db513","resolution":{"observed_at":"2026-08-06T21:02:19.543296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.01873","last_updated":"2025-07-02T16:38:51Z","latest_version":1,"primary_category":"cs.DS","snapshot_observed_at":"2026-08-06T20:38:58.737259Z","submitted_at":"2025-07-02T16:38:51Z","title":"Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":3,"verified_fuzzy":24},"total_outbound_references":35},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2507.01873."}