{"as_of":"2026-08-12T16:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4906d857a7f3046df75e9eab8c7560ac3b197898db2a62fa1efa797eec9853ae","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":8,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T18:18:01.507265Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":2,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-08-09T18:18:01.507265Z","title":"Schaefer, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.00680","last_updated":"2025-02-02T05:54:54Z","snapshot_observed_at":"2026-08-12T09:02:25.234144Z","submitted_at":"2025-02-02T05:54:54Z","title":"Some structural complexity results for $\\exists\\mathbb R$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-09T18:18:01.507265Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2502.00680"},"observation_digest":"sha256:7786ef05d178ef748855ec2d4cbb67cab35ab29303e2896ec825b9bd9974a09e","observation_id":"89317f54-75e2-45f0-83a3-8da9d796f776","resolution":{"observed_at":"2026-08-09T18:18:01.507265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-08-06T15:42:40.233535Z","title":"Schaefer, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15532","last_updated":"2025-08-18T18:41:23Z","snapshot_observed_at":"2026-08-10T21:07:57.755331Z","submitted_at":"2025-07-21T12:00:03Z","title":"Data-Efficient Safe Policy Improvement Using Parametric Structure","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:42:40.233535Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2507.15532"},"observation_digest":"sha256:e113e8ed3b64d4f15f0ae5d11afde7fec229980394a77b3378d51c39dabdf370","observation_id":"91905365-b6ad-4e63-aba1-d08667b2e6ed","resolution":{"observed_at":"2026-08-06T15:42:40.233535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":"2407.18006","doi":"10.48550/arxiv.2407.18006","metadata_source":"arxiv_reference","pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"CoRRabs/2407.18006(2024).https://doi.org/ 10.48550/ARXIV.2407.18006,https://doi.org/10.48550/arXiv.2407.18006","venue":"arXiv (Cornell University)","work_id":"3f782cda-5bf1-421a-b838-a3a1970a18bc","year":2024},"citing_paper":{"arxiv_id":"2603.07094","last_updated":"2026-05-13T15:34:58Z","snapshot_observed_at":"2026-08-12T16:26:29.296745Z","submitted_at":"2026-03-07T08:04:08Z","title":"Randomise Alone, Reach as a Team","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-15T15:50:26.361353Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2603.07094"},"observation_digest":"sha256:e7db03289ad2732a36604b7c2d3963e78629b4cd6785d56afc7014fae52819ab","observation_id":"c3307a4e-3907-47d3-9f77-39b7e92c4917","resolution":{"observed_at":"2026-05-15T15:51:12.505641Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":"2407.18006","doi":"10.48550/arxiv.2407.18006","metadata_source":"arxiv_reference","pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"CoRRabs/2407.18006(2024).https://doi.org/ 10.48550/ARXIV.2407.18006,https://doi.org/10.48550/arXiv.2407.18006","venue":"arXiv (Cornell University)","work_id":"3f782cda-5bf1-421a-b838-a3a1970a18bc","year":2024},"citing_paper":{"arxiv_id":"2604.17061","last_updated":"2026-04-18T16:29:32Z","snapshot_observed_at":"2026-07-06T23:04:14.688737Z","submitted_at":"2026-04-18T16:29:32Z","title":"$\\exists\\mathbb{R}$-Completeness of Tensor Degeneracy and a Derandomization Barrier for Hyperdeterminants","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T06:23:50.427348Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2604.17061"},"observation_digest":"sha256:4758c5e63bfe74b779cfddb9cdde7eec2ea81d5c8724225e3de21495f559b393","observation_id":"e9618248-c156-4f78-b8a4-a16ed2b30f7e","resolution":{"observed_at":"2026-05-10T06:26:27.441131Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":"2407.18006","doi":"10.48550/arxiv.2407.18006","metadata_source":"arxiv_reference","pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"CoRRabs/2407.18006(2024).https://doi.org/ 10.48550/ARXIV.2407.18006,https://doi.org/10.48550/arXiv.2407.18006","venue":"arXiv (Cornell University)","work_id":"3f782cda-5bf1-421a-b838-a3a1970a18bc","year":2024},"citing_paper":{"arxiv_id":"2605.00917","last_updated":"2026-04-30T03:12:40Z","snapshot_observed_at":"2026-07-06T23:14:15.780028Z","submitted_at":"2026-04-30T03:12:40Z","title":"Tensor Spectral Threshold is $\\exists\\mathbb{R}$-Hard","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-09T20:40:34.507088Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2605.00917"},"observation_digest":"sha256:a09a984462de978461ef7d96043c5f5b5239bad581a75a031cedf239b349b3c1","observation_id":"2d37c204-f505-4b1b-b24f-50d341935e25","resolution":{"observed_at":"2026-05-11T15:01:09.386835Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-07-12T05:50:11.701730Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.02958","last_updated":"2026-07-03T05:05:02Z","snapshot_observed_at":"2026-08-06T23:13:48.764748Z","submitted_at":"2026-07-03T05:05:02Z","title":"Toward Satisfiability Modulo Realizability","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-12T05:50:11.701730Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2607.02958"},"observation_digest":"sha256:3eb5c8730f5a4976b07e1cd05b20c8bf006012a8fad7a37ddcb54173658cdb62","observation_id":"97af865c-2eb0-4c02-9421-bafd6dfc2868","resolution":{"observed_at":"2026-07-12T05:50:11.701730Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-07-31T21:54:09.802975Z","title":"2024 , copyright =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.24182","last_updated":"2026-07-27T09:04:34Z","snapshot_observed_at":"2026-08-07T17:26:34.898948Z","submitted_at":"2026-07-27T09:04:34Z","title":"Point Set Embeddability with List Constraints","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-31T21:54:09.802975Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2607.24182"},"observation_digest":"sha256:d8d943857a1b950a7dc1081004a1c5965051fe50df0fe8b75277f9402eb13d7a","observation_id":"e7e3799b-6101-4c68-b5bd-88d8a569656d","resolution":{"observed_at":"2026-07-31T21:54:09.802975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18006","snapshot_observed_at":"2026-07-31T20:47:12.366520Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.24219","last_updated":"2026-07-27T09:50:25Z","snapshot_observed_at":"2026-08-07T22:41:20.132377Z","submitted_at":"2026-07-27T09:50:25Z","title":"Algorithms for Equilibria in Concurrent Stopping Games","version":1},"reference_index":273,"source":"arxiv_source","source_observed_at":"2026-07-31T20:47:12.366520Z"},"links":{"cited_paper":"/paper/2407.18006","citing_paper":"/paper/2607.24219"},"observation_digest":"sha256:186579a38ab060d6a99cdbb33a17a09c093aceb8776a96559f7b050b15871ee3","observation_id":"9fc9dedf-fdaf-481b-9459-a3825934327c","resolution":{"observed_at":"2026-07-31T20:47:12.366520Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2407.18006/citation-record","integrity":"/paper/2407.18006/integrity","json":"/paper/2407.18006/citation-record.json","paper":"/paper/2407.18006"},"outbound":[],"paper":{"arxiv_id":"2407.18006","last_updated":"2024-07-25T13:02:06Z","latest_version":1,"primary_category":"cs.CC","snapshot_observed_at":"2026-08-12T14:05:17.846023Z","submitted_at":"2024-07-25T13:02:06Z","title":"The Existential Theory of the Reals as a Complexity Class: A Compendium"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:2407.18006."}