{"as_of":"2026-08-08T18:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9751a96b5fbb78c5eb75c93c538d2d791d04e121634de7d4f6287e00270b4ed3","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:02:31.068733Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.09377/citation-record","integrity":"/paper/2507.09377/integrity","json":"/paper/2507.09377/citation-record.json","paper":"/paper/2507.09377"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:02:34.750297Z","title":"An optimization approach for resource allo- cation in surveillance systems,","venue":null,"work_id":"36333ac7-c3a5-4d37-868b-97dae4d826ac","year":2007},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.788622Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:9d4211ea8df0048fc2ea93ca0edb4b838cd4add65ae6b24640e04d63c1aa3248","observation_id":"cc3d9629-6e57-45a8-b05a-ec7f2ac84da8","resolution":{"observed_at":"2026-08-06T18:02:34.839231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:34.615029Z","title":"Scalable attack graph generation using an agent-based model,","venue":null,"work_id":"b0b02428-e2d7-4795-905b-e27c8d660b9e","year":2006},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.796949Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:d4b17c324f39590519d8d51b2f6a02d95aab80684252e5a13c67182cdb14fe0c","observation_id":"b2018d73-6beb-45cc-a5e4-de63f53be483","resolution":{"observed_at":"2026-08-06T18:02:34.684015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:34.483958Z","title":"Approximation algorithms for k-coverage in wireless sen- sor networks,","venue":null,"work_id":"3ad82b22-344b-4082-a04a-8caf457be1cf","year":2009},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.808974Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:338308002d2d89f62b0c0b4b158ecd1ba912cb62e2ef474aa5e078cf23279c47","observation_id":"972ed243-b0e6-4a56-87e3-51ca6bd6407f","resolution":{"observed_at":"2026-08-06T18:02:34.534132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.17395","last_updated":"2025-05-17T13:16:54Z","snapshot_observed_at":"2026-08-07T16:55:23.968596Z","submitted_at":"2025-03-18T10:01:06Z","title":"CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.17395","snapshot_observed_at":"2026-08-06T18:02:30.820193Z","title":"Cp-ncbf: A conformal prediction- based approach to synthesize verified neural control barrier functions,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.820193Z"},"links":{"cited_paper":"/paper/2503.17395","citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:ca1557e8247d524401f5d19d88ddada920873ce228cc3ff57d98e9ce42a01c05","observation_id":"1a915bad-b880-4df3-ab32-9d4fbbfaf13c","resolution":{"observed_at":"2026-08-06T18:02:30.820193Z","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":"2026-08-06T18:02:34.295243Z","title":"A physics-informed machine learning framework for safe and optimal control of autonomous systems,","venue":null,"work_id":"455bfcd5-9099-49d0-baa8-d40ea7aa2e03","year":2025},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.827333Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:dbf3183f7dbe9bef858fbb4c80c9c0287e7f88199b0d43cda00e24df6ca36573","observation_id":"4f329446-2c41-4588-bb3f-d92029d2b3f4","resolution":{"observed_at":"2026-08-06T18:02:34.370002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:30.841273Z","title":"Genosil: Generalized optimal and safe robot control using parameter-conditioned imitation learning,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.841273Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:9761f3bbdbdec29ac7be85b1d1fc138ef3337d6a408cd924423e045085345a28","observation_id":"7bec81ac-ba1a-4530-a98d-2b10acec3d51","resolution":{"observed_at":"2026-08-06T18:02:30.841273Z","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":"2026-08-06T18:02:34.083444Z","title":"Control barrier functions in dy- namic uavs for kinematic obstacle avoidance: A collision cone approach,","venue":null,"work_id":"24790e68-1b76-4e11-9160-44acafba6ec7","year":2024},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.856534Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:46a248d68d4d1a14380096fee40b2ef123b1a93febebb87c3990f1fe82ec2829","observation_id":"3510fbe1-a315-497f-b477-73564d532d76","resolution":{"observed_at":"2026-08-06T18:02:34.196961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:33.853412Z","title":"Learning a formally verified control barrier function in stochastic environment,","venue":null,"work_id":"d91f8c07-0688-46a2-980d-2be8da348caf","year":2024},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.863653Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:b0236a9ce5ed4fc9b516f81f2ceca6fb9ba51ea2d1e32870374cdb94459fcc47","observation_id":"dc909a2b-8062-41de-b9f9-8125e525ecd2","resolution":{"observed_at":"2026-08-06T18:02:33.918372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:33.645314Z","title":"Polygonal cone control barrier functions (polyc2bf) for safe navigation in cluttered environments,","venue":null,"work_id":"2c81e3e8-7069-4f68-a8b2-bbeb5a09e4de","year":2024},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.879267Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:24f3dc8f3e39da79da45a39209df820c459255540d2c046171214c78b146818b","observation_id":"c7e5e960-1e40-483f-a3d0-e7349d7679ba","resolution":{"observed_at":"2026-08-06T18:02:33.714447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:33.437542Z","title":"Semi-supervised safe visuomotor policy synthesis using barrier certificates,","venue":null,"work_id":"d1bd9b03-0372-4469-9822-c8d4d594ce5b","year":2024},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.896083Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:eca5b429b79a7d5999b73e27d6603fc2d255eb66dd33229f93ac0ba198ce31c7","observation_id":"9e44a91a-e914-4498-99ca-49714021cd80","resolution":{"observed_at":"2026-08-06T18:02:33.515602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:33.213550Z","title":"Protein–protein interaction prediction: the contribution of structural biology,","venue":null,"work_id":"ea671ebd-ab09-4e7d-9730-91b69ae1d592","year":2004},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.907026Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:a608ad9fe774d2692b0dbbbea225eacb73a48ff0aba5c3ebd0ccd2ac29b99703","observation_id":"faf1abfd-b526-487b-9842-88d96347229f","resolution":{"observed_at":"2026-08-06T18:02:33.343424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:33.059580Z","title":"Topological network alignment uncovers biological function and phylogeny,","venue":null,"work_id":"64de0d4f-17fd-4aea-8efb-261d182ea6e4","year":2010},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.922638Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:1308d2639c592a827a2098a6c1f0bdc77057b1cbc16cb8359965e524cb1fcb87","observation_id":"fedd6aea-c904-466b-a8fe-12cc466d304b","resolution":{"observed_at":"2026-08-06T18:02:33.122566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.891415Z","title":"Identification of disease genes by integrating gene expression and protein–protein interaction data,","venue":null,"work_id":"33555bc5-4a6e-4a0c-bed5-5332d52aec84","year":2009},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.937902Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:402c0df9fbcfba65f16c7b75a6937b17dcbbb2621e16834ecd36b81577b6f0bf","observation_id":"804b91a3-ae74-4bfa-90fa-75f22a302487","resolution":{"observed_at":"2026-08-06T18:02:32.988977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.704996Z","title":"Vlsi circuit partitioning by cluster-removal using vertex- cover approximation,","venue":null,"work_id":"557548b3-8022-4053-8a42-8d2f861fe7b6","year":1998},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.954741Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:6bac2cab7efc8682c95c26bb3582e8b6cef178bd23267986c07eb788640ff654","observation_id":"20c55627-e3df-4c1e-be85-d70fa972c279","resolution":{"observed_at":"2026-08-06T18:02:32.800573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.550002Z","title":"Efficient floorplanning based on a modified vertex cover algorithm,","venue":null,"work_id":"354456be-7d8c-461a-af0d-4bd3d09cab57","year":1999},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.965402Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:77361aafdbced64174b439afe1965fbbf15e26a4856f0fb510e7bd82a9631e21","observation_id":"c06d3fcc-bf45-4dc5-8522-73ceb6a0958e","resolution":{"observed_at":"2026-08-06T18:02:32.642865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.390472Z","title":"An efficient heuristic procedure for test generation based on computing maximum independent sets,","venue":null,"work_id":"dc11f73a-5a66-4b27-a60f-0b15aecd7c7d","year":1995},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.972839Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:1d502274a30813e66919503f67b5189aa09a9710a0b71d111ed0844c9028b528","observation_id":"8d346426-9f95-44d4-a05e-fd2d58e17400","resolution":{"observed_at":"2026-08-06T18:02:32.475570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.243740Z","title":null,"venue":null,"work_id":"e0a3225c-4f14-4f18-9ac2-6ac6ee5005bc","year":1979},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:30.987765Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:45144b535a156ad62830d4dffefa85b5a94c5f845c0bbe3b1e1415f562ad3995","observation_id":"aa8d0dd8-eaeb-48ec-9dac-0256b526f3b8","resolution":{"observed_at":"2026-08-06T18:02:32.311916Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:32.120044Z","title":"Sagemath, the Sage Mathematics Software System (Version [insert version used]),","venue":null,"work_id":"a43e1c5a-007f-4f03-8859-fed1967571f8","year":null},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.009488Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:232263567d0d5e23524cc0386f90a9209b019f19a3fa5e5d7e1d5116aabbf19c","observation_id":"6d484278-e3e2-42e8-8fe1-f0f4c0360fe1","resolution":{"observed_at":"2026-08-06T18:02:32.171650Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:31.950365Z","title":"Diestel, Graph theory","venue":null,"work_id":"0b290592-4143-4349-a161-8e0e2099c2d9","year":2017},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.022306Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:3363c2556e3cba7a768d31120082eaa6e7397823c29fb844d9a1a6c30dc99163","observation_id":"41ea5249-b497-4115-96fc-9da9ae4f3383","resolution":{"observed_at":"2026-08-06T18:02:32.047712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:31.704165Z","title":"Fixed-parameter tractability and completeness,","venue":null,"work_id":"b84e8279-431c-4fc4-8faf-43ca75edeef0","year":1999},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.039005Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:e4b83c0004a41026c6e495a4bde7494afb5828d4dc56c16a0de2d921870f68f5","observation_id":"fafd6e92-3451-47f1-8d3c-2a2c2a868532","resolution":{"observed_at":"2026-08-06T18:02:31.827304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:31.528763Z","title":"A new branching strategy for vertex cover,","venue":null,"work_id":"b15f8846-db48-47eb-810b-3e234f2c323c","year":2010},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.046875Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:7b9d446715ede7c9e73393f873f42faf931956c5787451da40395257c9272c15","observation_id":"5f354302-50c5-4633-aaad-0d6a081795dd","resolution":{"observed_at":"2026-08-06T18:02:31.572225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:31.475208Z","title":"Cygan, F","venue":null,"work_id":"73d1f6a2-4c7f-4fe9-a651-ffbb567adbd8","year":2015},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.056349Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:2d74241981022e2f032c93ee4852e2649b7d366a3370f8485c7eb6347ef44764","observation_id":"86361376-eb0e-4c12-ae70-ecc971f5d37a","resolution":{"observed_at":"2026-08-06T18:02:31.494540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:02:31.415872Z","title":"Niedermeier, Invitation to Fixed-Parameter Algorithms","venue":null,"work_id":"69a03e98-e1b9-44b9-9375-0c4f774e1c87","year":2006},"citing_paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:02:31.068733Z"},"links":{"citing_paper":"/paper/2507.09377"},"observation_digest":"sha256:d2d0c33b2ee06b026bc8eed89dda69427918ea2f72822d0aff3e5f689a9117b1","observation_id":"65172f44-0b3a-4066-bbca-b0070117d74d","resolution":{"observed_at":"2026-08-06T18:02:31.435996Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.09377","last_updated":"2025-07-12T18:49:32Z","latest_version":1,"primary_category":"cs.DS","snapshot_observed_at":"2026-08-06T17:55:03.127426Z","submitted_at":"2025-07-12T18:49:32Z","title":"A Fixed Parameter Tractable Approach for Solving the Vertex Cover Problem in Polynomial Time Complexity"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":20},"total_outbound_references":23},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2507.09377."}