{"as_of":"2026-08-08T03:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:929a7ee61513cb4da8b326a61da0ff64fdd8aed3fac54e65c75f1da1b4ea28b5","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":"2026-08-07T04:56:29.603325Z","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":"2026-08-07T06:34:17.273281+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/2506.09529/citation-record","integrity":"/paper/2506.09529/integrity","json":"/paper/2506.09529/citation-record.json","paper":"/paper/2506.09529"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:56:30.159228Z","title":"Stable border bases for ideals of points","venue":null,"work_id":"3b8b47f3-b70e-48c6-879a-8282d39878d7","year":2008},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.441323Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:a80c1be4c8faf7c9afe8a9be500ec945d89eebb0e7a67e1e926486404c204f48","observation_id":"7bb64087-781a-471b-b9fc-09fcf6d81538","resolution":{"observed_at":"2026-08-07T04:56:30.164241Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.08718","last_updated":"2020-10-06T19:43:50Z","snapshot_observed_at":"2026-08-06T16:02:58.877029Z","submitted_at":"2020-06-15T19:33:47Z","title":"Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.08718","snapshot_observed_at":"2026-08-07T04:56:29.447038Z","title":"Analytic 32 Table 1: Summary of the Scaling Consistency Test of 20 independent runs with 1 % noise","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.447038Z"},"links":{"cited_paper":"/paper/2006.08718","citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:9b6e999c1a4f54d0b5036412b5ffbdf8d96aa454d931bd8d53554ea4009bc6ec","observation_id":"ce47f3fb-9001-4d36-8cf6-8eb848d6b65e","resolution":{"observed_at":"2026-08-07T04:56:29.447038Z","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":"2026-08-07T04:56:30.142969Z","title":"Ideals, varieties, and algorithms , volume 3","venue":null,"work_id":"d558ccfb-32b0-4725-9f49-a2794636f1fa","year":1992},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.452751Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:49a2f2fdb29a79d64f0ceacfdc941ede7c434225f70ae57b269c4622dff9b259","observation_id":"4dd761a9-d662-47b3-a4a0-18b93b63abe7","resolution":{"observed_at":"2026-08-07T04:56:30.147915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.128137Z","title":"Emiris, editors","venue":null,"work_id":"8198c401-0846-427f-979a-e4eeecd82d0f","year":2005},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.457814Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:ee29d976b1e05ec62e23614014252ff8768a065351608f0da1422d5291d0ac2b","observation_id":"99c7cff8-8735-4738-804b-7564999a7403","resolution":{"observed_at":"2026-08-07T04:56:30.132713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.113292Z","title":"Symboli-numeric methods for solving polynomial equa- tions","venue":null,"work_id":"199cca88-500e-44f8-9322-78cf266778ab","year":2005},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.463020Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:510d0a51310a10433b85e08c9a993e8f30bf7706f0be8fbc5152e90eb6411f51","observation_id":"2469eae2-4195-440f-a4bc-1ccb1f998f75","resolution":{"observed_at":"2026-08-07T04:56:30.118102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.098482Z","title":"Almost vanishing polynomials for sets of limited precision points","venue":null,"work_id":"3d8c9283-20e1-4572-baaa-b5c4b0e784db","year":2010},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.468020Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:daf47c673eea4cd2ff81698b02e456d3424428ba01997127bb0430c0de94e95d","observation_id":"cb9033d2-98e3-420b-8115-d2c81a835848","resolution":{"observed_at":"2026-08-07T04:56:30.103541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.082692Z","title":"Simple varieties for limited precision points","venue":null,"work_id":"d6282f05-a74e-47e9-b1ee-2014e475198f","year":2013},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.473502Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:335a040430bedf3b5a04ccdcbcec74ee66c75857b030eae137de8475fd41f995","observation_id":"d1a07dbf-df36-47b1-a47b-b628d7679dba","resolution":{"observed_at":"2026-08-07T04:56:30.088088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.066532Z","title":"Approximate computation of zero-dimensional polynomial ideals","venue":null,"work_id":"ccebdaad-6136-446f-8c14-cf89cde7c976","year":2009},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.478438Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:b3a299b919987522d9df93ed75aa709c2883cbc8706b2c058d076ec9f74cfb42","observation_id":"f37690ff-b30a-45b4-a02c-e389f7913142","resolution":{"observed_at":"2026-08-07T04:56:30.071646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.050436Z","title":"Discriminative vanishing component analysis","venue":null,"work_id":"5dcc6d2d-559d-48ae-a05f-fdd70a7624e4","year":2016},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.483631Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:045c5ecfd648a187b50f94492eaeee00e9f8f970ff486b528f6057545ace434b","observation_id":"5ba7ee56-ac00-4c0b-9913-a059733bf99f","resolution":{"observed_at":"2026-08-07T04:56:30.055638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.034905Z","title":"Principal variety analysis","venue":null,"work_id":"e1cc29f7-3d0b-4b1a-a905-cf42ec1075ab","year":2017},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.488554Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:247c5e9c24a7bbfa8d042ccaf316060b896d564e4c92b92a4a3982cea9e96bcf","observation_id":"5ed38f1b-52e6-4c01-b0f3-d9a06a8193fe","resolution":{"observed_at":"2026-08-07T04:56:30.039764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.017866Z","title":"Nepomuceno, Aleksandra Tutueva, and Denis Butusov","venue":null,"work_id":"c90ec140-202c-4c47-9af1-30ba468f3889","year":2020},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.493287Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:f96ff3cd8c0bc72119b909ab4547165fb30131c5c3faf3622f32aa971730a5e9","observation_id":"0788de50-8360-4869-b2a6-061138826367","resolution":{"observed_at":"2026-08-07T04:56:30.023759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:30.001611Z","title":"Identifying empirical equations of chaotic circuit from data","venue":null,"work_id":"951a15ba-81bb-496d-a728-a6c3c40f9b70","year":2023},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.498000Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:75f008d330ee27866b74aa2f734f7af5283eac32c7e69f572ef1a3db047629e3","observation_id":"2d076560-750d-4c66-a9cd-002410dd0170","resolution":{"observed_at":"2026-08-07T04:56:30.007381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.986608Z","title":"Characterizations of border bases","venue":null,"work_id":"0c9241bc-abed-458e-b3fc-7bcce501e2a4","year":2005},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.502827Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:9ca79c93465a1b02fac9e8f5cf72e4b7d216d9c0165db78aaba1eec7e1a817ac","observation_id":"36a42283-7542-4daa-9352-21863d32d604","resolution":{"observed_at":"2026-08-07T04:56:29.991653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.971546Z","title":"An algebraist’s view on border bases","venue":null,"work_id":"6c2d79b4-558f-4e58-a842-9249731e5f6d","year":2005},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.507604Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:6c3220b517eeea3fe67853dec998390cf7e1dcff1bfeca874ea2257e46ad1e13","observation_id":"daffff7c-a768-4069-b8a1-caa35d6ddbe5","resolution":{"observed_at":"2026-08-07T04:56:29.976395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.956089Z","title":"Border basis computation with gradient-weighted normalization","venue":null,"work_id":"88862901-205d-47f7-9671-36d89ad86324","year":2022},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.512259Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:6301fba5f327a967408aca977a1020c929cba93520f6c3c3e0267ce4e8c2a5c1","observation_id":"3f5d30e5-8bf3-4861-8896-345014eba4e7","resolution":{"observed_at":"2026-08-07T04:56:29.961105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.941361Z","title":"Noise-tolerant algebraic method for reconstruction of non- linear dynamical systems","venue":null,"work_id":"7b45d168-ec60-4fd7-9b98-c38ca9bdf53d","year":2016},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.516681Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:7d25c254eadbd10ea2c8f6cad39b818b53ce1fc9b6f3c442302bddf6d95b32f6","observation_id":"5e97c507-22cb-4c30-9485-cddc6ebc48f6","resolution":{"observed_at":"2026-08-07T04:56:29.945933Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.927184Z","title":"Approximate vanishing ideal via data knotting","venue":null,"work_id":"4a65defd-053b-4d48-93a5-0d1918ebc936","year":2018},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.521197Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:8adbf241e44dbb73e0726ee175681d85ae5cf6c7ad37dca629adf52f915f7275","observation_id":"8089ef00-732c-41f1-bc2d-baa7da7fd5fe","resolution":{"observed_at":"2026-08-07T04:56:29.931820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.912922Z","title":"Spurious vanishing problem in approximate vanishing ideal","venue":null,"work_id":"7e6e1b40-358f-415e-9d3f-97ffcecb30ce","year":2019},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.525565Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:99318094efc7340407ab5f6e38dcdf358b65819c28d324a6bd28675333ca4818","observation_id":"02431a28-c876-42b5-967e-97c3e109a7c3","resolution":{"observed_at":"2026-08-07T04:56:29.917581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.898741Z","title":"Gradient boosts the approximate vanishing ideal","venue":null,"work_id":"732077b8-7e16-45db-b50a-96a0ba14f229","year":2020},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.530166Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:ba5529f7fd2426f731aea888355129912f286731f7048d74c505ba8e0e50b4ef","observation_id":"ab02879a-5e9e-4c00-8a9d-6c6267e5938c","resolution":{"observed_at":"2026-08-07T04:56:29.903205Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.884074Z","title":"Monomial-agnostic computation of vanishing ideals","venue":null,"work_id":"2dcd9354-6ba2-478d-a687-a9dffdde04e6","year":2024},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.534866Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:e6fc46c10138cfdacd89089bb0b5384331c8c358736fa3fd711b1de9d17804ea","observation_id":"8000933c-f358-4b09-8c7a-72ca94ad565e","resolution":{"observed_at":"2026-08-07T04:56:29.888785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.868955Z","title":"Vanishing ideal genetic programming","venue":null,"work_id":"0eb35736-e68e-440b-9128-f08b4747d2fd","year":2016},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.539554Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:60f71a6a11ffe31f108b9af89f0863f4900d1f6f3650b051cb211204f21d11ef","observation_id":"8250002b-a82e-4923-9c1f-a1a6449b9ce3","resolution":{"observed_at":"2026-08-07T04:56:29.874138Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.853972Z","title":"Dual-to-kernel learning with ideals","venue":null,"work_id":"45779cf1-40ae-4b62-be9d-e128f6ae6c81","year":2014},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.544217Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:367c25deb04b2f4151b2ee120bdcb86099e47093d4e4c1e151e947a2c577b924","observation_id":"e051240f-b97f-4003-806e-b1fa26532db8","resolution":{"observed_at":"2026-08-07T04:56:29.858847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.839786Z","title":"Computational commutative algebra 2 , volume 2","venue":null,"work_id":"4b932b2c-ebef-4af2-a24c-f715cb5980d2","year":2005},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.548817Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:bd2aef6578281525266d524b9cf0a813b54fdf1471ee1b22d463b517234ccf53","observation_id":"4d55f81a-aa3f-4dfe-a604-7d216f31744f","resolution":{"observed_at":"2026-08-07T04:56:29.844535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.824868Z","title":"Computation of approximate border bases and applications","venue":null,"work_id":"e841c344-c194-44e4-acbf-c0492897faf7","year":2013},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.553673Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:4b7343ef6248c8161964608c23303403e7fb47f58092865faabd5d012060b648","observation_id":"151612a3-5cda-4971-8b12-2609be74b488","resolution":{"observed_at":"2026-08-07T04:56:29.829809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.809990Z","title":"Vanishing component analysis","venue":null,"work_id":"a9a762f1-f8d6-4e8f-a22e-d717733a0e21","year":2013},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.558429Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:45d228ec6197d40b0716c26bb9e92373ffc6c44c01ce2819e4eacb4bd7a24d87","observation_id":"cfe6542c-5520-4adf-a5b1-36ff7428daf4","resolution":{"observed_at":"2026-08-07T04:56:29.814918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.795286Z","title":"Approximating latent manifolds in neural networks via vanishing ideals, 2025","venue":null,"work_id":"63bdbd64-ab17-405c-8404-ed712ad187f6","year":2025},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.563039Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:7d6d03411483b994764a72974e3f3df296f0f79ea1b0e09c23e5b33ca10969db","observation_id":"cbf16748-fd00-47d0-8c81-2f25f1eb42ed","resolution":{"observed_at":"2026-08-07T04:56:29.800108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.780381Z","title":"Approximate Commutative Algebra","venue":null,"work_id":"39d86312-46e6-4b6d-965b-5cf37081d8bd","year":2010},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.567948Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:389f113e0f1fb0f2379cc927878f4ab8d1baab8e250e982685f1952fd484efe5","observation_id":"25986325-cbce-46fb-9e7d-fae017442c3d","resolution":{"observed_at":"2026-08-07T04:56:29.784952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.765786Z","title":null,"venue":null,"work_id":"ce53eb46-bd43-4ed1-a241-190ea0e3ea8a","year":2004},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.572720Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:a75f202c7994b408922bb62be6ee17763f76dae0458561002fbb082e7137fc92","observation_id":"88b48ee5-4e23-4835-bf56-16d1dae35bd0","resolution":{"observed_at":"2026-08-07T04:56:29.770328Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.750749Z","title":"Application of algebra in the oil industry","venue":null,"work_id":"1990e93d-f01d-4fc0-bf87-f392884ea483","year":2008},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.577422Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:c196597d31a2e6f123936ae24e6b5369ff97fae12518fd821daa4d655dfe4683","observation_id":"2fb81fd8-f010-43dd-aa08-0c2b901d64cd","resolution":{"observed_at":"2026-08-07T04:56:29.755510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.734247Z","title":"Wang and T","venue":null,"work_id":"fe1021ca-1f93-4b59-ab0d-32739c507e84","year":2018},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.581853Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:e522b46ac866facaf049dffc59427256414961ba19e64bd1e83e1a0e32838041","observation_id":"1c1766da-9d14-446d-a96c-35404fa492a4","resolution":{"observed_at":"2026-08-07T04:56:29.739362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.717950Z","title":"Polynomial representation for persistence diagram","venue":null,"work_id":"91ae02bb-23ce-4cb1-886b-a093e94481d6","year":2019},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.586306Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:724354fe06787cb99601ec6035c71c3900420966218cc8c48edd118c5c978cdb","observation_id":"93857726-5d48-43a9-a6fb-4aa339552d0c","resolution":{"observed_at":"2026-08-07T04:56:29.722904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.702291Z","title":"Conditional gradients for the approximately vanishing ideal","venue":null,"work_id":"cf176571-0e77-41fb-8030-56a6bd40c826","year":2022},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.590964Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:b9e2f45c45b73bd4d18c73e35125ca0af3f32dda4bdf79794266f284f0f56f9f","observation_id":"9da2a9ae-cb24-4eac-ae7a-d23fc7158a52","resolution":{"observed_at":"2026-08-07T04:56:29.707232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.686589Z","title":"Approximate vanishing ideal computa- tions at scale","venue":null,"work_id":"e3cfdb3e-540c-4bcb-8ee1-dbc89db9a095","year":2023},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.595042Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:c37068ae55d2ebaf7daed829687f86c9c63d8414f0422170821753d0eb156fbb","observation_id":"4a841db9-4543-4a92-824f-f660a1a44385","resolution":{"observed_at":"2026-08-07T04:56:29.691952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.670777Z","title":"Deep vanishing component analysis network for pattern classification","venue":null,"work_id":"453c0a73-1646-4f36-81d4-e58bd3937756","year":2018},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.599105Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:7a6db2612f4c676900f1eb55e9b43b3a618430ba96cbbca6d2b52250de100fad","observation_id":"3c5716e5-548b-42d3-8a46-5c5fa64e950c","resolution":{"observed_at":"2026-08-07T04:56:29.675848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T04:56:29.652844Z","title":"Hand posture recognition using approximate vanishing ideal genera- tors","venue":null,"work_id":"99cae46a-eaf9-4dd8-aa09-9bda0814a932","year":2014},"citing_paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T04:56:29.603325Z"},"links":{"citing_paper":"/paper/2506.09529"},"observation_digest":"sha256:36b129b91276a22307dcd1ae52f630e8664cc113fa9f60ca9b9a05d336cb4d15","observation_id":"6f0713ff-3be1-4dde-9210-367810b163f3","resolution":{"observed_at":"2026-08-07T04:56:29.659595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.09529","last_updated":"2025-06-11T08:57:45Z","latest_version":1,"primary_category":"cs.SC","snapshot_observed_at":"2026-08-07T04:44:03.444519Z","submitted_at":"2025-06-11T08:57:45Z","title":"Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":33},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.09529."}