{"as_of":"2026-08-08T01:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d40e3fc5bcc4f68f4923531f6e188f7e485fb68d86baeff3120dd75fd9dc31e5","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T06:11:28.260490Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T16:48:05.855663Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.06264","snapshot_observed_at":"2026-08-01T16:48:05.855663Z","title":"The Milnor number and deformations of complex curve singularities","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.17966","last_updated":"2026-07-20T14:07:00Z","snapshot_observed_at":"2026-08-05T16:52:32.304772Z","submitted_at":"2026-07-20T14:07:00Z","title":"Degenerating Discriminants","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-01T16:48:05.855663Z"},"links":{"cited_paper":"/paper/2506.06264","citing_paper":"/paper/2607.17966"},"observation_digest":"sha256:952813c151a4136780499b26c93eda7024a59bd8f1a252cf28ccc5e4baa87136","observation_id":"af138f93-a0fb-4a2a-bd29-3ad7e95f586b","resolution":{"observed_at":"2026-08-01T16:48:05.855663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2506.06264/citation-record","integrity":"/paper/2506.06264/integrity","json":"/paper/2506.06264/citation-record.json","paper":"/paper/2506.06264"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T06:11:28.408336Z","title":"Bertini: Software for Numerical Algebraic Geometry","venue":null,"work_id":"e91b04a0-4e10-46c2-b044-7af8e943c833","year":2013},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.219660Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:4eeb33477894a45acc6cfbaa5481cbb2298dc0f2a65947a3c8dc917950189861","observation_id":"bac6cf41-eab9-4406-bfbc-2a082e265db7","resolution":{"observed_at":"2026-08-07T06:11:28.411794Z","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":"2026-08-07T06:11:28.366263Z","title":"Polyèdres de Newton et nombres de Milnor","venue":null,"work_id":"72f0a493-3e9a-4370-962f-360acef8fda6","year":1976},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.248411Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:0a510aa9a6525df875f62f44ead5abcca91a53c6ed9093688191723d5f2292da","observation_id":"b632bbe7-fd2b-48b1-ae94-b4865b62369f","resolution":{"observed_at":"2026-08-07T06:11:28.370839Z","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":"2026-08-07T06:11:28.377979Z","title":"Algebraic Equations and Convex Bodies","venue":null,"work_id":"e00095fb-c7f9-4337-92ca-9b059a4ac368","year":2019},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":159,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.244400Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:4e82f2d757907876fb72839fbda5db38b322bbe0276e7b180cefe9cd04f11296","observation_id":"73649f0e-6e02-4070-9145-8e2c2c5f5a23","resolution":{"observed_at":"2026-08-07T06:11:28.381817Z","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":"2026-08-07T06:11:28.355352Z","title":"New York: Springer, 2005, pp","venue":null,"work_id":"50a73351-238e-45e4-8f1a-1e5cc52dd9c3","year":2005},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":227,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.252653Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:0ba6663627cdcc15a699fa5efc05cbbc92859cf9cb382d529b185be4bd367c7a","observation_id":"f6dd9fac-8623-4695-b785-ccd84323ef0d","resolution":{"observed_at":"2026-08-07T06:11:28.359462Z","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":"2026-08-07T06:11:28.333251Z","title":"Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation","venue":null,"work_id":"b5da0fc6-057a-40af-b72e-dc0c893ca8a4","year":1999},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":1996,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.260490Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:84b22e2d8f53a9f06d1d95022412ebd8eced97fe76796e07ef6fa4e4372c6186","observation_id":"e8074541-321b-49d5-9a81-852c1b98d318","resolution":{"observed_at":"2026-08-07T06:11:28.336937Z","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":"2026-08-07T06:11:28.388341Z","title":"A Polyhedral Method for Solving Sparse Polyno- mial Systems","venue":null,"work_id":"0a3188de-1842-443a-b206-bbfdaf298a89","year":1995},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2000,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.240591Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:656fbe03af5d46a59a371ede9c859a8211181db7f78257da3c11c7c72750cea3","observation_id":"0a527074-989a-4d47-be22-6690c510b576","resolution":{"observed_at":"2026-08-07T06:11:28.391676Z","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":"2306.13299","last_updated":"2023-06-23T05:25:45Z","snapshot_observed_at":"2026-07-06T15:45:47.517122Z","submitted_at":"2023-06-23T05:25:45Z","title":"Homotopy continuation methods for coupled-cluster theory in quantum chemistry","version":1},"cited_work":{"arxiv_id":"2306.13299","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.13299","snapshot_observed_at":"2026-08-07T06:11:28.289263Z","title":"Homotopy continuation methods for coupled-cluster theory in quantum chemistry","venue":"quant-ph","work_id":"e11f03ba-9415-4bf8-a76d-c236915ed79f","year":2023},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.236398Z"},"links":{"cited_paper":"/paper/2306.13299","citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:eaaa8d1ed7a54ad1523a37f3ed241a2e5fba58eeb555ddadcf68ca3287eeff03","observation_id":"9dd728ce-fb94-4ff8-b635-b5057076990a","resolution":{"observed_at":"2026-08-07T06:11:28.295760Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"2026-08-07T06:11:28.343955Z","title":"Coefficient-parameter polynomial con- tinuation","venue":null,"work_id":"3ee2c644-462d-4240-86e9-a98ed0a7521f","year":1989},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.256137Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:dde4d9fccca9740d190dae21fec607c43fd68d585974153a02067385572b05d2","observation_id":"11df93b9-bdb4-4f47-94a3-a6d533a0094b","resolution":{"observed_at":"2026-08-07T06:11:28.347953Z","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":"2026-08-07T06:11:28.397938Z","title":"Coupled cluster degree of the Grassmannian","venue":null,"work_id":"2243eddb-1af9-4180-a5ec-b97c38ef7680","year":2025},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.232151Z"},"links":{"citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:24c9bec2f80ceac6ca87c95736eb7be0dafb4457a1693214409effb1cf1a3ad7","observation_id":"d03de062-c542-42b9-935b-21943f096f10","resolution":{"observed_at":"2026-08-07T06:11:28.402063Z","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":"2301.02545","last_updated":"2023-01-06T14:55:51Z","snapshot_observed_at":"2026-07-06T14:38:04.867942Z","submitted_at":"2023-01-06T14:55:51Z","title":"A survey on toric degenerations of projective varieties","version":1},"cited_work":{"arxiv_id":"2301.02545","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.02545","snapshot_observed_at":"2026-08-07T06:11:28.306707Z","title":"A survey on toric degenerations of projective varieties","venue":"math.AG","work_id":"b5bffe8b-0aae-4503-b6fb-d0ca2ed883d7","year":2023},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.228159Z"},"links":{"cited_paper":"/paper/2301.02545","citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:ac47d197e09980e018c51fa84006af6f4381f660839a4eb8e9ebca755ecdc1e7","observation_id":"f1d7f619-0326-436e-a832-b513c463ede9","resolution":{"observed_at":"2026-08-07T06:11:28.310589Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2404.16796","last_updated":"2024-04-25T17:42:32Z","snapshot_observed_at":"2026-07-06T18:05:42.862609Z","submitted_at":"2024-04-25T17:42:32Z","title":"SAGBI and Gr\\\"obner Bases Detection","version":1},"cited_work":{"arxiv_id":"2404.16796","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.16796","snapshot_observed_at":"2026-08-07T06:11:28.320505Z","title":"SAGBI and Gr\\\"obner Bases Detection","venue":"math.AC","work_id":"767bc27b-3c56-4dba-a4ed-909152f74bba","year":2024},"citing_paper":{"arxiv_id":"2506.06264","last_updated":"2025-06-06T17:46:43Z","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-07T06:11:28.224030Z"},"links":{"cited_paper":"/paper/2404.16796","citing_paper":"/paper/2506.06264"},"observation_digest":"sha256:52e61c4f7e5ecada75da06ac6107f1edbd0a7c2a056477f8575e2390d4e87be0","observation_id":"133783b3-a133-476f-b202-8e4838d67f73","resolution":{"observed_at":"2026-08-07T06:11:28.324440Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2506.06264","last_updated":"2025-06-06T17:46:43Z","latest_version":1,"primary_category":"math.AG","snapshot_observed_at":"2026-08-07T05:55:00.595376Z","submitted_at":"2025-06-06T17:46:43Z","title":"The SagbiHomotopy.jl package for solving polynomial systems"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":0,"verified_exact":2,"verified_fuzzy":8},"total_outbound_references":11},"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 11 of 11 outbound references and 1 inbound Pith citation observation for arXiv:2506.06264."}