{"as_of":"2026-08-18T01:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cf5d458bd3ad26c7c1f14ece1f0c47aef1780e4e785f0c1bd1ebd54f71c8ef28","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T15:51:50.063181Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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":"2026-05-13T18:06:56.705675Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-13T18:08:15.346928Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"cited_work":{"arxiv_id":"2509.19011","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.19011","snapshot_observed_at":"2026-06-11T02:08:34.179457Z","title":"https://arxiv.org/abs/2509.19011","venue":null,"work_id":"da7ba798-5cfd-4b30-b330-ecebcb7adc53","year":2025},"citing_paper":{"arxiv_id":"2604.02995","last_updated":"2026-05-05T21:28:00Z","snapshot_observed_at":"2026-08-15T13:06:25.019036Z","submitted_at":"2026-04-03T12:20:09Z","title":"A semicontinuous relaxation of Saito's criterion and freeness as angular minimization","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-13T18:06:56.705675Z"},"links":{"cited_paper":"/paper/2509.19011","citing_paper":"/paper/2604.02995"},"observation_digest":"sha256:a0680109972a703022e1e2ad6972d5a7904e4dc28ebff06792adc85229da3701","observation_id":"0e02e75b-1447-4d47-bcae-beabdb26baa1","resolution":{"observed_at":"2026-06-11T02:08:34.179457Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.19011/citation-record","integrity":"/paper/2509.19011/integrity","json":"/paper/2509.19011/citation-record.json","paper":"/paper/2509.19011"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:50:42.948782Z","title":"Addition-deletion theorems for the Solomon-Terao polynomi- als andB-sequences of hyperplane arrangements","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T15:50:42.948782Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:bc732d361ea152135a32de44a334143527be021de56dbb4d5b7a07be7a0d783f","observation_id":"33712a25-f85d-4c04-85a6-2b1f2e6b4921","resolution":{"observed_at":"2026-08-04T15:50:42.948782Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.04364","last_updated":"2024-04-05T19:22:22Z","snapshot_observed_at":"2026-08-16T14:03:15.679196Z","submitted_at":"2024-04-05T19:22:22Z","title":"Modular curves $X_1(n)$ as moduli spaces of point arrangements and applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.04364","snapshot_observed_at":"2026-08-04T15:51:38.136332Z","title":"13 [CL25] D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:38.136332Z"},"links":{"cited_paper":"/paper/2404.04364","citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:f10020bb50507fef334ee6d972860ba8805d7f2ceee7a5b5404f52280617862a","observation_id":"83ef2a1d-2f08-4d61-937d-214dcab48c24","resolution":{"observed_at":"2026-08-04T15:51:38.136332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11915","last_updated":"2025-03-14T12:21:04Z","snapshot_observed_at":"2026-08-16T15:14:12.694776Z","submitted_at":"2023-07-21T21:39:24Z","title":"Singular matroid realization spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11915","snapshot_observed_at":"2026-08-04T15:51:44.608298Z","title":"Singular plane curves: freeness and combi- natorics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:44.608298Z"},"links":{"cited_paper":"/paper/2307.11915","citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:4af141cb2fc6dc774195d2e02861536a4d62e437183350a0b56a82ae34610e10","observation_id":"9d4af5c4-3ce2-4161-8b9b-38c9dc2f395f","resolution":{"observed_at":"2026-08-04T15:51:44.608298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:51:46.358521Z","title":"[OT92] P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:46.358521Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:7f78eadc47f55c936fa8785cd8fcfcffd0e27c52ed6dcf1ab7d1c631735a7a1c","observation_id":"68a517b1-1b85-4bc9-ad4f-e3003083a453","resolution":{"observed_at":"2026-08-04T15:51:46.358521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:51:50.063181Z","title":"Combinatorial construction of logarithmic differential forms","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:50.063181Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:ebb15e6e14ad9a5907775a116d956d26acd0bb0d71d8790e50f3640899f5fef1","observation_id":"abc60c26-70f6-4ba1-8994-cb00763db8e5","resolution":{"observed_at":"2026-08-04T15:51:50.063181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:51:48.942902Z","title":"Springer-Verlag, Berlin, 1992, pp","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":300,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:48.942902Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:4f089b66808fd6dcb24a39517da382ec7c538fabe5e983ce1f31c6e19ffeb749","observation_id":"e188d6a8-61a7-4693-906e-b089d7e0aa23","resolution":{"observed_at":"2026-08-04T15:51:48.942902Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.03838","last_updated":"2019-02-11T12:10:09Z","snapshot_observed_at":"2026-08-14T17:18:10.850735Z","submitted_at":"2019-02-11T12:10:09Z","title":"Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.03838","snapshot_observed_at":"2026-08-04T15:51:50.056000Z","title":"Elementary modifications and line configurations in P2","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:50.056000Z"},"links":{"cited_paper":"/paper/1902.03838","citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:a62365836d0aa9fa42803aab94d5520b06d88454d736f9f29120a18cc36bd659","observation_id":"5673fb68-1c3e-4365-ae9f-52da95521692","resolution":{"observed_at":"2026-08-04T15:51:50.056000Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:50:50.692971Z","title":"[BHKL25] M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-04T15:50:50.692971Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:baf3e4ec8b4dee0a2aa6cbc695c964592a3ad30ee6f73a07aaacc9610f3ce823","observation_id":"17179b60-1cb1-4460-8c7d-cb5d4d5ea9a9","resolution":{"observed_at":"2026-08-04T15:50:50.692971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T15:51:15.933691Z","title":"Computing the nonfree locus of the mod- uli space of arrangements and Terao’s freeness conjecture","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements","version":2},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-04T15:51:15.933691Z"},"links":{"citing_paper":"/paper/2509.19011"},"observation_digest":"sha256:127cfa185f50479bc0cf0540fd17bd36e69d0a56d0c3c2ae672d3e090da3db43","observation_id":"204e162e-14a0-4cf3-b74b-99005c38718b","resolution":{"observed_at":"2026-08-04T15:51:15.933691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.19011","last_updated":"2026-06-10T06:13:34Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-17T18:18:40.784033Z","submitted_at":"2025-09-23T13:53:31Z","title":"Addition theorems for Ziegler pairs of hyperplane arrangements"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":9},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 1 inbound Pith citation observation for arXiv:2509.19011."}