{"as_of":"2026-08-16T04:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dabc350d39ab1ae6554b6a0c09b23e045cd5f5691aa263ac7f948ed7d533e46c","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:22:28.754725Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/1908.09386/citation-record","integrity":"/paper/1908.09386/integrity","json":"/paper/1908.09386/citation-record.json","paper":"/paper/1908.09386"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:22:29.010661Z","title":"1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid","venue":null,"work_id":"d6167e9d-35d7-4fed-9a9a-28182b4448ca","year":1968},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.680171Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:47d794dc0092ea743f6a53a84f7467552167d2616ca5235b83a0449752463e5a","observation_id":"df8dacf6-3dd4-4fbc-9ef2-995f68523a26","resolution":{"observed_at":"2026-08-14T11:22:29.016437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.992434Z","title":"1993 Numerical simulation of gravity waves","venue":null,"work_id":"1bd02e79-ce96-43e4-af5e-fde268b21c7a","year":1993},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.686266Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:88631ab322dff41a8e90f1d009df3137c8e57b6ff4b92186c343ede53bacc3a3","observation_id":"9a0aed38-fed3-4867-a6f3-a1163139f4cc","resolution":{"observed_at":"2026-08-14T11:22:28.997863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.976885Z","title":"1967 A variational principle for a fluid with a free surface","venue":null,"work_id":"10c7048e-63a9-4b61-998f-f38433ddd94e","year":1967},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.691426Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:e2c838980a5682b2fd7af98f07d378d224d63d41443de5f629555cfbbb2118bc","observation_id":"17a00d13-1cbd-42df-a60f-1665017b33b8","resolution":{"observed_at":"2026-08-14T11:22:28.981727Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.961308Z","title":"2015 A kinematic conservation law in free surface flow","venue":null,"work_id":"f8c6169c-7ab0-4c67-8b62-c91f4d1ddcef","year":2015},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.697490Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:653067281519f027c05c708794e1b71f2e40f8fc6d8aa2bb7d491cb94c0a8610","observation_id":"b625137a-ebfc-41b2-94a0-e92f5255398f","resolution":{"observed_at":"2026-08-14T11:22:28.966527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.946135Z","title":"2015 Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity","venue":null,"work_id":"22df4a39-5fbb-400e-bb44-3358c719381f","year":2015},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.703200Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:684df63f7900b386babcd062a1bfb3177fafd6ef2ab1df1c55e432b6a732b614","observation_id":"abf6bc85-63a8-4bd0-ae0a-a64574376ba5","resolution":{"observed_at":"2026-08-14T11:22:28.951111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.930450Z","title":"1958 A theorem on force-free magnetic fields","venue":null,"work_id":"2977489b-f5d0-4460-90cb-7555a513703a","year":1958},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.708862Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:85fafcb97e9d3d750046f8ea624f536bb6c2a27d1a42307355202fbd4e6f5bbd","observation_id":"631c84d1-e6ec-47ff-b1b5-6a6c258188b9","resolution":{"observed_at":"2026-08-14T11:22:28.935540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.914626Z","title":"1991 On Woltjer’s variational principle for force-free fields.J","venue":null,"work_id":"95b3dd50-587b-414e-b0ed-c3e382c16fdd","year":1991},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.714989Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:c185d3485a422e090027449eee779aa1c8b8057b7eb14e6eafc65b3067217951","observation_id":"f2738b3e-4897-4a83-885b-75d1b7267c38","resolution":{"observed_at":"2026-08-14T11:22:28.919863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.898369Z","title":"1984 Impulse, flow-force and variational principles","venue":null,"work_id":"1e24202a-85d1-4286-a4e8-4cdab7d70f5a","year":1984},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.721839Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:46ead2e9a7a95f3d486ca216b3e7abf7254744c63599a2511a5cbe022d4f7907","observation_id":"14b9bdee-964d-4d6d-83f0-1629fb2170f6","resolution":{"observed_at":"2026-08-14T11:22:28.903583Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.879149Z","title":"2019 A variational principle for three-dimensional water waves over Beltrami flows","venue":null,"work_id":"68b7fc0d-39bd-4efa-983a-3a6b36492c41","year":2019},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.726928Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:1016de6330b7363a68dd0ba8c372edc371f57b645e5783c36a452f2210365a3a","observation_id":"ec8f9078-e504-4a06-9eb0-25027ca9cb78","resolution":{"observed_at":"2026-08-14T11:22:28.885824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.859576Z","title":"1988 Mathematical Analysis and Numerical Methods for Science and Technology, Volume 3: Spectral Theory and Applications","venue":null,"work_id":"6fdd0170-3c2b-49a8-aede-971f5a07d5c6","year":1988},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.732774Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:3f1e9a813d76f7e201a17c5839317ff8051555c779e905e222bd9d1eb9976c51","observation_id":"4b40368a-503a-47d8-bb10-5337cc441555","resolution":{"observed_at":"2026-08-14T11:22:28.865889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.842650Z","title":"2013 The Water Waves Problem: Mathematical Analysis and Asymptotics","venue":null,"work_id":"d7c9ff64-f7bc-46c8-b0d1-adebefa0f991","year":2013},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.738065Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:df1531f24f6b58463c8985a4db8c5404e5675c4b0da51c84c13fd3f33b9012eb","observation_id":"2c20e0dc-28c4-4bdc-9643-b753ac385019","resolution":{"observed_at":"2026-08-14T11:22:28.847794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.825551Z","title":"1975 Sobolev Spaces","venue":null,"work_id":"17d97230-180d-4123-8b20-c3b95d3064f7","year":1975},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.743685Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:b94433b1b9356b6ce7945a5a2942f972ffc83ed3eb18b245d1629e7605402572","observation_id":"476ab60d-c6b3-4279-ab54-09edf118c39a","resolution":{"observed_at":"2026-08-14T11:22:28.831740Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.808959Z","title":"1997 Lectures on Nonlinear Hyperbolic Differential Equations","venue":null,"work_id":"37a5d806-a626-40a7-8a13-00c7bf4a2923","year":1997},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.749181Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:8c3e5f26d8405273d30a2f56901488aba17572652c353c0e7dfb9f8c3872d32d","observation_id":"f9a0d840-809b-4a90-ba5d-158d57eab974","resolution":{"observed_at":"2026-08-14T11:22:28.814164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T11:22:28.789159Z","title":"2003 Analytic Theory of Global Bifurcation","venue":null,"work_id":"b05fe76d-6fb4-4c86-8526-30c373c8408d","year":2003},"citing_paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T11:22:28.754725Z"},"links":{"citing_paper":"/paper/1908.09386"},"observation_digest":"sha256:da94f5f3684c5f3dcd8bf5451c06d41496b153e7ca64e00ef88b9d0ae7bbae0d","observation_id":"14893b39-04e7-4adc-9f18-49f9feb15609","resolution":{"observed_at":"2026-08-14T11:22:28.796342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.09386","last_updated":"2019-08-25T20:31:37Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T03:37:00.771889Z","submitted_at":"2019-08-25T20:31:37Z","title":"A variational formulation for steady surface water waves on a Beltrami flow"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":14},"total_outbound_references":14},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:1908.09386."}