{"as_of":"2026-08-16T17:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2dd45733c7608516155347a4125f9db407d9ffb25364b9ab5e99b484368f8274","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":"2026-08-14T12:42:40.424966Z","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":"2026-08-16T06:30:59.297886+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/1908.06736/citation-record","integrity":"/paper/1908.06736/integrity","json":"/paper/1908.06736/citation-record.json","paper":"/paper/1908.06736"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:42:40.808946Z","title":"F., Houston P ., Pennesi G., Fast Numerical Integration on Polytopic Meshes with Appli- cations to Discontinuous Galerkin Finite Element Methods, J","venue":null,"work_id":"36abf75b-397d-4c05-8582-9cfa3acb9543","year":2018},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.309049Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:4c3632c515bb2287b7c314f93c9e6435fbf8418b8e83f2e97325f3804bdf9582","observation_id":"c7ba8854-a94e-451c-a967-8551df58c702","resolution":{"observed_at":"2026-08-14T12:42:40.814718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.783421Z","title":"How to integrate a polynomial over a simplex, Math","venue":null,"work_id":"75c93819-9b61-4537-bebc-e38b2c7d6af2","year":2011},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.317395Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:b316ea872f8b565b15abb98f428a0ed818f6f9b7742d610d552c291471592065","observation_id":"78668728-674c-48d6-bca1-1326b307fa6a","resolution":{"observed_at":"2026-08-14T12:42:40.790722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.752140Z","title":"In Gil Kalai and G¨ unter M","venue":null,"work_id":"47dc2bce-bde6-4125-932f-f2455b70739a","year":2000},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.325537Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:d172daad3ae21bbf05647994c749a6aa8c48e260500c528c06ef53b472fd4f54","observation_id":"b3a8120a-9595-4992-86dd-4c9d0b071cab","resolution":{"observed_at":"2026-08-14T12:42:40.760883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.730268Z","title":"Mech., 56, pp","venue":null,"work_id":"1b33666b-9359-4252-82ac-ed0f8a7f589b","year":2015},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.331574Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:355b790f8ee34995fd8725435c20498a097ff8c600274846e67fe338136486ee","observation_id":"a57bfe66-d975-4e73-b8eb-4b18489234dc","resolution":{"observed_at":"2026-08-14T12:42:40.736560Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/nme.6150","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:08:47.750906Z","title":"B., Sukumar N., Modeling curved interfaces withou t element-partitioning in the extended ﬁ- nite element method, Int","venue":"International Journal for Numerical Methods in Engineering","work_id":"cf846c1b-4c80-4ffd-84ff-102c9809a1c3","year":null},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.339819Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:5d85d7640fe20abbae4fb56288d8d1c9efe12f2ee805ec335025a8e7c59dce1e","observation_id":"523e7f1b-6b27-4027-8864-2e7127b0e594","resolution":{"observed_at":"2026-08-14T12:42:40.486842Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.711222Z","title":"e79-e90 (2015)","venue":null,"work_id":"445a7cf9-2355-4120-b115-2474df0f9b3c","year":2015},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.350683Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:b284490d072c15696935ef8f72e112ae0aa9c9d944164201cab5f360ac5ad2c6","observation_id":"ca55a29d-afe6-4b4e-ab17-8da44bf4f6cf","resolution":{"observed_at":"2026-08-14T12:42:40.718347Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.04191","last_updated":"2019-08-12T15:14:33Z","snapshot_observed_at":"2026-08-14T13:46:18.002986Z","submitted_at":"2019-08-12T15:14:33Z","title":"Positivity Certificates via Integral Representations","version":1},"cited_work":{"arxiv_id":"1908.04191","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.04191","snapshot_observed_at":"2026-08-14T12:42:40.507949Z","title":"Positivity Certificates via Integral Representations","venue":"math.FA","work_id":"acc22330-19a6-4047-a356-0a761a2fa3c5","year":2019},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.360110Z"},"links":{"cited_paper":"/paper/1908.04191","citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:e9b577952263af5c5e5bb9e3e7146e6adb9db9b95422114cf2078e74841654fe","observation_id":"3f324d33-a915-44b4-ac81-4a503fa4cf3d","resolution":{"observed_at":"2026-08-14T12:42:40.516920Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.690368Z","title":null,"venue":null,"work_id":"dc9225b3-298b-4987-80a6-2e2aa4aec37b","year":2001},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.367772Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:b032db2db4ffbf5a83feb587f0be6fee374eea19cc4f07921d92386bab24fed3","observation_id":"0a218c9d-bc72-45f0-a46d-ebd2e845a252","resolution":{"observed_at":"2026-08-14T12:42:40.696955Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.670938Z","title":null,"venue":null,"work_id":"96c5b720-08d8-4282-b18d-7846fa56d328","year":2001},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.375873Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:f57d84c948d7ef336b308fb2b6c5d4d42c179d78e725f6a5718f0698192c366c","observation_id":"0c878015-7748-4fea-9adf-55cea08f353e","resolution":{"observed_at":"2026-08-14T12:42:40.677068Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.646361Z","title":"1126–1140 (2001)","venue":null,"work_id":"c44f5152-587a-4ffc-8a14-aa742c54cf50","year":2001},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.384114Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:d4c81611a9076646fe62385811b9b4d1220eb7cd04cb31c2a13df34c96d47349","observation_id":"7f574676-20aa-4acf-baf9-60699d8ad6db","resolution":{"observed_at":"2026-08-14T12:42:40.653209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.617177Z","title":null,"venue":null,"work_id":"59607839-a933-4586-b73f-497ebf12e9ae","year":1998},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.393560Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:767f2e032a7f99be0b6142e69a6a1fa0133fea6fa53c96285d35bc537e18ae11","observation_id":"94e8005c-7a1c-407c-a1ba-d42242007b70","resolution":{"observed_at":"2026-08-14T12:42:40.627402Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.586885Z","title":null,"venue":null,"work_id":"5ad93eb7-acfd-42fd-87c9-d5b238bdd1f8","year":2017},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.401465Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:204773959f852199b4fdebd21bf69161cb05631da9babd536cf049c0efeac93f","observation_id":"42a5dea6-32d4-4034-83ef-3ecf28c7820e","resolution":{"observed_at":"2026-08-14T12:42:40.597486Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.561213Z","title":"Methods Appl","venue":null,"work_id":"fd68cbda-3f74-4e5b-9cdf-eb85937143c0","year":2015},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.412184Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:5cf7e361753ef94e0704c69c8df385b51285bf29994c05055d7f2068dbfd9d19","observation_id":"cc8d4c36-e983-4477-9e73-030c9f3a81e1","resolution":{"observed_at":"2026-08-14T12:42:40.567539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:42:40.535091Z","title":"Quantitative Spec- troscopy & Radiative Transfer, 129, pp","venue":null,"work_id":"12b1b0f9-1683-484f-8c26-75416386491b","year":2013},"citing_paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T12:42:40.424966Z"},"links":{"citing_paper":"/paper/1908.06736"},"observation_digest":"sha256:b2f5455355f7dd2cf82a50f66a334ad65491cf0f538c51b577816e5bf0e677fe","observation_id":"cd5732c4-1329-4b47-8161-59d8ae0b2441","resolution":{"observed_at":"2026-08-14T12:42:40.541378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.06736","last_updated":"2020-08-27T08:25:30Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-16T02:25:20.015253Z","submitted_at":"2019-08-19T12:27:41Z","title":"Simple Formula for Integration of Polynomials on a Simplex"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":8},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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:1908.06736."}