{"as_of":"2026-08-17T00:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3639113dfacaca7eae0bc92928f3704213f7c632ac50c263c777d26158b6ab55","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T19:10:34.698863Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"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/2411.11071/citation-record","integrity":"/paper/2411.11071/integrity","json":"/paper/2411.11071/citation-record.json","paper":"/paper/2411.11071"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T19:10:35.198362Z","title":"On kernels, eigenvalues, and eigenfuncti ons of operators related to elliptic problems","venue":null,"work_id":"02c8c756-5538-425f-bca7-51dfa39fa565","year":1965},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.573411Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:07dd4b4a7a54fc29f649753b69b74ed24ac81cabc62d8aff62beb9311409d25f","observation_id":"ce1d031a-a52e-46e1-968a-17d489853dc1","resolution":{"observed_at":"2026-08-12T19:10:35.201580Z","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":"2026-08-12T19:10:35.188378Z","title":"Eigenvalue sum estimates for lattice subgraphs","venue":null,"work_id":"0eb7b49a-10b7-4c77-b622-37206fd1be9f","year":2022},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.577000Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:b16b8c8f0b04e88df9ecd98f7cc391cc13c78a921a7f04ea148a50223bd8d5e9","observation_id":"2d4c782e-9aaa-416e-81af-5d7a5a238501","resolution":{"observed_at":"2026-08-12T19:10:35.191280Z","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":"2026-08-12T19:10:35.179133Z","title":null,"venue":null,"work_id":"b76f516e-9e2c-4640-b366-f97061c1b8f3","year":1972},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.580645Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:614f922dc48a2ce22924852a59580a9a497c29e4f1f347b407e1577359209e5f","observation_id":"6506e578-2114-4b91-8982-4fd5ec6e01b6","resolution":{"observed_at":"2026-08-12T19:10:35.182024Z","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":"2026-08-12T19:10:35.168748Z","title":"Asymptotic behavior of the sp ectrum of differential equations","venue":null,"work_id":"b441e616-6d0f-4728-8bc0-c7a2c1876aec","year":1979},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.584248Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:73c2755c2e504ff49cfc82694a17a0c6761b29b102ae60e965b4df6ee3a6b64e","observation_id":"4bb2430f-1ea8-4377-b7f1-34364e1345ef","resolution":{"observed_at":"2026-08-12T19:10:35.172538Z","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":"2026-08-12T19:10:35.157971Z","title":null,"venue":null,"work_id":"af20917b-e481-447c-a5e4-9b6b73822a37","year":1980},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.588581Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:a69fa0ec092d8d852bb9e00b8d132f5cdffdd1f1c9049427af355d3fe44cd8d0","observation_id":"8e08e486-0cf1-4c18-a82b-80d6d701c09d","resolution":{"observed_at":"2026-08-12T19:10:35.161530Z","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":"2026-08-12T19:10:35.146853Z","title":"A lower boun d for eigenvalues of the poly-Laplacian with arbitrary order","venue":null,"work_id":"b596fb5c-fc49-4455-9cee-303202c64178","year":2013},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.593385Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:e916d4f1c5b1e632116b78358d17dce1926584d474a7b2d435cdfc42737ac093","observation_id":"8ac3b95b-d888-4aef-b40e-088b7231497b","resolution":{"observed_at":"2026-08-12T19:10:35.151054Z","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":"2026-08-12T19:10:35.135394Z","title":"Upper and lower bounds fo r eigenvalues of the clamped plate problem","venue":null,"work_id":"c02f4911-d46c-4a71-8e11-13a44a8c02af","year":2013},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.598267Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:9b202445e437f24bd7a3043b44420415bcc0fccf5938f3034dd2a831025dfd07","observation_id":"dff944cf-13b6-4c3e-a3e3-f9d8fa360097","resolution":{"observed_at":"2026-08-12T19:10:35.139529Z","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":"2026-08-12T19:10:35.125694Z","title":"Difference equations of polyharmon ic type","venue":null,"work_id":"a602deae-142b-4bc9-babe-85b36c7a4a03","year":1958},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.602017Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:d16eefbe7b8e5e0b06d26e28cd87de4e3e1d99df38cc4c6265c2baef749e7b26","observation_id":"637013cd-07b9-438f-be7a-21e2a3db035c","resolution":{"observed_at":"2026-08-12T19:10:35.129139Z","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":"2026-08-12T19:10:35.115123Z","title":"Discrete bi-laplacians and bi harmonic b-splines","venue":null,"work_id":"4e460d16-5ca4-4664-ae17-4b03af7e8fe7","year":2012},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.606057Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:671d8d394657cd2032f98faa2011758de966e1387ca98a6771e3082304d94f16","observation_id":"61f277dc-4b41-4305-a3d1-eae7d7ed06fc","resolution":{"observed_at":"2026-08-12T19:10:35.118574Z","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":"2026-08-12T19:10:35.104554Z","title":"Lieb-Thirring inequalities for higher order differential operators","venue":null,"work_id":"3d73ba35-57ed-4cd8-80a5-4084d40a20a7","year":2008},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.610436Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:22f9e53ffed13d19f04651e224dc48b469df31cb3a3ebe6fc909f5f348108e92","observation_id":"83a01439-aa26-405e-9d4a-75d72282e150","resolution":{"observed_at":"2026-08-12T19:10:35.108030Z","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":"2026-08-12T19:10:35.094942Z","title":"Polyharmonic bound- ary value problems , volume 1991 of Lecture Notes in Mathematics","venue":null,"work_id":"cf6fff85-ac19-418f-a6aa-47349df031b5","year":1991},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.614848Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:73ab565a55bfa8bd5a359db3bf25d8aa8d6915aca1357fa07591b021b5515083","observation_id":"0121e744-df61-4e7c-9e18-955a7408330a","resolution":{"observed_at":"2026-08-12T19:10:35.098085Z","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":"2026-08-12T19:10:35.084136Z","title":"The laplacian spec- trum of a graph","venue":null,"work_id":"eb1480ba-9bb9-4025-93de-939fc195ffd4","year":null},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.618448Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:fb589e3da1f0314ac38f9a098c719054bf1051b7af1dae74312319d9e8125246","observation_id":"fbcca447-29cc-4cdc-8b52-110272372aa5","resolution":{"observed_at":"2026-08-12T19:10:35.088003Z","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":"2026-08-12T19:10:35.073929Z","title":"Graph embeddings an d laplacian eigenvalues","venue":null,"work_id":"66a32b07-6f5f-4454-b9ef-c648abe7805b","year":2000},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.621610Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:52dc3fecb5e03f58001f11fac1cdd4dc4e0bfcfd090646db2dd2b2a8fa0cea43","observation_id":"3efbcfc4-4217-496b-a405-7a477f0b53b2","resolution":{"observed_at":"2026-08-12T19:10:35.077051Z","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":"2026-08-12T19:10:35.062850Z","title":"Extremum problems for eigenvalues of elliptic operators","venue":null,"work_id":"da9253e2-fa0b-4bbf-8d4e-bb0a8571cac3","year":2006},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.624510Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:06e04d7010d55b00ccd07cc9e112812af97c9518a7cee9a01d51d75cd49fd0f3","observation_id":"b168f03c-92d9-4a5a-96cb-4f3ecb9471ce","resolution":{"observed_at":"2026-08-12T19:10:35.066586Z","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":"2026-08-12T19:10:35.051625Z","title":"Laplace and bi-la place equations for directed networks and markov chains","venue":null,"work_id":"ef66bf9e-6021-47e5-bca1-d55d9e7e9a80","year":2021},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.627144Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:0dba6cb9b0595d2dbaf065312c8759c49956723f783a37937142c6002610e6ca","observation_id":"56b325ac-3b76-40d0-b9e0-89c41040402e","resolution":{"observed_at":"2026-08-12T19:10:35.056015Z","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":"2026-08-12T19:10:35.040195Z","title":"Harmonic functions of gen eral graph laplacians","venue":null,"work_id":"5e06dbee-6665-4b51-818a-c352da0d1812","year":2014},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.629738Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:e53136bfa4e2086016785a686b6f1f6e23ceb39572942384cea468d9a5cd4bf3","observation_id":"6378701a-e6ea-4c7d-a5a7-f659423e14d3","resolution":{"observed_at":"2026-08-12T19:10:35.043918Z","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":"2026-08-12T19:10:35.028572Z","title":"Universal bounds for eigenvalues of the polyharmonic operators","venue":null,"work_id":"bf14a034-ce47-439e-aa28-7bc94595f229","year":2011},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.632558Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:5d4a6e56c9b7d002576c8462088a5b7767268de798956ad63e4634e692333415","observation_id":"3a4be6ed-3241-480e-8495-fec98e720ba3","resolution":{"observed_at":"2026-08-12T19:10:35.032437Z","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":"1910.01369","last_updated":"2019-11-19T11:08:44Z","snapshot_observed_at":"2026-07-06T08:26:35.289279Z","submitted_at":"2019-10-03T09:18:31Z","title":"Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian","version":2},"cited_work":{"arxiv_id":"1910.01369","doi":null,"metadata_source":"pith","pith_arxiv_id":"1910.01369","snapshot_observed_at":"2026-08-12T19:10:34.737109Z","title":"Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian","venue":"math.SP","work_id":"2b520222-d4f5-4c77-84bd-72b1204d9942","year":2019},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.635702Z"},"links":{"cited_paper":"/paper/1910.01369","citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:5224acb1164b7648b9af9ecd65229a5328aac98a7a02409b755949e5f47a1aec","observation_id":"8f408530-21f1-4e69-a4c0-ab4b9279aeba","resolution":{"observed_at":"2026-08-12T19:10:34.744331Z","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":"2026-08-12T19:10:34.922563Z","title":"Two- dimensional Berezin-Li- Yau inequalities with a correction term","venue":null,"work_id":"596f276b-ac65-4ad0-8f88-07d30e153c90","year":2009},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.638871Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:aaff077ba8ef32247a3be5a6ccbb68afb2ecd8c38d5efeb3bf70ded3dbb0d75d","observation_id":"6c759a18-0c26-4fa8-b4d2-2fc533b117f8","resolution":{"observed_at":"2026-08-12T19:10:34.926536Z","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":"2026-08-12T19:10:34.912852Z","title":"Kr¨ oger","venue":null,"work_id":"d313d35a-f310-4938-9577-d3f29903b34a","year":1992},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.642052Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:a86cf25222aa0401aaab45cd49a0fa6976335d08bcabeb5b5e2d8336290b9b49","observation_id":"e668fef8-95b0-4415-a140-95ae29e007fb","resolution":{"observed_at":"2026-08-12T19:10:34.916231Z","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":"2026-08-12T19:10:34.901627Z","title":"Estimates for sums of eigenvalues of the Laplacian","venue":null,"work_id":"7c1acf58-3b13-4c2d-a938-448b27ebe2ab","year":1994},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.644719Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:aa091d209ed9ee12d48aba980ccf35c42a496b2b1eace01e1f08866e39cfce95","observation_id":"51978313-171f-4ad3-9a3b-f1c3dd855429","resolution":{"observed_at":"2026-08-12T19:10:34.906084Z","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":"2026-08-12T19:10:34.891960Z","title":"´Equations aux D´ eriv´ ees Partielles","venue":null,"work_id":"c826aace-2cc2-43e6-a361-b5b870573b29","year":2000},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.648066Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:e5e5896577c8ab4a7e2c4c3979ef09a818d15929952baa651ed79629f894f770","observation_id":"7b414f68-2cde-4102-bec7-88ee558da3a5","resolution":{"observed_at":"2026-08-12T19:10:34.894990Z","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":"2026-08-12T19:10:34.881798Z","title":null,"venue":null,"work_id":"93182030-a812-4083-94a0-9a4cd965452f","year":1985},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.651713Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:42432b26fafb990a04fd3709f7af006e35f4e552aca4510323bb96a98f1356d4","observation_id":"9d26276a-7cc4-4b2e-9e05-769f91639389","resolution":{"observed_at":"2026-08-12T19:10:34.884429Z","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":"2026-08-12T19:10:34.870767Z","title":"On the Schr¨ odinger equatio n and the eigenvalue prob- lem","venue":null,"work_id":"9e9f8719-ca8b-463f-80a5-2787957dbe21","year":1983},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.654749Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:f09870fdbd69ab54ec1d3ddb0f315b33046b2f47a99431b51d61d2d8dc2b2d1a","observation_id":"e202820d-542e-4524-a8db-05045a572310","resolution":{"observed_at":"2026-08-12T19:10:34.874468Z","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":"2026-08-12T19:10:34.860281Z","title":null,"venue":null,"work_id":"19377497-d40e-4b1c-a3e0-532f498359ea","year":1979},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.657672Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:6cc2387c25ed6f5e47372e82538eaa69b6817d0f846223373366bee73d2b6be2","observation_id":"4a2927c8-5143-4bdf-9789-75eab2d2f9a9","resolution":{"observed_at":"2026-08-12T19:10:34.863807Z","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":"2026-08-12T19:10:34.849679Z","title":null,"venue":null,"work_id":"9e9dfa2c-3b1c-4d06-a962-3ca5ed17754f","year":2003},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.660495Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:4b64f0bd72cd8b43e46669fbfb20a82b9a53dcbdc6692aae2e41f3858cd330f6","observation_id":"6e226cee-fd77-47c6-95ef-7b380500751a","resolution":{"observed_at":"2026-08-12T19:10:34.853076Z","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":"2026-08-12T19:10:34.839479Z","title":"Netrusov and T","venue":null,"work_id":"515d7846-6e4f-485c-94c0-cdbce4f71f9b","year":1996},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.663436Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:9bb537e6777819d32bd50d681339b2d45fbc1e58d8cc3c9e2fdf88aff54c26a8","observation_id":"7a23a029-1f99-4761-a1e9-b9d494ca7165","resolution":{"observed_at":"2026-08-12T19:10:34.843071Z","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":"2026-08-12T19:10:34.829503Z","title":"On the eigenvalues and eigenfunctions of elast ic plates","venue":null,"work_id":"9596e539-1bc4-4a1b-8e8b-c438f26e4ead","year":1950},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.667570Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:5ac2a82a597820a3180c3947cc0cb8b0bb24266efd27322b19b3773534cd1df9","observation_id":"28f9f71f-dcce-40eb-b258-310e013d40cd","resolution":{"observed_at":"2026-08-12T19:10:34.832894Z","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":"2026-08-12T19:10:34.819656Z","title":null,"venue":null,"work_id":"0b7a0447-c3de-49b3-984e-70ea7d489932","year":1961},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.674468Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:31958f402d5db5d5417790b7047954795cdb240fbaef635d085c93fd3e3e9643","observation_id":"5ba15d38-6f78-46b4-a452-cc9b9ef01d61","resolution":{"observed_at":"2026-08-12T19:10:34.822591Z","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":"2026-08-12T19:10:34.809154Z","title":"On the membrane model and the discrete Bilaplacian","venue":null,"work_id":"11825686-bfcf-4a6b-8f9e-2b3f8417e31c","year":2021},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.677514Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:b4d971ec2dfb99c3191b5ed1d0e3e07eb865ee23dd53d4ab24eb968a67efb6d2","observation_id":"31c15571-5874-48f8-962d-fa6cc52dfa64","resolution":{"observed_at":"2026-08-12T19:10:34.811992Z","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":"2026-08-12T19:10:34.797610Z","title":"Strichartz","venue":null,"work_id":"6c51a3e7-c4f9-4113-a327-0cc491aed9f9","year":1996},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.680823Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:fe6d86caaf733bb9c83cd5afaffff6b4ae4e9047c41a4586637d947319ad113e","observation_id":"f86e9c68-cce3-45f8-b047-e6733026ef52","resolution":{"observed_at":"2026-08-12T19:10:34.801132Z","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":"2303.15766","last_updated":"2024-08-05T11:25:03Z","snapshot_observed_at":"2026-08-16T15:44:49.475868Z","submitted_at":"2023-03-28T06:48:53Z","title":"Eigenvalue estimates for the fractional Laplacian on lattice subgraphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.15766","snapshot_observed_at":"2026-08-12T19:10:34.683723Z","title":"Eigenvalue estimates for the fractional laplacian on lattice subgraphs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.683723Z"},"links":{"cited_paper":"/paper/2303.15766","citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:efc20e35b1e2fd1a705d04dda1a047e3315121271c5567267e5cea430867aa2c","observation_id":"0a90724d-a0d2-4390-bf06-7e86cb6c337a","resolution":{"observed_at":"2026-08-12T19:10:34.683723Z","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":"2026-08-12T19:10:34.785761Z","title":"Estimates for eigenvalu es of poly-harmonic opera- tors","venue":null,"work_id":"f892f9d1-d69f-491e-bffd-3a2466354cf3","year":2016},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.687301Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:08ff28c30ba678d913bc81a6c7610a71ba629d6c7dc8708a8d0be97543307f8f","observation_id":"10db5772-29e2-47fa-8092-aff3c5cabfaf","resolution":{"observed_at":"2026-08-12T19:10:34.789217Z","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":"2026-08-12T19:10:34.775411Z","title":"Das asymptotische Verteilungsgesetz de r Eigenwerte linearer par- tieller Differentialgleichungen (mit einer Anwendung auf d ie Theorie der Hohlraum- strahlung)","venue":null,"work_id":"f0f73b0e-52b2-4c49-b01b-c893df1b9a2a","year":1912},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.690862Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:837d56dd09d4d942d826b85a3b6dbc5833c8c04a4d168eacbd29e86971a1f2ea","observation_id":"ae3a42bf-819e-426d-97ff-cb68bea3be74","resolution":{"observed_at":"2026-08-12T19:10:34.778632Z","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":"2026-08-12T19:10:34.763760Z","title":"Eigenvalue bounds for the poly-harmonic operators","venue":null,"work_id":"39f53b9f-8882-4374-908f-feea3183a122","year":2014},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.694435Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:891585253dd62a3d6312fc5f2d855a35f35fd3f133ba37245e13b69698d3c69c","observation_id":"46e0cd20-aee8-48c1-a52c-cbe5255dadf3","resolution":{"observed_at":"2026-08-12T19:10:34.767862Z","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":"2026-08-12T19:10:34.753175Z","title":"Multidimensio nal lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators","venue":null,"work_id":"4e8e0a1f-1734-4d5b-a8d8-e7fa84118732","year":2012},"citing_paper":{"arxiv_id":"2411.11071","last_updated":"2024-11-17T13:19:59Z","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T19:10:34.698863Z"},"links":{"citing_paper":"/paper/2411.11071"},"observation_digest":"sha256:72e96acacff8d809a2ab5d5acef88365bb0b46689b1b7f7af88d9ee32a4f517a","observation_id":"0ef0388a-2c97-4b8a-a00a-d8ab287c5765","resolution":{"observed_at":"2026-08-12T19:10:34.756609Z","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":"2411.11071","last_updated":"2024-11-17T13:19:59Z","latest_version":1,"primary_category":"math.SP","snapshot_observed_at":"2026-08-16T10:59:30.665874Z","submitted_at":"2024-11-17T13:19:59Z","title":"Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":1,"verified_fuzzy":28},"total_outbound_references":36},"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 17 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2411.11071."}