{"as_of":"2026-08-13T02:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a14458abe26638923295ee72e9869163a9c4d09f0bf3fd69d1feda33450cc7ed","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T11:39:12.494670Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2411.18120/citation-record","integrity":"/paper/2411.18120/integrity","json":"/paper/2411.18120/citation-record.json","paper":"/paper/2411.18120"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:39:13.126926Z","title":"Barden, H","venue":null,"work_id":"837276e3-5621-4875-8bf8-1ffc367e57cb","year":2012},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.370070Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:d87db038212e9ef1afc0f0568cff451ebd9aac1ba1c2e722afe68c4503f634a2","observation_id":"e4823072-3915-400f-a2b4-057daa7b4ad3","resolution":{"observed_at":"2026-08-12T11:39:13.131213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.112928Z","title":"Brooks, R","venue":null,"work_id":"b9d53a11-8dc1-470f-b9be-2b6ecca1013f","year":1987},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.375612Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:c5d699ddc0f0c7c5cb948ceb2e4373f36b0b84f9bed4f76b8a3e0c3ae5461778","observation_id":"1ac5073e-215a-4dd3-baad-91123ff9a77a","resolution":{"observed_at":"2026-08-12T11:39:13.116913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.098857Z","title":"Brooks, Constructing isospectral manifolds , Amer","venue":null,"work_id":"e4eea185-7d7f-4e6c-bd50-64764dbb167f","year":1988},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.380455Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:87ba3685d9fb6196224d5f766e9162fc154668e4bfae474f216e48dc50300907","observation_id":"5e292826-1dca-45cf-96e5-529c899bc6eb","resolution":{"observed_at":"2026-08-12T11:39:13.102951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1239.32001","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:39:12.744369Z","title":"Buser, Geometry and spectra of compact Riemann surfaces , Progress in Mathematics, 106, Birkh¨ auser, Boston, MA, 1992","venue":null,"work_id":"4e752722-cc44-427d-8057-186da6b37f7b","year":1992},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.385331Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:90325b00587fa62c648f254a38426c6387b4d9558cb4fd6f7d262a195ce95415","observation_id":"5f4bbd49-b4cd-4cbc-af18-5d0b9755af9d","resolution":{"observed_at":"2026-08-12T11:39:12.753698Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.085316Z","title":"Buser, Isospectral Riemann surfaces, Ann","venue":null,"work_id":"4b5a067d-19e9-4eda-8830-7f0b9c11fe46","year":1986},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.390160Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:d9b2ed28b9ed55bf65f58771ec21f74248d8d87089ed15e0604822ab2e921f91","observation_id":"01d5ade0-cd4c-4737-a5ad-20171658c907","resolution":{"observed_at":"2026-08-12T11:39:13.089357Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.071721Z","title":null,"venue":null,"work_id":"022b2c36-5994-49b0-bdbb-23eb4b9b0cff","year":1992},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.395228Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:5813d12c5a95a083239f861df46a03f4e4d9e3943c88419c57dd79c378e55704","observation_id":"58e32091-5661-4d7e-a64a-e23ac6b5e032","resolution":{"observed_at":"2026-08-12T11:39:13.075887Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.057413Z","title":null,"venue":null,"work_id":"fa940c56-1511-4335-9208-3fb120afc1af","year":2003},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.400148Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:799c12151f5d1f9685ab4a44b6508928d73891d5a8736fe9fceb5306da2d8d96","observation_id":"59865e6c-2295-494f-a237-79014c97bc0e","resolution":{"observed_at":"2026-08-12T11:39:13.062073Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.042633Z","title":null,"venue":null,"work_id":"dba9fb95-f9fb-40d6-b157-0941e05f240e","year":1991},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.404382Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:53de3ace3cbf5a745f296299ab75902c2b281240474752ee1ba4ea8251ae995a","observation_id":"a84ffde0-65fb-46ff-a39f-13f579f121b1","resolution":{"observed_at":"2026-08-12T11:39:13.047231Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.027159Z","title":"Fiedler, Algebraic connectivity of graphs , Czech","venue":null,"work_id":"9d9433b6-475b-4c4f-9b2a-7061c785f825","year":1973},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.408663Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:c9ecc404bc67ef4921770dd5c34be416752095f7d8d7e3db597e763990acfb52","observation_id":"42e8522e-1e3e-43c8-a451-d1576fc1a446","resolution":{"observed_at":"2026-08-12T11:39:13.031948Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:13.012102Z","title":"Friedli, The bundle Laplacian on discrete tori , Ann","venue":null,"work_id":"72cee336-a764-4307-98d4-2578f4efedf7","year":2019},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.412911Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:ab3b1c94b4c7d6a9afc3e763ecb87a2c764a6d78ab9f43246657b9c9761c6835","observation_id":"3cc909c4-3e75-43bc-b459-0f727398a6f0","resolution":{"observed_at":"2026-08-12T11:39:13.016866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.996305Z","title":"Godsil, D.A","venue":null,"work_id":"55f9c3b6-2330-42b9-b01c-4bdcb259b00c","year":1977},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.417147Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:99b642d756b21acb8b07d51fa72d9794c815d4b762315407d6ff480f579dc448","observation_id":"5197315b-1e34-44bd-bd54-07ff4477e98a","resolution":{"observed_at":"2026-08-12T11:39:13.001152Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.980134Z","title":"Imrich, S","venue":null,"work_id":"0d685f09-04fa-4183-9278-2156115b26b3","year":2000},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.421436Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:54413ae15e7951540aafc68294160f558ffc1a13a4fe0fc18b5fd55b6204289c","observation_id":"bb48b9ed-427c-41f6-8c14-6d4c347d9fc9","resolution":{"observed_at":"2026-08-12T11:39:12.985022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"0983.58016","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:39:12.666663Z","title":"Isangulov, Isospectral flat Klein bottles (Russian), Mat","venue":null,"work_id":"012867fb-f1c0-4525-94fe-7d9709951fc1","year":2000},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.425671Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:7fe9e65f0e8d67f6e0f67bec6e4278eab7fcd0d56a291902e64eb07b2e26bb7c","observation_id":"924235fb-d4a0-4e98-9d51-6601d2501408","resolution":{"observed_at":"2026-08-12T11:39:12.674593Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.965517Z","title":"Kac, Can one hear the shape of a drum? , Amer","venue":null,"work_id":"5563d122-22a1-4c7f-a7b3-a74e6986a7fd","year":1966},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.430158Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:0e564d5cf3c4af321e99aa00a87828586f46fec36f7ac60bfacf477159dcaa7e","observation_id":"21531a50-e209-42c2-b846-f5e37e2b0526","resolution":{"observed_at":"2026-08-12T11:39:12.969976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.951218Z","title":"Kitaoka, Positive definite quadratic forms with the same representat ion numbers, Arch","venue":null,"work_id":"59dc40d8-31bf-42f2-ab97-54fb535b6c10","year":1977},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.434363Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:98b2c5394ec443bf92f68f37251d509ababdf54d76700b2d4d2c121fb7f0024b","observation_id":"35d1c7c5-49fb-4c70-8c49-94f31e844139","resolution":{"observed_at":"2026-08-12T11:39:12.955745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.936874Z","title":"Kneser, Lineare Relationen zwischen Darstellungsanzahlen quadra tischer Formen (German), Math","venue":null,"work_id":"fc9658ba-42bb-4b05-9534-e7902110e214","year":1967},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.438516Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:3b6e0e59b9da87437285a5a43ab652c47698a49583a8d769fcb15ce558e21b2d","observation_id":"57fa1069-4c5e-4b4b-a7a0-e172f3bc1536","resolution":{"observed_at":"2026-08-12T11:39:12.941244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06105","last_updated":"2024-03-10T06:17:23Z","snapshot_observed_at":"2026-08-13T00:58:19.264767Z","submitted_at":"2024-03-10T06:17:23Z","title":"Connection Laplacian on discrete tori with converging property","version":1},"cited_work":{"arxiv_id":"2403.06105","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.06105","snapshot_observed_at":"2026-08-12T11:39:12.531496Z","title":"Connection Laplacian on discrete tori with converging property","venue":"math.SP","work_id":"05a31dd1-d099-4cdd-9b72-e9134d9bc46c","year":2024},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.442832Z"},"links":{"cited_paper":"/paper/2403.06105","citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:ac5f1f426b244c0c48042e8c3267d560a5dfb06f77be5462110702248e77d205","observation_id":"e29dcc5d-725c-45b8-b347-4d34225182e2","resolution":{"observed_at":"2026-08-12T11:39:12.538600Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.921474Z","title":"Algorithms Appl., 8:2 (2016) 1650028 (10 pages) MR3505475","venue":null,"work_id":"bb6ff5b0-7a55-456f-b652-f09828874d43","year":2016},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.447369Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:68f2008bdd7d30f699b287be5bde38d54e96211373342924e43def2fbf6eda9b","observation_id":"b00ee7f7-f0b5-48fb-98b3-af348dc28fbf","resolution":{"observed_at":"2026-08-12T11:39:12.926509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.905412Z","title":"Louis, Asymptotics for the determinant of the combinatorial Lapla cian on hypercubic lattices European J","venue":null,"work_id":"2399ca29-39fe-4f05-a6ef-3f079087586d","year":2017},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.451967Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:61dfae4132c0d804fa87fd778cf76086c0aa2d208f7cafaf7af36349247c905a","observation_id":"9d577d6f-dc10-4795-8577-93f1d0b2ed6c","resolution":{"observed_at":"2026-08-12T11:39:12.910371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.889656Z","title":"Mednykh, I","venue":null,"work_id":"57920831-1c59-4757-929a-cec2af5eb23e","year":2015},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.456548Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:e9525b599a042a0d9a7950ccb242698de3605ceb16c01931a55b1191613ee1fe","observation_id":"fbec0bbb-0c43-444b-a01c-928880241b5c","resolution":{"observed_at":"2026-08-12T11:39:12.894506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.873962Z","title":"Milnor, Eigenvalues of the Laplace operator on certain manifolds , Proc","venue":null,"work_id":"5b27fa43-4452-4017-a446-8b565c7fb838","year":1964},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.461264Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:1168f135f45e2f80ed2d27709001731963131acf13d868a98a1b4168109824df","observation_id":"2c00412d-1c5e-4a9a-8cfc-8eaed6192749","resolution":{"observed_at":"2026-08-12T11:39:12.878715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.858194Z","title":"Mohar, The Laplacian spectrum of graphs , in Graph theory, combinatorics, and applications 2, Ed","venue":null,"work_id":"a142995c-6aec-431b-8b51-c48884b1d452","year":1991},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.466294Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:6ae016d6d1e80457b5a9eec53b38f8780dba2e7a7213da17346a8918c4a7d0e5","observation_id":"68791c81-e4e4-4821-ba15-dbb7f4125146","resolution":{"observed_at":"2026-08-12T11:39:12.863018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.843222Z","title":"Nilsson, J","venue":null,"work_id":"1b0686fc-ef7f-4acc-ae87-a34c0b0c7e51","year":2023},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.470903Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:28813a015e457e7b6bd64bcdc85b772a70389703cad43426bf2627e97347b004","observation_id":"112e9588-6a43-4371-8fe5-b6bd2e0c5aab","resolution":{"observed_at":"2026-08-12T11:39:12.847911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.827431Z","title":"Sabidussi, Graph multiplication, Math","venue":null,"work_id":"939ae966-695d-4b49-aa1c-36250d490469","year":1960},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.475754Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:ab5d2fd792deef6ee6a412bb2822a15cb38a7a36bba5d833cc8c79c397f6bd8f","observation_id":"6d00e02b-64d4-49b5-9aca-5c20dd563753","resolution":{"observed_at":"2026-08-12T11:39:12.832531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.811681Z","title":"Schiemann, Ein Beispiel positiv definiter quadratischer Formen der Dim ension 4 mit gleichen (German), Arch","venue":null,"work_id":"f26b4e29-51b0-43d8-9d61-4003ca18d88b","year":1990},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.480690Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:9dac2b90d9bbc84bc547593292b82e0c32ef1a133dc97d6057f3e65119738b61","observation_id":"15ee5651-f91a-4c32-a654-6637001020ad","resolution":{"observed_at":"2026-08-12T11:39:12.816826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.794834Z","title":"Shiota, On theta series and the splitting of S2(Γ 0(q)), J","venue":null,"work_id":"7e0e572e-0ac7-4823-b710-479d90cb62e7","year":1991},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.485237Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:edfdab250ed2ea8c691856adc79cb8c4a9b8fe8330eb2fa6bfccdd282fa0e045","observation_id":"4dc844bb-a8f7-4db9-8df8-5bb85177d697","resolution":{"observed_at":"2026-08-12T11:39:12.799982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.779383Z","title":null,"venue":null,"work_id":"5137c749-3fce-4184-8519-84fb0f1fe6f9","year":1963},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.489993Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:ffbcfbd7e796953583801dd2c1519aadccca828c5ee6bc2d64bdf1a3d9b50310","observation_id":"04ec04ec-3263-48d9-9dc9-19f28f1a0106","resolution":{"observed_at":"2026-08-12T11:39:12.783907Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T11:39:12.764209Z","title":"Wolpert, The length spectra as moduli for compact Riemann surfaces , Ann","venue":null,"work_id":"f4c9c656-885c-4318-a466-def0c869730b","year":1979},"citing_paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T11:39:12.494670Z"},"links":{"citing_paper":"/paper/2411.18120"},"observation_digest":"sha256:d296dce0a06c6372a9cd7c19b5d7937719c7e634b13030c67e0a7f2a79b6542a","observation_id":"0e5755c4-1312-40d9-bafe-0e9064da0573","resolution":{"observed_at":"2026-08-12T11:39:12.768883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.18120","last_updated":"2024-11-27T07:58:48Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T19:05:13.610180Z","submitted_at":"2024-11-27T07:58:48Z","title":"One can hear a discrete rectangular torus"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":3,"verified_fuzzy":21},"total_outbound_references":28},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2411.18120."}