{"as_of":"2026-08-15T02:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:53146b27592ba9151ddc930cfa5db3f3f1ccb6faf734a838ce6cdcd1b40a6512","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":"2026-08-05T12:17:29.873924Z","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":"2026-08-14T06:32:32.682623+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/2509.01927/citation-record","integrity":"/paper/2509.01927/integrity","json":"/paper/2509.01927/citation-record.json","paper":"/paper/2509.01927"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T12:17:31.302358Z","title":"Nauk 38 (1983), no","venue":null,"work_id":"fcbe5e55-abae-4ccd-aa40-9f98e73c6e00","year":1983},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.012265Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:916711626febe6de5f3b0f0f4fa65fa1fba15b796b7f746d9e58ea5b88017880","observation_id":"8e81b557-1718-4539-8285-ec36aebcc49e","resolution":{"observed_at":"2026-08-05T12:17:31.308711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.272343Z","title":null,"venue":null,"work_id":"bd7c9e77-ce04-4e0b-b518-a49308380d38","year":1976},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.105659Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:f314b75d4015ab02420627ebf39f6ef6a4fac0957e7f8e68408be5b05d19892c","observation_id":"81387ffb-d7e0-471f-a1c8-367703c9fd1b","resolution":{"observed_at":"2026-08-05T12:17:31.278898Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.242904Z","title":"Sh., Suslina T","venue":null,"work_id":"5f2dce75-45fb-4579-b175-1fc65f4c0c12","year":1999},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.198868Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:e48dd63b23afc455801d396915c892eeb1efc05fe6e1da35ac16753b431128df","observation_id":"9418f0bf-2c19-4b78-b03e-6eb3ee805ae5","resolution":{"observed_at":"2026-08-05T12:17:31.258839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.209983Z","title":null,"venue":null,"work_id":"7115c270-cf42-471b-9401-61da249339b8","year":2007},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.313234Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:36c55d2a3d5e164af40fb7de260ee3113a2781ce86b4c3a4fdefaaa9d3bf1baf","observation_id":"62fda2b7-3ffe-4479-98a4-28b4866ac9fd","resolution":{"observed_at":"2026-08-05T12:17:31.220688Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.03632","last_updated":"2025-03-25T19:26:22Z","snapshot_observed_at":"2026-08-09T12:50:38.536369Z","submitted_at":"2025-03-05T16:11:32Z","title":"Rare Flat Bands for Periodic Graph Operators","version":2},"cited_work":{"arxiv_id":"2503.03632","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.03632","snapshot_observed_at":"2026-08-05T12:17:30.576178Z","title":"Rare Flat Bands for Periodic Graph Operators","venue":"math.SP","work_id":"db9af96d-dc4a-405c-9cea-66680b2761a0","year":2025},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.503020Z"},"links":{"cited_paper":"/paper/2503.03632","citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:7a7e646e2c045f52d8d7459a12d95e2e627ed8541a66418d5e0db33d0f570df9","observation_id":"36f05517-1e26-4596-865c-6c1b5b62bf6a","resolution":{"observed_at":"2026-08-05T12:17:30.584869Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.189192Z","title":"L., Irreducibility of the Dispersion Polynomial for Periodic Graphs , SIAM Journal on Applied Algebra and Geometry 9, (2025), no","venue":null,"work_id":"4006383e-8856-4b52-8720-3c3ad29aaa3e","year":2025},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.618172Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:40a0cf8457cc287c76883e9ace352e1a16e22a906871172846cfb1266a3c6a83","observation_id":"fe72587a-52a1-46c6-8272-7404fc75421d","resolution":{"observed_at":"2026-08-05T12:17:31.196181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.163289Z","title":null,"venue":null,"work_id":"5db6525e-7aa1-4fcf-b694-d96c0f6742f3","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:23.745211Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:a20d62d96c8eaeebf5c455fe9b32055f1ab50d327d780c2815e47127cd784122","observation_id":"261df3c0-15a3-4d40-9af0-37e473aef189","resolution":{"observed_at":"2026-08-05T12:17:31.172201Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.136690Z","title":null,"venue":null,"work_id":"901ad824-c428-4381-8cc5-8d8b79b11006","year":2022},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:24.106336Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:16f3208135c07413e7add45df3cafd7fba385c0c865481ee32e9f6bfb48b669c","observation_id":"65d0dbdb-3800-4b85-9459-cebbaf339670","resolution":{"observed_at":"2026-08-05T12:17:31.144852Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.105085Z","title":null,"venue":null,"work_id":"9cdf272c-8013-4a1d-9d3d-abf7c57822c0","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:24.773816Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:e564832cde58b6e7764f1a4c378b2fbc56fe7dcb348761e3d0cacc1f37abb5fb","observation_id":"2b77f75d-6cc9-405c-b8e7-ac1e650103b6","resolution":{"observed_at":"2026-08-05T12:17:31.110519Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.084208Z","title":"2 (2006), 3826 – 3831","venue":null,"work_id":"da76d13e-c32b-4acc-9218-4a5f800632cb","year":2006},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.827070Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:55fb02dc3616632850b81a4963441467bbfd4f3620b2b020d023e16de7a0cc23","observation_id":"32c87c0e-c528-49a0-8c3f-88c76afbfff2","resolution":{"observed_at":"2026-08-05T12:17:31.091396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.062226Z","title":"P., Reducible Fermi surface for multi-layer quantum graphs including stacked graphene, Comm","venue":null,"work_id":"9a92fd9b-3b8e-482f-b758-f19fe401cd71","year":2021},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.837436Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:21bd96dbff1a7e463f4b3b667b7cfb0068c11db33e892ec9f3561f15810cc463","observation_id":"4856923f-8523-4226-bb25-e1c14ea85cda","resolution":{"observed_at":"2026-08-05T12:17:31.070822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.042202Z","title":"2, 570 – 585","venue":null,"work_id":"06eef0e6-1d37-4922-bb24-0920489f6709","year":2009},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.846264Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:736061c6d1ac917ebd4510bc08f6d71f07dd6f3764a84bc3a6797b856b9590e4","observation_id":"7d1daf4b-50f0-4532-9ec9-870dc09bdcfe","resolution":{"observed_at":"2026-08-05T12:17:31.047662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.024247Z","title":null,"venue":null,"work_id":"649ec8e6-0fd2-4dc6-b12d-260f4f3ce235","year":2022},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.854700Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:9ab1bb52e120784056463dde356ab47567bfb9f21a9878fc5abdfa147db06730","observation_id":"15fcbbd7-8e50-489e-8b99-dab78e0d028e","resolution":{"observed_at":"2026-08-05T12:17:31.030289Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:31.001978Z","title":"Henri Poincar´ e 25, (2024), no","venue":null,"work_id":"db59ab28-8cf0-4fae-8f99-a2c0b5c0a669","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.864632Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:57223e0bdfca80c42b8fdcf56114b0fc27033c61bf9ad71b7d19497edb66032f","observation_id":"b7e2b425-3e9f-47de-bda8-8a985b8f61a4","resolution":{"observed_at":"2026-08-05T12:17:31.009193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.983232Z","title":null,"venue":null,"work_id":"6ece3a3c-0e82-446d-ab0c-7cf6bc92ddb4","year":2025},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.870555Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:9e5fd2e0cb1859f8684f1428ea922db67abb8dd43534aaf7e90374081a64993f","observation_id":"5935e6b0-f8c1-43e4-b600-eefa755ea884","resolution":{"observed_at":"2026-08-05T12:17:30.989274Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1108.1584","last_updated":"2011-08-07T22:49:24Z","snapshot_observed_at":"2026-07-06T02:32:04.778988Z","submitted_at":"2011-08-07T22:49:24Z","title":"Periodic and limit-periodic discrete Schr\\\"odinger operators","version":1},"cited_work":{"arxiv_id":"1108.1584","doi":null,"metadata_source":"pith","pith_arxiv_id":"1108.1584","snapshot_observed_at":"2026-08-05T12:17:30.398619Z","title":"Periodic and limit-periodic discrete Schr\\\"odinger operators","venue":"math.SP","work_id":"ec4e05e7-4074-400b-9740-73535a5a9734","year":2011},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.876870Z"},"links":{"cited_paper":"/paper/1108.1584","citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:b1c03bb19ece6f1b28f8f2ec53ee9611453f9a58c80d39fd2a3a87125b921fa8","observation_id":"b4f388a7-29ad-4f22-99f8-2c09d569a69f","resolution":{"observed_at":"2026-08-05T12:17:30.508913Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.963882Z","title":null,"venue":null,"work_id":"4c9f48a3-eb4c-4627-bb06-0fc8373b4c8e","year":2014},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.882889Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:eaf427022e33056bd72787e0127e9d8695c3414ea63f7d34226f3273fd9d1536","observation_id":"04277c8f-ad3e-4e26-a27f-fea60b959dfd","resolution":{"observed_at":"2026-08-05T12:17:30.969092Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.944907Z","title":"What is known and unknown , J","venue":null,"work_id":"8619cc4f-b12a-4319-a2d6-5861de2e9f3e","year":2023},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.887758Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:5b69c80b1b86386ff532a7982f048b452154f44c65d5efa4b6554977066f6067","observation_id":"7e56cd88-6387-44fd-804e-472bbfe2dc7a","resolution":{"observed_at":"2026-08-05T12:17:30.949690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.925378Z","title":"ABSENCE OF FLAT BANDS FOR DISCRETE PERIODIC GRAPH OPERATORS WITH GENERIC POTENTIALS 19","venue":null,"work_id":"04cf1ddb-f5c6-4388-abf3-b3592d91a87d","year":1998},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.893664Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:3b6c447740b74bc9662bf6e64b43ff784a2c1531ee363165a43e2a340e481c67","observation_id":"21d16a30-8abd-495b-a53a-b18ef632c686","resolution":{"observed_at":"2026-08-05T12:17:30.930824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.901372Z","title":null,"venue":null,"work_id":"a076efc9-2eba-45e3-877a-b2ec70e0bd4a","year":2016},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.900157Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:dd8f66b714141e5fbbaa172a943ca32d8ccc52379f0a089af3ae1155b4d739cc","observation_id":"453c1375-0073-40b9-aab6-8ffe7ff4d283","resolution":{"observed_at":"2026-08-05T12:17:30.909575Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.882066Z","title":null,"venue":null,"work_id":"ea55adda-9bd6-49d3-ab08-017e7dff733d","year":1993},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.907947Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:7cdcf49973c706d80bf8e0c17c11ead1290751205c400c3f959ef71c161509c4","observation_id":"8a5a31d0-870d-463d-ac5b-e9792113b1a3","resolution":{"observed_at":"2026-08-05T12:17:30.889150Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.858585Z","title":"9 – 10, 1809 – 1826","venue":null,"work_id":"442e0e4f-f7a8-4e86-b343-97b63ccdbe01","year":2000},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.915955Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:9c0379814bc8853fd77946ccdfb3de9a5e5d9daaa993c5a058438d24b91e508b","observation_id":"82b8d2ed-c5f5-411b-b868-d1ad0638b7a8","resolution":{"observed_at":"2026-08-05T12:17:30.865854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.839699Z","title":"3, 673 – 686","venue":null,"work_id":"d839644f-cc19-47c8-b8a2-b94f72783b1c","year":2006},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.923765Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:1ca568f5a599887434cc28b59091af7be0720f5e4ec6b1429c0505b963e6aa23","observation_id":"22361d19-2f49-47ec-8db1-e5182e5bd2c7","resolution":{"observed_at":"2026-08-05T12:17:30.844819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.820987Z","title":"P., Irreducibility of the Fermi surface for planar periodic graph operators , Lett","venue":null,"work_id":"c23dd117-eca2-448a-9ba3-565a78f6f8f9","year":2020},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.930555Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:e9184fafde7429161423e75a7fc0ca52b76fb779e3686672b0565121f77224b2","observation_id":"bc5f1b5e-9913-4d95-b31e-7819535d0aad","resolution":{"observed_at":"2026-08-05T12:17:30.826897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.795826Z","title":null,"venue":null,"work_id":"587cbb57-8804-4b65-95d1-3c3b9df87d8a","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:27.938821Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:f7646ef98cc715dcac34bf775b36673925fa484766cca13611274f59c52cb499","observation_id":"ea12006c-2201-4bca-9be6-3b04be991cb6","resolution":{"observed_at":"2026-08-05T12:17:30.802281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.10387","last_updated":"2024-09-16T15:21:55Z","snapshot_observed_at":"2026-08-12T22:43:57.837140Z","submitted_at":"2024-09-16T15:21:55Z","title":"Sharp decay rate for eigenfunctions of perturbed periodic Schr\\\"odinger operators","version":1},"cited_work":{"arxiv_id":"2409.10387","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.10387","snapshot_observed_at":"2026-08-05T12:17:30.129773Z","title":"Sharp decay rate for eigenfunctions of perturbed periodic Schr\\\"odinger operators","venue":"math.SP","work_id":"47c1ce86-1eb5-4369-b4de-645aa29809ff","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.795036Z"},"links":{"cited_paper":"/paper/2409.10387","citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:d391048c59ac9387c0754374dca6975177ddf62f394719f1ad1a4934e00e32d6","observation_id":"7abdcf65-d293-470f-8cb5-63ff23b538ed","resolution":{"observed_at":"2026-08-05T12:17:30.258780Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.774648Z","title":null,"venue":null,"work_id":"151dd1f1-e6e3-4ca0-a91d-71a5a882c1df","year":2022},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.803977Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:9271dc767aad71c6f6ae9244d2878ea16c91fd2e8537703b5f4d414ad238008b","observation_id":"e48d5a7d-5a15-4918-8bb3-0c3221ce1c51","resolution":{"observed_at":"2026-08-05T12:17:30.781052Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.743744Z","title":null,"venue":null,"work_id":"1c05a970-5893-4627-b106-28f702a6a6c4","year":2021},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.809819Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:553cf1c71af983f14dbec6fb0608ecbd7cab202b0d3da69fe1dcde6fe118d036","observation_id":"ecb43c4b-0b3b-4156-9c4f-d8b714db3ede","resolution":{"observed_at":"2026-08-05T12:17:30.750406Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.722269Z","title":null,"venue":null,"work_id":"d14ed47e-f736-4767-8708-66d18df47c0f","year":2024},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.815898Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:3f5fa4c30425973c03f6d34e4b25baa694d09e38995f7ffa7c2baddfac1cc378","observation_id":"6e7d5c99-4d30-46c9-87f9-c7e04f960aed","resolution":{"observed_at":"2026-08-05T12:17:30.728968Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.701699Z","title":null,"venue":null,"work_id":"a4e95209-0116-4aa9-b2b1-92041152f1cb","year":2022},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.821582Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:59051ae97e1a511ff8ec42c9b5b840b5e5612c188915635d66ad4af0e6ecd8f7","observation_id":"13b9ef65-af56-42be-b4b2-d7bc9db16117","resolution":{"observed_at":"2026-08-05T12:17:30.709234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.679955Z","title":null,"venue":null,"work_id":"df2cfeb6-3932-4516-8782-0b4fef89388d","year":1978},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.828211Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:08972b6ee4830269ba94417936979442babdf097de99a06ab2ec2ae66fa78fa8","observation_id":"a567e517-7071-4a08-b443-2aaa19308577","resolution":{"observed_at":"2026-08-05T12:17:30.687762Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.660683Z","title":null,"venue":null,"work_id":"4a0d40b4-c551-4830-ab3b-78b977fad18f","year":2023},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.834974Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:ff8c3bc26c71fb413314bb9512155a8141f1901527cd9be7ed0fb4a79cab0de2","observation_id":"7d2950f3-8da8-4cd8-9011-15f24a8671e3","resolution":{"observed_at":"2026-08-05T12:17:30.666012Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.642890Z","title":"P., Reducible Fermi surfaces for non-symmetric bilayer quantum-graph operators , J","venue":null,"work_id":"9cf2cd82-6377-4cbc-a813-8061590e3aca","year":2020},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.842020Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:b45a955a75272692f534365a25aa8865fcd6fbbc506e54c1c524235ae18c0c32","observation_id":"943fd28f-002c-4466-a178-138debd7b624","resolution":{"observed_at":"2026-08-05T12:17:30.648438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.619029Z","title":"P., Eigenfunctions of unbounded support for embedded eigenvalues of locally perturbed periodic graph operators, Comm","venue":null,"work_id":"b7345424-285c-4b2c-9b7c-c86c1d460445","year":2014},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.852344Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:70a19f0af8834ba07ce5bf4cb1b45c34f43f0163f5ff7a9a66545a8981a81645","observation_id":"48b16e1e-ae0f-4445-b16c-f326ba3dcdc6","resolution":{"observed_at":"2026-08-05T12:17:30.625837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.03659","last_updated":"2025-02-05T23:01:24Z","snapshot_observed_at":"2026-08-13T07:31:20.412040Z","submitted_at":"2025-02-05T23:01:24Z","title":"Algebraic Aspects of Periodic Graph Operators","version":1},"cited_work":{"arxiv_id":"2502.03659","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.03659","snapshot_observed_at":"2026-08-05T12:17:29.930842Z","title":"Algebraic Aspects of Periodic Graph Operators","venue":"math.SP","work_id":"b5140335-fb04-4068-9d72-56edb7ff1c4d","year":2025},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.865965Z"},"links":{"cited_paper":"/paper/2502.03659","citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:c2de8d6d8a3f44b6358f77d1d09e1a12fb7e8c43fc6fa6a7fdb2793b3d93d18e","observation_id":"0388d72c-0066-42a2-932d-d3a76038dc16","resolution":{"observed_at":"2026-08-05T12:17:30.009293Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T12:17:30.600374Z","title":null,"venue":null,"work_id":"79d0982c-a5a2-4f9c-a8dc-53ad9fa8faff","year":1973},"citing_paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T12:17:29.873924Z"},"links":{"citing_paper":"/paper/2509.01927"},"observation_digest":"sha256:c7e6ed7573e94ec34132f0059c6a9f4f1c3a126c8978889d785428932c2fcefb","observation_id":"f20542dd-7bd0-49b1-bb7d-5c42b8531e44","resolution":{"observed_at":"2026-08-05T12:17:30.605766Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.01927","last_updated":"2025-09-02T03:46:49Z","latest_version":1,"primary_category":"math.SP","snapshot_observed_at":"2026-08-11T09:37:18.659625Z","submitted_at":"2025-09-02T03:46:49Z","title":"Absence of flat bands for discrete periodic graph operators with generic potentials"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":4,"verified_fuzzy":14},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2509.01927."}