{"as_of":"2026-08-18T23:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2eff672eae80955740c68648bca344d2ea3e1d48191b06639aec38eefbd110c5","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T11:19:15.715865Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2412.15769/citation-record","integrity":"/paper/2412.15769/integrity","json":"/paper/2412.15769/citation-record.json","paper":"/paper/2412.15769"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T11:19:16.723682Z","title":null,"venue":null,"work_id":"aec9a2fe-1803-46f7-88f1-f9a2d3e18fce","year":2021},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.461027Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:d3445b68a4f75aeb18459b99097c911ff146a8cd72ea79f170efb4c8436d68b7","observation_id":"2a7a4ced-8deb-4e85-8dd9-b42376f29fc4","resolution":{"observed_at":"2026-08-11T11:19:16.733605Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.680238Z","title":"Aharony, A","venue":null,"work_id":"9f988e3d-20b3-4f73-95cb-2167c60ea2ae","year":1998},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.471310Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:67f09c5399d1eb434c8a194e896e526a5bb3fba41ab6327778032f02be567f69","observation_id":"b795343d-a6b2-4be0-9dd0-e8c94a13eb5a","resolution":{"observed_at":"2026-08-11T11:19:16.690111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.636718Z","title":"Altmann, The versal deformation of an isolated toric Gorenstein sing ularity, In- vent","venue":null,"work_id":"769f26ac-74f2-446f-bc72-633a859ef36f","year":1997},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.481152Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:980f504d5520b371d2fc4ce253fcd18a3189128492c3b1da6d38b8a28489ce68","observation_id":"60d7c0c3-85f7-4acf-8cd1-8eb096175d9e","resolution":{"observed_at":"2026-08-11T11:19:16.656005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.604479Z","title":"Apostolov and S","venue":null,"work_id":"e1215c90-6a0a-4eb5-bfe5-4b90c4c287f6","year":2004},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.486644Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:9524d857f976ae73503ac5f36a0c68aa36381959832c76aeaa8b2d365fe0f2b0","observation_id":"aa10259b-0366-4d40-9fd1-733d3b9dc2ce","resolution":{"observed_at":"2026-08-11T11:19:16.612833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0702063","last_updated":"2007-02-08T18:36:43Z","snapshot_observed_at":"2026-08-15T10:48:16.645187Z","submitted_at":"2007-02-08T18:36:43Z","title":"Lectures on complex geometry, Calabi-Yau manifolds and toric geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0702063","snapshot_observed_at":"2026-08-11T11:19:15.502550Z","title":"Bouchard, Lectures on complex geometry, Calabi-Yau manifolds and tor ic geome- try, preprint arXiv: hep-th/0702063, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.502550Z"},"links":{"cited_paper":"/paper/hep-th/0702063","citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:02b3c5f8774ee79180828ba9c4d36e6083daf2fe075b276a5b0c0a48a1ea248b","observation_id":"594a7c4f-2203-4644-8cd4-ccd465917c20","resolution":{"observed_at":"2026-08-11T11:19:15.502550Z","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":"2026-08-11T11:19:16.574607Z","title":null,"venue":null,"work_id":"857526e3-ce4e-41be-8bbf-de1154854465","year":1987},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.518144Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:1ac36b6c1802142038e18a334e6f288627c5c1be9c4718c69dcdd6db5a53ec74","observation_id":"fa865ee9-a97d-4d40-b315-73f4907a0154","resolution":{"observed_at":"2026-08-11T11:19:16.583667Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.545877Z","title":null,"venue":null,"work_id":"9b516f54-3ac8-422d-9ca2-6d0b31d67b54","year":1989},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.527793Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:b4334bf06daf865052d7f89860c3e17a1f0086eb8c13af71ca5ea2337e49137a","observation_id":"fa145ca1-a20c-485e-abe3-17ace61871b8","resolution":{"observed_at":"2026-08-11T11:19:16.554761Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.19486","last_updated":"2025-01-16T16:15:37Z","snapshot_observed_at":"2026-08-16T21:21:44.286006Z","submitted_at":"2024-07-28T12:42:19Z","title":"Complete non-compact $\\operatorname{Spin}(7)$-manifolds from $T^2$-bundles over AC Calabi Yau manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.19486","snapshot_observed_at":"2026-08-11T11:19:15.534047Z","title":"Cavalleri, Complete non-compact Spin(7)-manifolds from T 2-bundles over AC Calabi-Yau manifolds , preprint arXiv: 2407.19486 [math.DG] , 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.534047Z"},"links":{"cited_paper":"/paper/2407.19486","citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:5e121fe653c4767ac0d0c02ddd8bc7c7ed20f5548b70c44f3356465aca972b82","observation_id":"d57d8e98-2d4e-4573-9044-a9821ae1c3e9","resolution":{"observed_at":"2026-08-11T11:19:15.534047Z","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":"2026-08-11T11:19:16.518382Z","title":null,"venue":null,"work_id":"21345535-cd59-4bf0-a0e6-398f634bc575","year":2008},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.541733Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:f40002307c37c20bc78c4ad2a4f2cb5dcfb7b3fe21d5121d801345d2276a1b25","observation_id":"044a6c04-c73b-47a0-b11e-30bedf7f2e35","resolution":{"observed_at":"2026-08-11T11:19:16.527176Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.479762Z","title":"Cleyton and A","venue":null,"work_id":"16c4dc7d-04b9-42c7-8320-dd384e4b11bb","year":2002},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.547265Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:fcae9117940f04cfef276a38c759c4e6ea05a5053e176934e93b35a1371c9213","observation_id":"d66f32e3-b46e-43a1-b771-bf239f7c0088","resolution":{"observed_at":"2026-08-11T11:19:16.490966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.459554Z","title":null,"venue":null,"work_id":"0e5cb0fc-a653-4cb8-b3e0-6f3cc143bf2a","year":2024},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.553067Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:be888b498c9dfa08c70039b74800011fbaffac3ad73ba6323970099cc273561a","observation_id":"23e7e460-cd44-4a5d-9856-9702fc1fc875","resolution":{"observed_at":"2026-08-11T11:19:16.466096Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.432770Z","title":"Conti and A","venue":null,"work_id":"4578a499-c665-4544-b0fb-7087395f4cba","year":2007},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.558757Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:4e09c9fe13293201f3a335552fabdba6d357c9d839ebc00bd9b7b6c63a6b9c60","observation_id":"ab4f121a-a5fc-401c-88d2-9991957ab9b5","resolution":{"observed_at":"2026-08-11T11:19:16.441712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.401513Z","title":null,"venue":null,"work_id":"fda7f7dd-f15d-4cd0-aa3c-a2baed176187","year":2011},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.564751Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:822a8e32ef218d557919369e3d727ed61640c364e77c88bb8bfc90e11d12d0da","observation_id":"ba5b71e4-a80e-470f-aab2-21361107e6ca","resolution":{"observed_at":"2026-08-11T11:19:16.412103Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.371070Z","title":null,"venue":null,"work_id":"cccca627-9d1c-45c1-a2e8-4e5c55019536","year":2020},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.569453Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:b231829d551928128d559fc51390b0ebcf045af7aee6d3904c2e61dad2a5df3f","observation_id":"3ed96e7f-791c-4c67-9714-65d48efd9267","resolution":{"observed_at":"2026-08-11T11:19:16.377904Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.341540Z","title":"Foscolo, M","venue":null,"work_id":"da6c57f1-4892-4be8-b9bc-476ce9478cbb","year":2021},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.577839Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:22c7891e324277acd046324aaec57da3c8893691615134900a9db357de8cf726","observation_id":"a0803b23-c935-483c-94e5-e85e27a94cc7","resolution":{"observed_at":"2026-08-11T11:19:16.349859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.315968Z","title":null,"venue":null,"work_id":"a2191af3-9718-4077-b9f0-62773c66f437","year":2021},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.586363Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:44d960d544370e743a534879ec057001208607e0c32d603b8931df2d70e21308","observation_id":"2c08c3b7-3e57-492e-9684-0ad7730b439c","resolution":{"observed_at":"2026-08-11T11:19:16.322266Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.289415Z","title":"Futaki, H","venue":null,"work_id":"645b0305-87aa-4b13-99ca-26914a3862bd","year":2009},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.598342Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:6ecf3e9490b61fbf3f2dee6eb87886b47a00005746f883df68efb70012552d47","observation_id":"9bd36445-2784-4982-a49d-f8ba56b51742","resolution":{"observed_at":"2026-08-11T11:19:16.297761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.261207Z","title":null,"venue":null,"work_id":"f45aef26-5355-45f3-bac7-44d4acd5cafc","year":1978},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.607718Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:e64e0bad500f360c7507dec48a5005d7499d862197a66e2cdb04a5f4f0b59ba9","observation_id":"a2937892-fa5e-43e3-8c4c-844b75fe99af","resolution":{"observed_at":"2026-08-11T11:19:16.267999Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.231989Z","title":null,"venue":null,"work_id":"fc2121d7-b46c-4da2-a488-1c15e026733a","year":1982},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.615145Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:4e78f151ea5c7b6770966fccb9d4bb987246865ef7d1f3a1f281338679936b9b","observation_id":"4463c4cc-1458-4261-9dff-5da8d3480f4d","resolution":{"observed_at":"2026-08-11T11:19:16.238072Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.206336Z","title":"Li, C.-C","venue":null,"work_id":"8d5ae675-6798-43dd-91c8-12afb4f6b8ee","year":2009},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.625568Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:28685865c2e59a6feddb9a6eaf225d737db3d67b4c21611a1c56221ae3462570","observation_id":"3a1f8216-8ab8-4938-9bcf-47604f0dcc22","resolution":{"observed_at":"2026-08-11T11:19:16.214349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.174677Z","title":"Li, SYZ geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa type met- rics, Mem","venue":null,"work_id":"2d1099dd-df0e-445f-aca9-87433381f308","year":2023},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.633549Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:2d08b31e19765a3b5c0a9b8fae8f6272836a108676d3d17fc969c0fdf3dbbc01","observation_id":"9e2c1065-207b-4247-8672-69e2da17bd3f","resolution":{"observed_at":"2026-08-11T11:19:16.188404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.148018Z","title":null,"venue":null,"work_id":"edc1252d-fb98-4db1-a484-48720df99522","year":2012},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.643625Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:9f7b40440d24dfed5f1a3c76849ca5bb72996048ab7d0c340eb55039524caf7e","observation_id":"1ee87675-7858-4a24-9967-38d237c9de41","resolution":{"observed_at":"2026-08-11T11:19:16.157129Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.121960Z","title":null,"venue":null,"work_id":"543b1475-9667-48cb-9dd9-74a902c21f6f","year":2019},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.649808Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:30a78017b702f7f76f598e56177e976dd76e26b39a7d5e03c57f54af9668a1a1","observation_id":"08a672f3-7beb-4fd4-b3db-c528c1749fc9","resolution":{"observed_at":"2026-08-11T11:19:16.128490Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.03693","last_updated":"2024-07-04T07:27:53Z","snapshot_observed_at":"2026-08-16T13:37:09.689404Z","submitted_at":"2024-07-04T07:27:53Z","title":"Multi-toric geometries with larger compact symmetry","version":1},"cited_work":{"arxiv_id":"2407.03693","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.03693","snapshot_observed_at":"2026-08-11T11:19:15.791763Z","title":"Multi-toric geometries with larger compact symmetry","venue":"math.DG","work_id":"01b0b892-ff36-48a7-8e7d-3d15cdb424c4","year":2024},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.655096Z"},"links":{"cited_paper":"/paper/2407.03693","citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:6495e6e1170b94cf04228b818b744e86f4576dee5a673cac662d90907934a5ae","observation_id":"ff7c7216-422c-4a36-a7ec-cda60420ff8f","resolution":{"observed_at":"2026-08-11T11:19:15.804191Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.087621Z","title":"Martelli and J","venue":null,"work_id":"dc85eac6-ffdb-4f07-8a3d-048930647625","year":2006},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.662098Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:4a8e4fe6cbc5d60673540d5a75b81ecf02dcc86adf04b8646bf65c04735b448d","observation_id":"77fe9fe4-ac2c-4898-bae5-186a5e1d80df","resolution":{"observed_at":"2026-08-11T11:19:16.096271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.050828Z","title":null,"venue":null,"work_id":"99554aeb-7c56-4e29-acfd-799ffd748a4a","year":2010},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.669751Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:74cc545e98da403feafb329792abc7fe59e840226c70dd70cb540206d002cd5c","observation_id":"e8f9b00e-6d14-45ae-a6d7-0bf1eeceece3","resolution":{"observed_at":"2026-08-11T11:19:16.061716Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:16.012353Z","title":"van Coevering, Ricci-flat K¨ ahler metrics on crepant resolutions of K¨ ahler cones , Math","venue":null,"work_id":"84635340-9d46-432c-8233-b0a2e9a9785a","year":2010},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.677843Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:49c2ffde743eb389b743a4a38f6d866baa38fc3ee61794c1e723e836c2a1de71","observation_id":"7155f7e3-b4fb-482c-9004-641e93127fa6","resolution":{"observed_at":"2026-08-11T11:19:16.030458Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:15.983502Z","title":null,"venue":null,"work_id":"270287bf-b4df-45b0-8bcd-b78e5948cbe1","year":2011},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.692049Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:92d5bbc6f8b4964ec0c924d7edd2263f2d74770a31a8811fb73b810782b6c789","observation_id":"ab097961-d0f3-467d-9815-2fa6f6559426","resolution":{"observed_at":"2026-08-11T11:19:15.993290Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:15.947277Z","title":"Xie and S.-T","venue":null,"work_id":"79ee7d8e-a5de-405f-9246-1dab32d123bd","year":2017},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.708445Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:43f8680bb3dcbaf003a368168580181fb47a63ab0bf4cd6875f217a272cf2e06","observation_id":"ff24ea12-952e-47c1-9bf7-2caa7bf2d165","resolution":{"observed_at":"2026-08-11T11:19:15.955694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T11:19:15.910465Z","title":"Yeats, A combinatorial perspective on quantum field theory , Springer Briefs in Mathematical Physics, vol","venue":null,"work_id":"e2082005-999c-4844-80a2-de88b540e257","year":2017},"citing_paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T11:19:15.715865Z"},"links":{"citing_paper":"/paper/2412.15769"},"observation_digest":"sha256:12f8b3dabb0dfa267940c0adf52908de886644aa4a51f3873384de061a590c95","observation_id":"78643dc8-9df9-4556-8907-ba7d7ecff2b5","resolution":{"observed_at":"2026-08-11T11:19:15.921174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.15769","last_updated":"2024-12-20T10:40:51Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-14T02:29:46.172065Z","submitted_at":"2024-12-20T10:40:51Z","title":"Cohomological lifting of multi-toric graphs"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":1,"verified_fuzzy":13},"total_outbound_references":30},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2412.15769."}