{"as_of":"2026-08-11T07:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f3277b2002a050f43e14664a633defb75e534b6d97a3350be6581c4c2396d66d","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T06:03:03.386325Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:32:39.441003Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T20:32:39.876969Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"cited_work":{"arxiv_id":"2506.06559","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.06559","snapshot_observed_at":"2026-08-06T20:32:39.876969Z","title":"Bi-infinite incipient cluster in high dimensions","venue":"math.PR","work_id":"2ed4a687-2cb0-41b9-ada1-6f938a17a2a4","year":2025},"citing_paper":{"arxiv_id":"2507.02676","last_updated":"2026-06-29T13:46:55Z","snapshot_observed_at":"2026-08-09T09:23:35.820380Z","submitted_at":"2025-07-03T14:38:47Z","title":"On Loops in critical high-dimensional percolation","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:32:39.441003Z"},"links":{"cited_paper":"/paper/2506.06559","citing_paper":"/paper/2507.02676"},"observation_digest":"sha256:cc4939917ebe77f737dbfe93e7b7c5213f782d7de08efb6c1538eb3033a35027","observation_id":"d4e572b7-69e0-4e8d-9542-d9d3e2f35d13","resolution":{"observed_at":"2026-08-06T20:32:39.880503Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.06559","snapshot_observed_at":"2026-08-01T05:00:15.917752Z","title":"Cabezas, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22387","last_updated":"2026-07-24T15:12:59Z","snapshot_observed_at":"2026-08-07T18:00:15.814092Z","submitted_at":"2026-07-24T15:12:59Z","title":"Super-Brownian limits and the $k$-point function for high-dimensional percolation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T05:00:15.917752Z"},"links":{"cited_paper":"/paper/2506.06559","citing_paper":"/paper/2607.22387"},"observation_digest":"sha256:4f990550b6010446637e2b44942469674309e332b47a8ac5dca6d0da66749c84","observation_id":"25fdfcee-623e-41df-9c87-0d0b88d72309","resolution":{"observed_at":"2026-08-01T05:00:15.917752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2506.06559/citation-record","integrity":"/paper/2506.06559/integrity","json":"/paper/2506.06559/citation-record.json","paper":"/paper/2506.06559"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T06:03:03.572955Z","title":"Ben Arous, M","venue":null,"work_id":"ed9b838e-34dd-4002-bc84-05a94373a08d","year":2019},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.329322Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:61004225644c8795ffe0ad5d46b16f379db64deeffced686773b9bceced61f9d","observation_id":"0e62e1aa-e2e2-436c-bb00-7497b04cb35b","resolution":{"observed_at":"2026-08-07T06:03:03.575449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.566266Z","title":"Ben Arous, M","venue":null,"work_id":"11c8be68-f768-4aef-b464-97780f4bad6d","year":2019},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.332573Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:a8135f76f2cf7b4191c408ac75501deaa2d8445f098bfe0261838c11a039d570","observation_id":"1c15f973-5024-48be-8154-809b05065369","resolution":{"observed_at":"2026-08-07T06:03:03.568707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.22538","last_updated":"2025-03-28T15:36:58Z","snapshot_observed_at":"2026-08-10T11:00:25.554386Z","submitted_at":"2025-03-28T15:36:58Z","title":"Scaling limit for the random walk on critical lattice trees","version":1},"cited_work":{"arxiv_id":"2503.22538","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.22538","snapshot_observed_at":"2026-08-07T06:03:03.433577Z","title":"Scaling limit for the random walk on critical lattice trees","venue":"math.PR","work_id":"35628d65-7ae5-4885-ab0b-c29c6ac017ca","year":2025},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.334852Z"},"links":{"cited_paper":"/paper/2503.22538","citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:b401c09dde1539a64623765e57530fdb997bfa63a94e5be529515eae59cea14e","observation_id":"ebfa33d0-5ee2-4ac1-886e-f6181e923880","resolution":{"observed_at":"2026-08-07T06:03:03.436597Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.559852Z","title":"van den Berg and H","venue":null,"work_id":"49254b6a-de48-4779-9951-7d519ac5eff6","year":1985},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.337473Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:870b25bf731b3db9bc094e8be1a2426c14283cd72506d0839e5340312794e5c0","observation_id":"536626a1-85c1-4e5c-9501-cb397a6a4672","resolution":{"observed_at":"2026-08-07T06:03:03.562151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.19230","last_updated":"2025-03-25T00:33:17Z","snapshot_observed_at":"2026-08-07T16:39:44.317618Z","submitted_at":"2025-03-25T00:33:17Z","title":"Random skeletons in high-dimensional lattice trees","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.19230","snapshot_observed_at":"2026-08-07T06:03:03.339890Z","title":"Cabezas, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.339890Z"},"links":{"cited_paper":"/paper/2503.19230","citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:8dcc644ec25df83f97d1ecfd192f69812a9694f5a846a143a3a99521059176ab","observation_id":"3cba01a3-3c24-43da-8649-36d4d65016fa","resolution":{"observed_at":"2026-08-07T06:03:03.339890Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.10882","last_updated":"2025-02-15T18:55:06Z","snapshot_observed_at":"2026-08-09T09:26:48.344961Z","submitted_at":"2025-02-15T18:55:06Z","title":"Robust construction of the incipient infinite cluster in high dimensional critical percolation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.10882","snapshot_observed_at":"2026-08-07T06:03:03.342392Z","title":"Chatterjee, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.342392Z"},"links":{"cited_paper":"/paper/2502.10882","citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:54a6f04c869253d390db19ce28abae2a08f351821734250f502e92f945c620b6","observation_id":"9b0eea4c-b5a4-42d0-bfb9-0525ffd12781","resolution":{"observed_at":"2026-08-07T06:03:03.342392Z","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":"2026-08-07T06:03:03.553235Z","title":"Damron and A","venue":null,"work_id":"af0bcdb7-ed48-4cea-aff4-ab61892c1fa0","year":2011},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.345134Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:1088899451f5479c34248c7fa908c0c43c621f4e2dd2fc3fed708912e9ee4fa3","observation_id":"f788ba94-285e-4614-bc35-20026d2290ab","resolution":{"observed_at":"2026-08-07T06:03:03.555573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.546757Z","title":"Fitzner and R","venue":null,"work_id":"d2d97579-67e4-40eb-bbb5-0218227d0832","year":2017},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.347214Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:eb21e20b9a587414da47479fcb2d06044f508e5db9e3e5065c8084e883a0d674","observation_id":"c5fdbdb8-5978-441e-8dbc-229a200a5c0c","resolution":{"observed_at":"2026-08-07T06:03:03.549139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.539870Z","title":"Grimmett","venue":null,"work_id":"11efbd0b-4214-4b90-a474-ebc16e0308e9","year":1999},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.349780Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:abd98f8fda054b865d2ba54a2a9306379cc594ca93cfceba218ee30607f8998f","observation_id":"ddb1505f-c7af-43d1-ad58-b05cfd55364a","resolution":{"observed_at":"2026-08-07T06:03:03.542395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.533355Z","title":null,"venue":null,"work_id":"d569339e-bb26-4a5c-a8ee-98a5ef8c0b07","year":2008},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.351940Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:11982c4419e52df152d34fe905cb9e2debbd48e3b9487fa5787225998cd05fa3","observation_id":"143d49d5-6549-4afc-bd58-fb16ba8514c2","resolution":{"observed_at":"2026-08-07T06:03:03.535787Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.526784Z","title":null,"venue":null,"work_id":"68b35de8-de51-44d4-acd2-f01bdbab1996","year":2003},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.354117Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:464e1886ad0930231650cebd007b7ca9306ca404161e6eda76785526dad377de","observation_id":"3eba4243-56eb-40e3-8c4e-bc9fa04b60a5","resolution":{"observed_at":"2026-08-07T06:03:03.529253Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.520186Z","title":"Hara and G","venue":null,"work_id":"487347d7-ca66-4c15-ad83-e3686b0f7acf","year":1990},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.356194Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:8b45ad68269e205d37816dcd0c16bfd94f5ead16148d2198a8084a20729263e6","observation_id":"9353f166-31f5-4977-aa72-5430d9b43f92","resolution":{"observed_at":"2026-08-07T06:03:03.522516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.513517Z","title":"Hara and G","venue":null,"work_id":"3ff89839-3f62-4e0b-af7d-eb0d7566adbd","year":1995},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.358438Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:f9773e5c3ef7c9e21ab25f21c82e5a9eaa63447bdff0b2f4ce17a102f8fee40a","observation_id":"d4c14b27-99f5-4d13-a3c6-3adcb9e09d19","resolution":{"observed_at":"2026-08-07T06:03:03.515928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.506554Z","title":"Hara and G","venue":null,"work_id":"cf607f88-a087-411a-90fa-3ddb50f16288","year":2000},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.360499Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:3a4014bd07b5efa6e44d4bdb90063fcd0b12853a6ecda73706981e0e7cf739da","observation_id":"26567f55-5fe9-4797-b753-2d68906e96ce","resolution":{"observed_at":"2026-08-07T06:03:03.509026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.499373Z","title":"Hara and G","venue":null,"work_id":"bf46b810-96b4-48ba-96e3-1dda15608e82","year":2000},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.362648Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:54e2f58828bb77145dda2578f95fec5c6e8c846b4cfc8e21db151a1684d00d0a","observation_id":"b05b826b-15ff-4d29-91d8-cd41f38e1860","resolution":{"observed_at":"2026-08-07T06:03:03.502133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.491946Z","title":"Heydenreich, R","venue":null,"work_id":"0fcd6a13-5954-4296-b25b-d5446a325f85","year":2014},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.365459Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:401c9520b9e045f309e627206174ac6590fc7814f3eb928b66a9d18e4c8a79e9","observation_id":"43e14d8b-c13f-438f-86d2-7f8141c1cd7c","resolution":{"observed_at":"2026-08-07T06:03:03.494402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.485041Z","title":"Heydenreich, R","venue":null,"work_id":"48b3a677-b6bf-4412-b7c5-552fdbe429cb","year":2008},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.367997Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:f7dd452e6fd353f796c3d5ff6877f70f83090a5461142c7a684dccbbb85ce837","observation_id":"f1dcdbfa-24a2-4a3a-b922-5a476d30e356","resolution":{"observed_at":"2026-08-07T06:03:03.487593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.478272Z","title":"Heydenreich and R","venue":null,"work_id":"71664798-8adc-4f1c-a864-ce8d32799e08","year":2017},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.370562Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:92033ba67079d06fe0a00805b802897056ef8a5b0797f0b8976b280138af6b6a","observation_id":"ab663fdb-7e3a-4f96-896f-ebda097f953c","resolution":{"observed_at":"2026-08-07T06:03:03.480765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.470602Z","title":"van der Hofstad and A","venue":null,"work_id":"6ec511aa-346e-42d7-b4f1-eb12f3dd8b73","year":2004},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.373008Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:61e23a677ccd619b4726653948aed65cd418712b1cca31d8a65d60d784b59c0e","observation_id":"5d3d590a-d20d-4192-a701-90481176acdf","resolution":{"observed_at":"2026-08-07T06:03:03.473201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.463436Z","title":null,"venue":null,"work_id":"be6dc31a-eabb-4d77-9e89-11496f4de92b","year":2003},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.375181Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:7050576a89ffb437c124999908d4dcbcd954156b5996b6dcb1840629686202bb","observation_id":"53be61fe-5410-4114-984e-c48c59b8f5a4","resolution":{"observed_at":"2026-08-07T06:03:03.465947Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.456458Z","title":null,"venue":null,"work_id":"200e6fbb-6c37-4782-9f14-fa09f16aa7e5","year":1986},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.377742Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:ecee77a3aaa09395e72c570490d9817627045e2cf89f405bd4af862198f61f39","observation_id":"78974302-0c07-4801-aead-4d3b253ca39d","resolution":{"observed_at":"2026-08-07T06:03:03.458939Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.01507","last_updated":"2024-10-03T20:50:22Z","snapshot_observed_at":"2026-07-06T19:26:02.193680Z","submitted_at":"2024-10-02T12:59:17Z","title":"Two-sided infinite self-avoiding walk in high dimensions","version":2},"cited_work":{"arxiv_id":"2410.01507","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.01507","snapshot_observed_at":"2026-08-07T06:03:03.406573Z","title":"Two-sided infinite self-avoiding walk in high dimensions","venue":"math.PR","work_id":"d8fc43d3-c0a4-4040-87f3-35f8691815b9","year":2024},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.380420Z"},"links":{"cited_paper":"/paper/2410.01507","citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:1fcd391be064b12750736d5e0044529fd5bf61bf395f98da9d32c254b60f155f","observation_id":"77f4bdd3-0995-45dc-b4d8-0944fc35c07c","resolution":{"observed_at":"2026-08-07T06:03:03.411788Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.448763Z","title":null,"venue":null,"work_id":"9913c2a9-806c-447b-b137-175bef140bc7","year":2006},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.383435Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:4c6d05d2480917db36cca35b1dbbad0300b0f4bcdecaab48cdd761d51c965f56","observation_id":"54df3366-1291-4220-a078-a68704fd27ec","resolution":{"observed_at":"2026-08-07T06:03:03.451425Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-07T06:03:03.441370Z","title":null,"venue":null,"work_id":"cc1e800c-24dd-4491-86b3-0bd83273cf1e","year":2018},"citing_paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T06:03:03.386325Z"},"links":{"citing_paper":"/paper/2506.06559"},"observation_digest":"sha256:fce2d9bf92412ba6f3e7aaae1601a8db881737ed2e1b368d9c7bbb6fee6d3b62","observation_id":"7bdb07d6-5bce-4021-afb2-92a8ffc3ab2a","resolution":{"observed_at":"2026-08-07T06:03:03.443952Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.06559","last_updated":"2025-06-06T22:14:05Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-09T09:25:00.091435Z","submitted_at":"2025-06-06T22:14:05Z","title":"Bi-infinite incipient cluster in high dimensions"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":2,"verified_fuzzy":14},"total_outbound_references":24},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 2 inbound Pith citation observations for arXiv:2506.06559."}