{"as_of":"2026-08-08T12:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:854d802f2ebdf5235f323cac2eb9f4d2aac282c1291e7bd251c50de63efaaa97","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T13:34:58.531678Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2512.24047/citation-record","integrity":"/paper/2512.24047/integrity","json":"/paper/2512.24047/citation-record.json","paper":"/paper/2512.24047"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.347031Z","title":"Angel, T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.347031Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:c3fc904079bc91ef0b5e014bdf58e1de7ff46c27e848b39b6ab3d2c797185abe","observation_id":"2b9358ca-59a0-42b6-a597-ba9f2f48a4cf","resolution":{"observed_at":"2026-08-03T13:34:58.347031Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.351328Z","title":"Asselah, I","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.351328Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:458f8262c439e7625ae06688df148d3c733f5cbd332ab671754d073ee46dbb73","observation_id":"ccf243d0-03e6-4917-9cc0-f2fca3b9e948","resolution":{"observed_at":"2026-08-03T13:34:58.351328Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.354850Z","title":"Asselah and B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.354850Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:71bc3cdc021f22728ecb9d0e96375a7b3d3fa6ddc01111b6bd667c4258ac1092","observation_id":"277f876c-1387-44d2-baef-4353d66ad6c7","resolution":{"observed_at":"2026-08-03T13:34:58.354850Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.358439Z","title":"Asselah, B","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.358439Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:ccba73cbfa1b58ca56e279c4ee1b38d8fa806b68484b0eb30f52a4e231d24272","observation_id":"7638bd0b-2c3d-4893-9a16-114083c2c2e2","resolution":{"observed_at":"2026-08-03T13:34:58.358439Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.361752Z","title":"Asselah, B","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.361752Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:da5c0c50571b45241b372c286d4b93aceba77db7a25ed1e9f6d1dcf2346f657b","observation_id":"9a237dd6-39f2-47ba-896e-28b5101ca237","resolution":{"observed_at":"2026-08-03T13:34:58.361752Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.365484Z","title":"Asselah, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.365484Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:885baed626692fd627148f8b92150784ef645d807f768a994280e2bf62c19959","observation_id":"baa77ad7-b0c9-4fd8-9e71-3e5e89c7b982","resolution":{"observed_at":"2026-08-03T13:34:58.365484Z","resolver_source":null,"status":"malformed_identifier"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.369129Z","title":"Baran (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.369129Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:937f668acec7eec48b91f1fb45f484326327a7e29704a64180281f29b92ca6ae","observation_id":"bc151d33-1f44-4a04-acbb-050c0b06a44e","resolution":{"observed_at":"2026-08-03T13:34:58.369129Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.372234Z","title":"Benjamini and N","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.372234Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:dab46d1c1660bd3d4e3bdc67df26b8759afdd92e6d7d0b32b5a3f7d79401c79b","observation_id":"2380e063-b5d3-440e-ad87-879607b54d18","resolution":{"observed_at":"2026-08-03T13:34:58.372234Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.375515Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.375515Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:8529fd5b6aa8e212d30953e21482bba9306475ea07f574220577de9a6f98278f","observation_id":"5d177922-9a11-4ad9-bea9-a74c907e0569","resolution":{"observed_at":"2026-08-03T13:34:58.375515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.13735","last_updated":"2024-02-22T03:34:40Z","snapshot_observed_at":"2026-08-04T05:38:24.480356Z","submitted_at":"2024-02-21T11:57:50Z","title":"Branching capacity and Brownian snake capacity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.13735","snapshot_observed_at":"2026-08-03T13:34:58.378701Z","title":"Bai, J.-F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.378701Z"},"links":{"cited_paper":"/paper/2402.13735","citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:23e7c7c0f0b33f052d34448dbe6c80da7bc38340814eae9a65149cc75abf69b4","observation_id":"2a1fbf59-6668-4ce4-a726-0b6cff1dabe0","resolution":{"observed_at":"2026-08-03T13:34:58.378701Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.382270Z","title":"Bai, J.-F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.382270Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:32bbe376beff2a6236e1f757f0c57a3655083cda4e45929ecfdb956d407b30bd","observation_id":"8648ea33-c52a-45c4-b087-53dc15badaaa","resolution":{"observed_at":"2026-08-03T13:34:58.382270Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.385978Z","title":"Bai and Y","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.385978Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:41587483b60e3ddf3b06a3ece357cab0387d99f96572917c0f3e362d16e6716e","observation_id":"a3e8432d-722f-41fe-864e-017055837096","resolution":{"observed_at":"2026-08-03T13:34:58.385978Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.389759Z","title":"Bai and Y","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.389759Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:a07db962c6b7a0b93501df5d149643d3f50bf926c24eadf069a4c34c0efe4848","observation_id":"dbda60f5-3a9c-49bd-9fb3-0788430066d3","resolution":{"observed_at":"2026-08-03T13:34:58.389759Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.392794Z","title":"Bai and Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.392794Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:0880d6c6b8017db78c92eb792dfa1455f2b3284ca98cdf780b8e83751d8503b7","observation_id":"193c1e9f-87f5-4efc-97b7-3b1c5b52dc17","resolution":{"observed_at":"2026-08-03T13:34:58.392794Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.395890Z","title":"Bai and Y","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.395890Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:ff80468a95fdfaf59afd2592fc69a9e3e616793b9d6cd978ff4b78de08b00ec1","observation_id":"f989c0d6-6510-4d09-995f-407549d1ecb4","resolution":{"observed_at":"2026-08-03T13:34:58.395890Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.398943Z","title":"Berestycki, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.398943Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:2ad1a201a6b1e3b2d98b550d7f975e3a957d957a09054ac3c70e2844d6e71738","observation_id":"fcb79a33-4d4c-4722-8db8-4ca697ce7765","resolution":{"observed_at":"2026-08-03T13:34:58.398943Z","resolver_source":null,"status":"malformed_identifier"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.402170Z","title":"Bousquet-M´ elou and S","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.402170Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:eb71a08f180ec299a900cd73dcb38a79ff2f15351266f4f22b7fe853dd31ee42","observation_id":"134b2820-a3f8-4401-bb39-f7f8057d43bb","resolution":{"observed_at":"2026-08-03T13:34:58.402170Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.405253Z","title":"Cardona-Tob´ on, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.405253Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:2b9a5c0d6a61b67c52284acdc72918b24986b34e4b1929fbd93e8b2c709692a4","observation_id":"98a289fa-78b0-40a0-a9e9-363c84e871b9","resolution":{"observed_at":"2026-08-03T13:34:58.405253Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.408349Z","title":"Cardona-Tob´ on and S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.408349Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:fbf60085315b6f2351bf2abcb3b16459310748c0c0286e8f966082bc08d392b7","observation_id":"f55af291-b4c9-4548-a99d-dce851254a0c","resolution":{"observed_at":"2026-08-03T13:34:58.408349Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.411417Z","title":"Chang (2017)","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.411417Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:ca5fdd5e9ed4f9bf482fa0804a57ff2f1debab83ae179dae38bc88a584b76048","observation_id":"188c0433-8af9-4a0d-b9bb-7b7242a43d73","resolution":{"observed_at":"2026-08-03T13:34:58.411417Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.414359Z","title":"Devroye and S","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.414359Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:1a92b51f0d1104f40dd796c87f21e30e38b4a4e7484ab50bebcb9dd936519c55","observation_id":"ee07e73b-487f-4d5c-8a61-07202a56e433","resolution":{"observed_at":"2026-08-03T13:34:58.414359Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.417421Z","title":"Durrett (2010).Probability: Theory and Examples, volume 31 ofCamb","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.417421Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:4ae3203a9d3b4cffafcbc39832e71874514580c147b1343715cb2ee55e739b26","observation_id":"43ff088d-6f9d-4e5a-896d-cec8bc445d68","resolution":{"observed_at":"2026-08-03T13:34:58.417421Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.420533Z","title":"Dvoretzky and P","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.420533Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:d720c8b74ab37bacfb76d2450884a4cf08d0722ccdcdb0c9a76f82cde5ad7e5c","observation_id":"5dadf7aa-c177-4ba1-9bbd-cc043be2770d","resolution":{"observed_at":"2026-08-03T13:34:58.420533Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.423786Z","title":"Fleischman (1978)","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.423786Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:6f4dccf1d80054a3937ab5e751f6aa477a96a2e07fdc10b349c7f14b3e0ec4d1","observation_id":"19fbb7bd-42a1-4bac-b2d9-7685d2bd7cda","resolution":{"observed_at":"2026-08-03T13:34:58.423786Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.426924Z","title":"Harris, E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.426924Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:c74aadff47b7e41516e3b4b885a053a4b57062f2e37be7682942083c2aa664e7","observation_id":"030921ad-486e-4560-9cd7-575ececaf818","resolution":{"observed_at":"2026-08-03T13:34:58.426924Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.430101Z","title":"Geiger (2000)","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.430101Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:692037b34afaa1ff2318ecf23c54d5fdf1714bca2c90eef741d075bf85c33ea5","observation_id":"a41af202-e119-41b2-bb83-1362d6e7e35a","resolution":{"observed_at":"2026-08-03T13:34:58.430101Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.433328Z","title":"Grama, R","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.433328Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:a7ca4c5353be09396def52f1d6d97eb3ef78d1058182293f6c5ddd5ea9ef515c","observation_id":"92de8e08-8c11-4d00-b28a-88c73cafbc04","resolution":{"observed_at":"2026-08-03T13:34:58.433328Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.436899Z","title":"Janson and J.-F","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.436899Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:070301633e2f79df54cb193609d4f9102eadb0e47622e912a658a516af92cfcd","observation_id":"08eb3ad1-1225-4119-b5c5-ca9a5d13a280","resolution":{"observed_at":"2026-08-03T13:34:58.436899Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.439969Z","title":"Jain and S","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.439969Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:00efca3fbb58511584c51c8998327fc6faf145be650fe9ef6fd872d4866b4a8d","observation_id":"c2a1900d-848b-4458-8ed2-3d80d482e51a","resolution":{"observed_at":"2026-08-03T13:34:58.439969Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.443245Z","title":"Kotz and F","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.443245Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:827c9e5377fac9ba40a576a164a9df3360fe42fbcbdc2252c7592681173c59e6","observation_id":"7ef2e945-0ecf-4a43-b499-25439a9c037a","resolution":{"observed_at":"2026-08-03T13:34:58.443245Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.446298Z","title":"Lalley and X","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.446298Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:07fb9d2ee033446402e1facb475d52d176b88716c6d1a836aca661afd223e987","observation_id":"3da3e2e1-6c7e-4817-bcc1-4bf9f70adcc8","resolution":{"observed_at":"2026-08-03T13:34:58.446298Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.449371Z","title":"Lalley and X","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.449371Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:4e7d7315426e6d829ab4cdf4fa743a173eea2d310e37319204a4096eb479813d","observation_id":"10266916-debe-46fe-890f-85f43fa407e0","resolution":{"observed_at":"2026-08-03T13:34:58.449371Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.452368Z","title":"Lawler and V","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.452368Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:034b2023ec9f4c9c9c22ec4d187439e1c2cf863315804555cad6f20091ae10a4","observation_id":"948a922b-d308-46cb-b3c9-5e36fc085c87","resolution":{"observed_at":"2026-08-03T13:34:58.452368Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.455669Z","title":"Le Gall (1986)","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.455669Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:07d6b8771e48e4ad24510c9f2e2d02d2593dfc681d7b820e2dbf8fc47263f594","observation_id":"ffdc3178-ef8a-46f2-9c82-d09fcbc82007","resolution":{"observed_at":"2026-08-03T13:34:58.455669Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.458962Z","title":"Le Gall and S","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.458962Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:09164b658d0d518516d636dd79e01ae4d445426a643f93f7472c42cb967ba60c","observation_id":"7081efa5-e8f3-4098-b055-ebaa0ab37e8f","resolution":{"observed_at":"2026-08-03T13:34:58.458962Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.462245Z","title":"Le Gall and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.462245Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:922c00a237281d079593f3fbca3b0b235d0e7b180a45f2779f1ede99b3df987e","observation_id":"926a83f3-9398-455e-8f17-6645c2514a85","resolution":{"observed_at":"2026-08-03T13:34:58.462245Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.465292Z","title":"Le Gall and M","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.465292Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:59cc3a6dbb7d7f44c3eb14bea9ae0f25403d5bf8caba42cd5ddd3fe92fd0cdef","observation_id":"fc7987da-081e-458d-978b-05aa195491f7","resolution":{"observed_at":"2026-08-03T13:34:58.465292Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.468384Z","title":"Legrand, C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.468384Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:7040d492c6bb0aa583d4bbe4488a6de2580015e954a595bef16b5f2eff07d628","observation_id":"393548fe-0594-41bc-b65a-5b85a7617555","resolution":{"observed_at":"2026-08-03T13:34:58.468384Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.471769Z","title":"Lyons, R","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.471769Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:6e83f85efefe4dc6ab13d513347ffacb5b791da3ea6e779f3aae9256d61a4688","observation_id":"78e58162-b55f-4c83-994b-381a75e08a83","resolution":{"observed_at":"2026-08-03T13:34:58.471769Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.475769Z","title":"Marzouk (2020)","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.475769Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:a7201f456f85a0d622654598b98d07fd2d9d702a3a0d855d78bb103e4849dc86","observation_id":"9a63ed49-62db-42cd-936d-ca83f4bd6592","resolution":{"observed_at":"2026-08-03T13:34:58.475769Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.478997Z","title":"Maillard and J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.478997Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:4716e8eb520ff3f45e194c03afcec47b1535de89714f6b84bf84ff6b2c4be356","observation_id":"97b47be2-0939-4f17-bcd4-fc517d6461b0","resolution":{"observed_at":"2026-08-03T13:34:58.478997Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.482001Z","title":"Pek¨ oz and A","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.482001Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:d46ed12cbb6f6ab2a32924bf4fbc473120d09a23753be99654aad39b7168c40c","observation_id":"15f5717b-cf74-4c2d-96b6-f87ac3a47de0","resolution":{"observed_at":"2026-08-03T13:34:58.482001Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.485598Z","title":"Pek¨ oz, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.485598Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:727de34c21f3eed35f2fe474564300493fd0a24b45b08f696603dad510955277","observation_id":"ff382feb-2c71-41dc-82b9-6110dd659dc6","resolution":{"observed_at":"2026-08-03T13:34:58.485598Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.488901Z","title":"Powell (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.488901Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:93277cfd604fdaea0510ec66c78cd3c934ba6487a1937d1afc06c47c769c6414","observation_id":"60b4d099-002d-41cd-9c4d-eda860ecfc34","resolution":{"observed_at":"2026-08-03T13:34:58.488901Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.492095Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.492095Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:e7a1667ae7bf084169efac280271222cd5a7731532b170cc51ed79832694362f","observation_id":"6579455e-90c6-4baf-a132-800baa9ce8ae","resolution":{"observed_at":"2026-08-03T13:34:58.492095Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.495171Z","title":"Revuz and M","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.495171Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:2e36463e5fa8e543ffd2df1970db1929f80aeaccb6fdff963c68511f8f86c8d3","observation_id":"85851ca7-67ab-4dc2-9004-8146712f1cf5","resolution":{"observed_at":"2026-08-03T13:34:58.495171Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.498302Z","title":"Schapira (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.498302Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:2a792b3821b6d60ae940a84bf0fa25acfe1fe657968077e98bb7b9ce9b39fbb0","observation_id":"23e281a3-d606-49c7-aef8-b220345a5968","resolution":{"observed_at":"2026-08-03T13:34:58.498302Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.501434Z","title":"Sugitani (1989)","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.501434Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:a0656f8d5d020ea686e85b44ddb141f35684bff7bb49eafcfa7a8843eb340825","observation_id":"5c34a32d-1bcf-428c-bcc7-29c643bc2426","resolution":{"observed_at":"2026-08-03T13:34:58.501434Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.504525Z","title":"Villani (2003).Topics in Optimal Transportation, volume 58 ofGraduate studies in mathematics","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.504525Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:d036ec296827a027c1b27980f01bade9c19e5a39fb10fb23e3255d4ffc4686fe","observation_id":"b75078e3-255d-4c45-a334-35064c103c01","resolution":{"observed_at":"2026-08-03T13:34:58.504525Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.507713Z","title":"Watanabe (1968)","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.507713Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:9e6d17cec2d95c8301ac86f67d4f7b7e95aad9db388ee2a036fd91af2c69956d","observation_id":"389f350e-48c6-4ff6-bac9-e2868d836e93","resolution":{"observed_at":"2026-08-03T13:34:58.507713Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.510880Z","title":"Yaglom (1947)","venue":null,"work_id":null,"year":1947},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.510880Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:ce4234dd8ad414975e33550e6fc9be09b0a0143de988517533ebc63163e0ecd4","observation_id":"4334d4a8-3cbf-4e5d-8c76-3d6597090e2e","resolution":{"observed_at":"2026-08-03T13:34:58.510880Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.514689Z","title":"Zaitsev (1998)","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.514689Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:25434274fdc091e92f2d1ca0e10de6a2e27c1285855c7d04d34fe1a138c42494","observation_id":"1160e194-cbd6-4a22-ae1b-77be80e1cbcb","resolution":{"observed_at":"2026-08-03T13:34:58.514689Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1611.10324","last_updated":"2017-01-31T04:35:30Z","snapshot_observed_at":"2026-08-06T09:31:49.805635Z","submitted_at":"2016-11-30T19:28:09Z","title":"On the critical branching random walk I: Branching capacity and visiting probability","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1611.10324","snapshot_observed_at":"2026-08-03T13:34:58.517965Z","title":"Zhu (2016)","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.517965Z"},"links":{"cited_paper":"/paper/1611.10324","citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:d818b4485f6f3b3a47b17748835024250e26fd7be645e195e149315bdcefa89d","observation_id":"c7e8e508-e831-4fc1-96e2-5a2775463852","resolution":{"observed_at":"2026-08-03T13:34:58.517965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.00161","last_updated":"2017-01-31T05:07:45Z","snapshot_observed_at":"2026-07-06T05:20:55.923354Z","submitted_at":"2016-12-01T06:47:56Z","title":"On the critical branching random walk II: Branching capacity and branching recurrence","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.00161","snapshot_observed_at":"2026-08-03T13:34:58.521393Z","title":"Zhu (2016)","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.521393Z"},"links":{"cited_paper":"/paper/1612.00161","citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:b8a923cf05436f892e7a26c355c5bcb891ca8680767fa27a3f9ab162361b178d","observation_id":"c918be97-2781-40c6-9222-cedc8da2cb31","resolution":{"observed_at":"2026-08-03T13:34:58.521393Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.10858","last_updated":"2019-12-02T11:47:11Z","snapshot_observed_at":"2026-07-06T07:23:46.396438Z","submitted_at":"2018-12-28T01:19:42Z","title":"Branching interlacements and tree-indexed random walks in tori","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.10858","snapshot_observed_at":"2026-08-03T13:34:58.524669Z","title":"Zhu (2018)","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.524669Z"},"links":{"cited_paper":"/paper/1812.10858","citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:e451c6168c014242980bd1c16a4615cbf38b838167f76be3b8a7ce71c078670f","observation_id":"b1ac0a80-be8b-4415-bcc0-6f86ce9650a4","resolution":{"observed_at":"2026-08-03T13:34:58.524669Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.528514Z","title":"Zhu (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.528514Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:e880bb6f76ae912b8f9ae8684fa1a3c6ac969a66d61409ab7b4fd0f14b0b191e","observation_id":"18e21344-b071-4079-8085-c232cbf75f0a","resolution":{"observed_at":"2026-08-03T13:34:58.528514Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T13:34:58.531678Z","title":"Zhu (2021)","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-03T13:34:58.531678Z"},"links":{"citing_paper":"/paper/2512.24047"},"observation_digest":"sha256:c0db911be0c0bd0e9d5320d6d230a48ab9a0f7fda5278db124e9e0880249a93b","observation_id":"7b2e7eb5-d2f8-4b85-bb57-9260a4367042","resolution":{"observed_at":"2026-08-03T13:34:58.531678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.24047","last_updated":"2026-07-24T08:39:43Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-07T19:49:04.267927Z","submitted_at":"2025-12-30T07:44:41Z","title":"Yaglom theorem for critical branching random walk on $\\mathbb{Z}^d$"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":55,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":57},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2512.24047."}