{"as_of":"2026-08-16T19:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d18ba50a2f95cb645ad1aae8b4ca57a87fea91a3e552ad6dfa6b348239fa9827","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T23:29:17.272402Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-07T15:45:14.897070Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-12T00:11:14.015533Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"cited_work":{"arxiv_id":"2505.05392","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.05392","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"549319fb-99a5-493c-b700-3811d851b9ba","year":2025},"citing_paper":{"arxiv_id":"2604.25671","last_updated":"2026-04-28T14:03:47Z","snapshot_observed_at":"2026-07-06T23:11:30.068819Z","submitted_at":"2026-04-28T14:03:47Z","title":"Arithmetical Structures on Ladder Graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-07T15:45:14.897070Z"},"links":{"cited_paper":"/paper/2505.05392","citing_paper":"/paper/2604.25671"},"observation_digest":"sha256:6c33b83d16a25db5c5d6dce5455e4d24ed443b1cb2dcf3913a2d97f145a7ceee","observation_id":"e6044dac-a294-4969-9199-07e7256eee79","resolution":{"observed_at":"2026-05-12T00:11:14.029054Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.05392/citation-record","integrity":"/paper/2505.05392/integrity","json":"/paper/2505.05392/citation-record.json","paper":"/paper/2505.05392"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2020.11185","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.685123Z","title":"Bishop, Alexander Diaz-Lopez, Luis D","venue":null,"work_id":"57777d6a-8644-4ec5-9a54-e0629455ebfb","year":2020},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.167885Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:61b6410c8dd197339a2e9fd7eecc5be80a413bd46122d813cbc7806dee4b5651","observation_id":"25c945e4-a676-4e54-a159-8a3de13b1c7c","resolution":{"observed_at":"2026-08-15T23:29:17.693620Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/11729","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.563324Z","title":null,"venue":null,"work_id":"311e5863-50d6-433e-af4d-39edd91947c1","year":2024},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.174186Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:3226a85884cd4bf3a008487a0c5734999f2c29e48783d62790fe12c6c2dcfd8b","observation_id":"e99345ba-e83b-42f9-8194-84bb3ac7f639","resolution":{"observed_at":"2026-08-15T23:29:17.568882Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1012.0287","last_updated":"2011-09-23T06:26:25Z","snapshot_observed_at":"2026-08-15T05:01:25.016481Z","submitted_at":"2010-12-01T20:26:47Z","title":"Chip-Firing and Riemann-Roch Theory for Directed Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1012.0287","snapshot_observed_at":"2026-08-15T23:29:17.179553Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.179553Z"},"links":{"cited_paper":"/paper/1012.0287","citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:d458c53316447d91ebff7a40efc58f71a508c99b6cebe8bfbe4ca8f32678ba1c","observation_id":"d8fd1c9f-2c5e-4243-b467-ce26768db5d3","resolution":{"observed_at":"2026-08-15T23:29:17.179553Z","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":"10.24033/bsmf.2303","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.523139Z","title":null,"venue":null,"work_id":"6f805165-7acd-45e0-9e89-0699d664b0f8","year":1997},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.185916Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:bfe487f9d90eeeaeeeaf3a440a6547e15031a315a7e3458ada85cbffeb2d30cb","observation_id":"09f19bcb-517b-4ccb-82ec-852f352ac5bf","resolution":{"observed_at":"2026-08-15T23:29:17.530806Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.191766Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.191766Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:b72c478256af58b95b16391b43145037f2e9872cf054b3730861fef7d5160148","observation_id":"a87fd85f-e1a0-4647-ad8e-fc1100fa7d3b","resolution":{"observed_at":"2026-08-15T23:29:17.191766Z","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":"2026-08-15T23:29:17.775423Z","title":"Glass, Cyclic critical groups of graphs , Australas","venue":null,"work_id":"bbd14c9e-8f10-4639-864c-24ed17c5779c","year":2016},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.196747Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:162072b1bb5457de4825743e1a60d113809194e48c6ea2034aa1184dfe010ecc","observation_id":"63d190a4-b600-4899-b5ae-f3aa8b727055","resolution":{"observed_at":"2026-08-15T23:29:17.780320Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1018611014097","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.491214Z","title":null,"venue":null,"work_id":"379471e8-4457-4237-9265-69a6dbb6854c","year":1999},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.201663Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:905499a6465a74f605886c94463ca4d5714916d234080d788511299314e30b00","observation_id":"d37c8669-64c6-4ab6-a812-182e8ee7275f","resolution":{"observed_at":"2026-08-15T23:29:17.496328Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.disc.2018.07.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.472675Z","title":"Martin, Gregg Musiker, and Carlos E","venue":null,"work_id":"92901da4-2bc4-44b9-bbfe-c857c7efeffa","year":2018},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.207648Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:dc8073d599ba6ae2dc9a9df5fbf56e88a4670a7c6623e343cefbcd477189b702","observation_id":"0765503a-9ae5-440b-8b99-b05825c17562","resolution":{"observed_at":"2026-08-15T23:29:17.479049Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1504.06239","last_updated":"2017-06-12T20:58:26Z","snapshot_observed_at":"2026-08-14T22:51:16.973283Z","submitted_at":"2015-04-23T16:11:41Z","title":"Critical ideals of trees","version":2},"cited_work":{"arxiv_id":"1504.06239","doi":"10.48550/arxiv.1504.06239","metadata_source":"pith","pith_arxiv_id":"1504.06239","snapshot_observed_at":"2026-08-16T12:16:17.039197Z","title":"Critical ideals of trees","venue":"math.CO","work_id":"5bc46bc9-14e5-4321-b89e-af2a6afe759e","year":2015},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.212365Z"},"links":{"cited_paper":"/paper/1504.06239","citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:dd758ebfe5781b5e37af448cec0361fc69a064342e23d7f04efd4dfa8bb9ab78","observation_id":"8c0d5095-af28-479a-ac11-5a86b2ff23f6","resolution":{"observed_at":"2026-08-15T23:29:17.457704Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.laa.2017.09.018","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.421569Z","title":"Valencia, Arithmetical structures on graphs , Linear Algebra Appl","venue":null,"work_id":"1f298f06-97d2-4dda-b088-6883ffbccb99","year":2018},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.217711Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:379735a6df91d02ce9ad4ad98107e3e6733bb3737639261a6816e610256c9b4e","observation_id":"accf8fa3-3b2d-4914-8284-b7a534bc5c3e","resolution":{"observed_at":"2026-08-15T23:29:17.426792Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0219498818501475","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.403590Z","title":"Valencia, Arithmetical structures on graphs with connectivity one, J","venue":null,"work_id":"ed524f0e-96eb-45a5-9e80-79a009bf4bf4","year":2018},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.222676Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:d88a54086d1bcdcac43b3887aa8a6ac4d2b1eb7413518fc781b3f2f7217e484b","observation_id":"2d137daf-d4a2-40be-871c-f3abed946a55","resolution":{"observed_at":"2026-08-15T23:29:17.409331Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.227834Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.227834Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:ee6269de31e1b77b75fcb8f04b1d20f0533af7aa93c1b30a671185d59549db62","observation_id":"65496129-37f4-4c36-bb67-97b6427d273f","resolution":{"observed_at":"2026-08-15T23:29:17.227834Z","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":"2026-08-15T23:29:17.232896Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.232896Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:d378e47c2e1a51e71f0179631e3714bd06f3d6261105ece65bd34e1cf6577431","observation_id":"47aa19b9-84fa-4bcf-8e5a-95e1b8528bec","resolution":{"observed_at":"2026-08-15T23:29:17.232896Z","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":"2026-08-15T23:29:17.759196Z","title":"22 KASSIE ARCHER, ALEXANDER DIAZ-LOPEZ, DARREN GLASS, AND JOEL LOUWSMA","venue":null,"work_id":"b867de40-fc79-4b25-8c46-49cc3736f24f","year":2009},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.237836Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:192673ae6ee3956633228c88e1d763e8f9ce05070ce6d0877300483c0a2902b6","observation_id":"fb0e8eb4-8dc0-422a-bb09-8f06fd51052e","resolution":{"observed_at":"2026-08-15T23:29:17.764294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.242742Z","title":"Klivans, The mathematics of chip-firing , Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019, https://doi.org/10.1201/9781315206899","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.242742Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:6b637d2c7daed1768f3a47e56cb01986abb9a562e49d370769ff52e21fcb983d","observation_id":"9df856a0-fb81-42f1-a673-3221cd0066d4","resolution":{"observed_at":"2026-08-15T23:29:17.242742Z","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":"2026-08-15T23:29:17.740674Z","title":null,"venue":null,"work_id":"9097304c-8cf1-4f5f-9b8a-f208797774a7","year":1989},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.247760Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:931f4f89dc16b991a5cb784be2ce1e7f907dc296463f7b6827a71c7705e21aaf","observation_id":"3e8412f5-9c83-4e7f-8326-1a8e3a9e9faa","resolution":{"observed_at":"2026-08-15T23:29:17.747953Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T23:29:17.724056Z","title":"73 (1990), no","venue":null,"work_id":"3e7482e7-768b-420f-8c5d-caf86ad20567","year":1990},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.252295Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:dc7a5df66b85c3a621a50f5b610bce1e26b0e4c907cec2ea7559ccbb7419dee1","observation_id":"d6ca74cb-e4af-4a55-a32a-0fadcd4ef131","resolution":{"observed_at":"2026-08-15T23:29:17.729770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/crll.1992.430.151","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.344291Z","title":"Reine Angew","venue":null,"work_id":"0a974e4d-6610-4c2e-86da-aaa086d0e413","year":1992},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.256998Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:d8681405306e17997360b0e5ab22d8c662b397c2596b298d13c971ce4a5d26dd","observation_id":"a92cfae9-493c-4f6e-b970-247471d28ac4","resolution":{"observed_at":"2026-08-15T23:29:17.349077Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/crll.2000.078","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.327327Z","title":"Reine Angew","venue":null,"work_id":"e1eadf33-b4da-4c60-b324-ec4c1d80de2d","year":2000},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.262200Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:bfa052621660d9e1ed9d4bc43b4484b8e4204b28492e861eb786d2551132e3f3","observation_id":"955ad753-c830-4aac-ad33-6b23be729df8","resolution":{"observed_at":"2026-08-15T23:29:17.332885Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jnt.2023.10.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:29:17.309090Z","title":"Number Theory 257 (2024), 215–248, https: //doi.org/10.1016/j.jnt.2023.10.009","venue":null,"work_id":"a2cd583c-24c8-4cc7-86b4-81c96e1cb019","year":2024},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.266918Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:22b22e7cb59e21dafd737c242972aef3e93f54e4406ad52776e543a6c08a3ce4","observation_id":"76d08530-024a-4584-ab99-106eac45798e","resolution":{"observed_at":"2026-08-15T23:29:17.315860Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T23:29:17.706837Z","title":"Raynaud, Sp´ ecialisation du foncteur de Picard, Inst","venue":null,"work_id":"49993477-6b6b-44b8-b028-02544a89eff1","year":1970},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.272402Z"},"links":{"citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:217f049173db371b428d2ffb11d9162d93794000f56ed6b86ae177acf9d838ad","observation_id":"f915c2f3-8f2c-4455-84e0-d471cb83eab1","resolution":{"observed_at":"2026-08-15T23:29:17.712227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":1,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":6,"verified_exact":9,"verified_fuzzy":4},"total_outbound_references":21},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2505.05392."}