{"as_of":"2026-08-19T02:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1fd9fcfce09db13936859e9a19f7b769b2d7bac992493c37a6ac83f0cc76c6f4","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T20:41:45.752896Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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":"2026-08-02T03:33:33.381708Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.09501","snapshot_observed_at":"2026-08-02T03:33:33.381708Z","title":"Bufitt and T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13906","last_updated":"2026-07-15T14:46:44Z","snapshot_observed_at":"2026-08-10T00:36:49.579289Z","submitted_at":"2026-07-15T14:46:44Z","title":"Inductive construction of path homology chains and the structure of $\\Omega_3(G;R)$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T03:33:33.381708Z"},"links":{"cited_paper":"/paper/2411.09501","citing_paper":"/paper/2607.13906"},"observation_digest":"sha256:b637dfc8b412facf6f4b79fd29f51a39816e1412ccce02236eb027a6fe7c4287","observation_id":"729673e3-4f46-4051-abae-4fcb8e21008b","resolution":{"observed_at":"2026-08-02T03:33:33.381708Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2411.09501/citation-record","integrity":"/paper/2411.09501/integrity","json":"/paper/2411.09501/citation-record.json","paper":"/paper/2411.09501"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.206839Z","title":"Asao, Magnitude homology and path homology , Bull","venue":null,"work_id":"69492bd5-a9e7-4297-a714-f289a2ef5da1","year":2023},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.627747Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:ffa231fa5d36db57a07211110192234e13c163fd3018731cbcf4d3725f192bae","observation_id":"ad33971a-140c-4607-b915-63eda4ed40a0","resolution":{"observed_at":"2026-08-12T20:41:46.211526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.191240Z","title":"Burfitt, Path homology with field coefficients , November 2024, https://github.com/MatthewBurfitt/Path-homology-with-field-coefficients.git","venue":null,"work_id":"08ed1509-7281-4c32-b307-0648a95e392d","year":2024},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.633673Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:f00dd4e86ecab567a892ad97f2ca3afb07a09eb1c72466ae71f744dff15e315d","observation_id":"a278f247-d17e-40e1-a550-637e09b7ad10","resolution":{"observed_at":"2026-08-12T20:41:46.196635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.175478Z","title":"Carlsson, Topology and data , Bull","venue":null,"work_id":"d8b54142-a152-415b-a22d-eaaf5a1512f6","year":2009},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.638873Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:4e36319d47042da7b57dc5975966057e2e23b05c91fb39463cc1777e034eba69","observation_id":"4ff99792-b8fc-43df-aeb6-908f05389ab9","resolution":{"observed_at":"2026-08-12T20:41:46.180599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.159434Z","title":"Carranza et al., Python script for computing path homology of digraphs , September 2022, https://github.com/sheaves/path_homology","venue":null,"work_id":"1c2ba8f8-eb27-4864-b76e-7f15ed2484f4","year":2024},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.643863Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:c5ce9bf97edb0bfa314a3b6f7aa44e90e88e2e56281dc3b1aab4bc39f79a8725","observation_id":"b79a468f-b2aa-4a41-aa57-49f1da406f41","resolution":{"observed_at":"2026-08-12T20:41:46.164677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.143615Z","title":"Chowdhury, T","venue":null,"work_id":"26c6c715-0974-4a02-b648-9175a1ec7bde","year":2019},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.649371Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:235d7e3c37946a0aebfc612ade18f568b51630b7220c6e416abe16011ad66a0b","observation_id":"5f4c29ac-091c-4626-b498-a893a0ff7a93","resolution":{"observed_at":"2026-08-12T20:41:46.148636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.127520Z","title":"Chowdhury, S","venue":null,"work_id":"ca3a1af3-d744-47b4-8690-898889a2456c","year":2022},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.654637Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:4d00653b6c6210eea3bdaeed28e6f40b3d80514dd2613834f7fa9766535afe1d","observation_id":"3ca45d3a-2843-4f07-b07f-7667401f8d97","resolution":{"observed_at":"2026-08-12T20:41:46.132516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.111479Z","title":"Chowdhury and F","venue":null,"work_id":"427987bf-a748-4e54-b416-f7e73f434378","year":2018},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.660500Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:95e17690a70e28eba8b5147f39bfec123cf39ae495a2007d61372c9c3b7c2fc1","observation_id":"272cd6d5-2e99-4f6d-8815-7eb3a636f7bb","resolution":{"observed_at":"2026-08-12T20:41:46.116599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.095527Z","title":null,"venue":null,"work_id":"8de1b901-078b-4615-a5ed-95d1afdca30c","year":2022},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.665507Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:77dfdf53b6a828596e6a267338aceef4593305653845c32616948de50614d1cf","observation_id":"fb7bb302-58d9-4e09-bd4b-dd5c11a76d66","resolution":{"observed_at":"2026-08-12T20:41:46.100616Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.079484Z","title":"Dimakis and F","venue":null,"work_id":"a694d9b8-f924-4e21-aa4c-91181a9ce962","year":1994},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.670204Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:cf80861dec92c76532c69eba7ae9384e16e51acfbf7d6f71e47976f5a9062669","observation_id":"0527eb51-8004-4c03-a037-16800034bb7b","resolution":{"observed_at":"2026-08-12T20:41:46.084444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.062502Z","title":"Edelsbrunner and D","venue":null,"work_id":"be746b00-570e-4415-bedd-f3385a0ae813","year":2014},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.674979Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:32180a753b8a26c571ab189e8cef709667211abcc320747effb6506b039d4079","observation_id":"c80179a0-4821-4d06-af2a-a1ec4e111f97","resolution":{"observed_at":"2026-08-12T20:41:46.067665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.17001","last_updated":"2024-07-24T04:49:26Z","snapshot_observed_at":"2026-08-16T13:31:33.289776Z","submitted_at":"2024-07-24T04:49:26Z","title":"Path homology of digraphs without multisquares and its comparison with homology of spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.17001","snapshot_observed_at":"2026-08-12T20:41:45.680024Z","title":"Fu and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.680024Z"},"links":{"cited_paper":"/paper/2407.17001","citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:e237b98a43079b8179ea508b55556ca5d99f96b9f4388b0b87ff91e45f704e9a","observation_id":"44760cfc-b8e6-424b-9768-308522c4fab0","resolution":{"observed_at":"2026-08-12T20:41:45.680024Z","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":"2026-08-12T20:41:46.043609Z","title":"Grbi´ c, J","venue":null,"work_id":"3fd6877d-fa9e-4921-9437-17cd6fbc3309","year":2022},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.685188Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:8b3e9df12d9b676713d2e395beff3ff92a564eefe9ba8b47602ab65f48319d97","observation_id":"f7685103-6faa-4650-962e-4caa7a9a0d0f","resolution":{"observed_at":"2026-08-12T20:41:46.050769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.025898Z","title":"Grigor’yan, R","venue":null,"work_id":"189db4ef-8c89-450d-bf6b-7f496d162354","year":2018},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.690254Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:dfe15b01ea7e73a057042b2245d0073e66227d559f2ee4b28d0535c4920ef4b7","observation_id":"4e601433-869c-4619-8a51-ace8121f8a7b","resolution":{"observed_at":"2026-08-12T20:41:46.031256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:46.009888Z","title":"Grigor’yan, Y","venue":null,"work_id":"f5a1658d-67f0-40be-9317-156530f77370","year":2021},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.694776Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:851822a3e9e3ebc8e03fe583ff9329899de2902f6c7339a7a2be8c95e6c3fc49","observation_id":"33a3c7a0-33a6-432e-9909-0dc3eb3f86a4","resolution":{"observed_at":"2026-08-12T20:41:46.014866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1207.2834","last_updated":"2013-05-11T18:11:47Z","snapshot_observed_at":"2026-08-15T00:53:31.944606Z","submitted_at":"2012-07-12T03:21:02Z","title":"Homologies of path complexes and digraphs","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1207.2834","snapshot_observed_at":"2026-08-12T20:41:45.699329Z","title":"Grigor’yan, Y","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.699329Z"},"links":{"cited_paper":"/paper/1207.2834","citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:09aa932d70b34db26a05d46ec9df8834b2511fdee6d185b0e85c5ba05a18c578","observation_id":"b591f69a-62a0-4d39-8f99-42f9d52ecea7","resolution":{"observed_at":"2026-08-12T20:41:45.699329Z","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":"2026-08-12T20:41:45.992993Z","title":null,"venue":null,"work_id":"7413e73d-8d2b-45ca-ba28-80f21dbdcf87","year":2014},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.704630Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:b68c9d5ad3bfda7f15f4987d39574e46498134ea2aaeabdb8dc5fff35b5e6f02","observation_id":"8bf4a8ce-6f65-4e8f-aa2d-250d4f202621","resolution":{"observed_at":"2026-08-12T20:41:45.997941Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.976773Z","title":"Grigor’yan and Y","venue":null,"work_id":"4772a6e0-3eee-4bda-b7aa-bf7058d814b8","year":2023},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.709321Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:ade00551f392827d7f1f49936034d80c0e0af2aa5af4a7ec78206d8a0f863375","observation_id":"06e0b1fc-6e79-4c68-ba83-d61fd78010af","resolution":{"observed_at":"2026-08-12T20:41:45.982099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.960138Z","title":"Grigor’yan, Y","venue":null,"work_id":"a509a337-0efd-42f5-a7c0-a101595e5c76","year":2014},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.713824Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:ffd2e5b152fabe7daa6852bc9140d46dfac2dbef585e67ba2b181d0e0888a718","observation_id":"21117cec-fa13-476e-810b-1cc49b650ca6","resolution":{"observed_at":"2026-08-12T20:41:45.965269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.943328Z","title":"Grigor’yan, Advances in path homology theory of digraphs , ICCM 10 (2022), no","venue":null,"work_id":"2cbea957-b8ca-423e-8a39-e3a42f94ca0d","year":2022},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.718647Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:77e19d3d6cf83dcd3acce74e5edf9cc8202d19b0032b8582a086bdc2e51de912","observation_id":"d639df30-82ff-4e2a-8499-db19d5b1064e","resolution":{"observed_at":"2026-08-12T20:41:45.948882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.925632Z","title":"Grigor’yan, Y","venue":null,"work_id":"3491a74a-51a8-4c4a-bd2d-a0764c41247e","year":2017},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.723378Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:023182595b9ebb8cb10e94afdb3796d2839c99ffa68e2103f41d40ad849b1c68","observation_id":"94524915-948d-4347-a797-e8e3262aed8c","resolution":{"observed_at":"2026-08-12T20:41:45.931406Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.06689","last_updated":"2026-04-27T10:13:43Z","snapshot_observed_at":"2026-08-17T04:20:54.565826Z","submitted_at":"2024-04-10T02:25:40Z","title":"Bigraded path homology and the magnitude-path spectral sequence","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.06689","snapshot_observed_at":"2026-08-12T20:41:45.728507Z","title":"Hepworth and E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.728507Z"},"links":{"cited_paper":"/paper/2404.06689","citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:7c70fcee5d8d9863b498479417a40c3ab5a67b25000235e787da53dc7432d015","observation_id":"87b0f16b-504f-4517-ba82-2ae9dd180614","resolution":{"observed_at":"2026-08-12T20:41:45.728507Z","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":"2026-08-12T20:41:45.907608Z","title":"Hepworth and S","venue":null,"work_id":"6c5393fc-ac3d-4135-9736-f1eeaf19b7d3","year":2017},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.733671Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:4ac43723450d2bb756d9ce95a12d165632d1fc8d45346dbb487ca6d56716357c","observation_id":"ac2679cc-843a-4662-94d0-0bc009643c5d","resolution":{"observed_at":"2026-08-12T20:41:45.912967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.890755Z","title":"Ivanov and F","venue":null,"work_id":"0527987a-a745-46ec-af26-96a9db3d8cf2","year":2024},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.738350Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:c35ca8654f5dc25459391e73a3228fa3ad2d99ec076224884165691d0c8e8d92","observation_id":"321de481-270b-4a2b-9d1f-c524ccc2afc1","resolution":{"observed_at":"2026-08-12T20:41:45.896154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.873432Z","title":"Leinster and M","venue":null,"work_id":"ac409a32-5fe0-457f-b213-2135bc42633a","year":2021},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.743249Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:7985e9cc0b1f96ae2654950b8847aac5d39b8760918249adb128d6fac6ba0cfc","observation_id":"fae09211-6c75-4013-bb57-3340bc40e2b5","resolution":{"observed_at":"2026-08-12T20:41:45.878874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.856499Z","title":"Masulli and P","venue":null,"work_id":"25c6c396-96be-4a1a-b861-c1539215881f","year":2016},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.748067Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:dbdba029adebc949e773eed5c04254c4313c04d71196b328f783674ff0044323","observation_id":"f0028cef-7f1e-4ee2-9f91-0ec921d6de51","resolution":{"observed_at":"2026-08-12T20:41:45.861881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T20:41:45.837031Z","title":"Reimann et al., Cliques of neurons bound into cavities provide a missing lin k between structure and function , Front","venue":null,"work_id":"7501e53b-8f1e-462b-8c19-6a346f29e722","year":2017},"citing_paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T20:41:45.752896Z"},"links":{"citing_paper":"/paper/2411.09501"},"observation_digest":"sha256:4984e1e6f3ac02ea9e20bd2ccd0fd0b056aa038b8629011b1d70d543a0628294","observation_id":"2956b858-4140-4f86-87e5-eb610ef67f16","resolution":{"observed_at":"2026-08-12T20:41:45.843595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.09501","last_updated":"2024-11-14T15:09:26Z","latest_version":1,"primary_category":"math.AT","snapshot_observed_at":"2026-08-13T23:12:07.616648Z","submitted_at":"2024-11-14T15:09:26Z","title":"Inductive construction of path homology chains"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":21},"total_outbound_references":26},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2411.09501."}