{"as_of":"2026-08-10T09:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e50fd96bb37f984fb62cda502d2ab38cabad91eaeb42a8b4d0284d870f2dd087","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":"2026-06-27T04:34:24.520652Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2606.15241/citation-record","integrity":"/paper/2606.15241/integrity","json":"/paper/2606.15241/citation-record.json","paper":"/paper/2606.15241"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T04:34:24.520652Z","title":"Adiprasito, J","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:708bcde815f5ea51e4ff7a2b7e739f0d355281f3ed5aba48ca5e76c1ee55f8e5","observation_id":"96e222cc-5b72-43ad-8be8-4f80f0d91dae","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:a90a354702782b28fc06385c59aecb70b4379625974ab7553456b740971adc47","observation_id":"f1dc903e-1046-405e-a703-61d49eba2a80","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Asao,Magnitude homology and path homology, Bull","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:654f29c7ac3f017f4124282f29eb5294581a9bb2c016ebadcbb43cb501d70890","observation_id":"38f0a12f-a1f2-4312-b8fb-4417724bae38","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.05677","last_updated":"2023-07-25T04:16:49Z","snapshot_observed_at":"2026-08-03T13:32:29.744692Z","submitted_at":"2023-03-10T03:09:40Z","title":"Magnitude and magnitude homology of filtered set enriched categories","version":2},"cited_work":{"arxiv_id":"2303.05677","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2303.05677","snapshot_observed_at":"2026-07-03T17:08:43.505425Z","title":"Magnitude and magnitude homology of filtered set enriched categories","venue":null,"work_id":"f5b79c33-a808-4d7b-ab64-63b0ff4419dc","year":2023},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/2303.05677","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:e59b6070ae0805f20ff80041caad5d3ace3575ff7657e181191dcf3dd4653b9a","observation_id":"f9bda939-2b64-4aa4-8246-71d45f5d0548","resolution":{"observed_at":"2026-07-03T17:08:43.507294Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T04:34:24.520652Z","title":"Bjorner, F","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:86e7ad13deef6e8a19d17bae93a0857384d9475399ecd01adbaa015a08cfc9fb","observation_id":"277eb583-2d4f-4aed-9f66-365fbc88af94","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:949183ac559fde4e67078a48effc11fd2928da12e602c894113026e7ea6582e6","observation_id":"c7a11860-f4e2-4b56-b543-35b2cdf2a796","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Hepworth, S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:f989785dc9b8537c27771fc054a82d22ad84ea2599df805dfc4bfc9085420540","observation_id":"b83e9e2f-706b-4c92-b503-3b52709e6a6c","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.06689","last_updated":"2026-04-27T10:13:43Z","snapshot_observed_at":"2026-07-06T17:58:05.136931Z","submitted_at":"2024-04-10T02:25:40Z","title":"Bigraded path homology and the magnitude-path spectral sequence","version":3},"cited_work":{"arxiv_id":"2404.06689","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.06689","snapshot_observed_at":"2026-07-03T17:08:43.514088Z","title":"Bigraded path homology and the magnitude-path spectral sequence","venue":"math.AT","work_id":"b1764d0d-5108-4b46-98bf-0b58545bef88","year":2024},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/2404.06689","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:d24bdcbc19e249809a04ad89fc5674b342db48579232d2b723600961f5975c4b","observation_id":"65d01f06-8928-43c7-a13f-b40d6debd94a","resolution":{"observed_at":"2026-07-03T17:08:43.515385Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.11878","last_updated":"2024-05-21T09:07:10Z","snapshot_observed_at":"2026-07-06T17:05:06.923713Z","submitted_at":"2023-12-19T06:10:19Z","title":"Nested homotopy models of finite metric spaces and their spectral homology","version":4},"cited_work":{"arxiv_id":"2312.11878","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.11878","snapshot_observed_at":"2026-07-03T17:08:43.505685Z","title":"Ivanov,Nested homotopy models of finite metric spaces and their spectral homology, (2024), arxiv:2312.11878","venue":null,"work_id":"cd4313e9-c4b2-434c-aa68-43c378240786","year":2024},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/2312.11878","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:481c6e1e1d7feb6b3fa93e5e869e608f02f14f44ffb2d475b543e1f5d9eaa46e","observation_id":"ea9fe26b-5585-42bd-8e78-2a46bc2b01e9","resolution":{"observed_at":"2026-07-03T17:08:43.507604Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04748","last_updated":"2026-07-18T09:14:49Z","snapshot_observed_at":"2026-08-05T03:14:18.555157Z","submitted_at":"2024-05-08T01:29:57Z","title":"On diagonal digraphs, Koszul algebras and triangulations of homology spheres","version":5},"cited_work":{"arxiv_id":"2405.04748","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.04748","snapshot_observed_at":"2026-07-21T01:19:44.474218Z","title":"Ivanov, L","venue":null,"work_id":"a0158a65-c3ba-4de6-bb35-157b2a9ce4c2","year":2024},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/2405.04748","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:d32bb3a46fc766e6860112df3273ce2f4ffd26036cabc26bf782492fec3dde4b","observation_id":"1ccdf2ab-5661-4d50-9501-7e7c110ae462","resolution":{"observed_at":"2026-07-21T01:19:44.474218Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T04:34:24.520652Z","title":"Kaneta, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:cd310c06e7a1d314497b26c9c03b9873ccc7b32bb65d05bb407d00b5846d5e84","observation_id":"0055cf6b-1b14-411f-a086-ccfd93aa5ca9","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Kozlov,Combinatorial Algebraic Topology, Algorithms and Computation in Mathe- matics,21(2008), Springer-Verlag Berlin Heidelberg","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:7c2734a227c1b40c2947ce7c185862eaf439cc7f543a2953f5b8d1ec4fd7b7e6","observation_id":"d34c1410-2c29-4542-a111-aac818c637fe","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Leinster,The magnitude of metric spaces, Documenta Mathematica,18(2013), pp","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:846d36faa27e736c06ac2c57c791ad475c6ee31cfcd376d8968f3e4b713220e6","observation_id":"045ad785-b72a-479b-91fc-eeace72afaea","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Leinster, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:162b2cfdda87335541e7796792dcbb2dd661edf0e71913ec07582c6be617f1af","observation_id":"21a82938-d05b-41cd-b07c-bcdce44aaec7","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.11976","last_updated":"2025-03-15T03:14:06Z","snapshot_observed_at":"2026-08-07T17:02:28.959800Z","submitted_at":"2025-03-15T03:14:06Z","title":"Torsion in Magnitude homology theories","version":1},"cited_work":{"arxiv_id":"2503.11976","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2503.11976","snapshot_observed_at":"2026-07-03T17:08:43.516752Z","title":"Martin II, R","venue":null,"work_id":"abcfdd00-e92d-4a63-9d58-dd7cb4919ecb","year":2025},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/2503.11976","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:90d38d26ba5aedb9bf36234eff807248c7840d530a8346ffc880e4e7f097bf7e","observation_id":"e8a1b415-819d-4e00-985a-ad7e8778356a","resolution":{"observed_at":"2026-07-03T17:08:43.518362Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T04:34:24.520652Z","title":"Munkres,Topological results in combinatorics, Michigan Mathematical Journal, 31(1984), pp113-128","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:617ab1efa1f3f8286f579a109572882e0940b53c205a5abe4c349c9a9028634b","observation_id":"894eb888-76fe-4d03-a77e-5f9323588379","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Munkres,Elements of Algebraic Topology, Addison-Wesley Publishing Company, (1984)","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:8cd3493cc3ddf7e33a74f0abcbd3afb59ee7172b9b8751182c1b50917b04a533","observation_id":"6d891909-4b25-40ac-9843-6fe68c0aaf2f","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Orlik, H","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:7538c3597c408fe1628d70c29fbf18c96efb2b6969e24178374b1ff2c0bffc59","observation_id":"460a5e76-c789-4a8f-9443-f48859290762","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.01540","last_updated":"2021-08-24T08:15:13Z","snapshot_observed_at":"2026-08-04T03:27:15.260431Z","submitted_at":"2018-07-04T12:26:33Z","title":"Magnitude meets persistence. Homology theories for filtered simplicial sets","version":3},"cited_work":{"arxiv_id":"1807.01540","doi":null,"metadata_source":"pith","pith_arxiv_id":"1807.01540","snapshot_observed_at":"2026-07-03T17:08:43.511437Z","title":"Magnitude meets persistence. Homology theories for filtered simplicial sets","venue":"math.AT","work_id":"1640bfee-e584-46dd-afbc-1e3c6340bddc","year":2018},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"cited_paper":"/paper/1807.01540","citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:6d5a1ecd3413cccd9dce21168144000f4089cc29ddfa557c389b7fb350d3e046","observation_id":"fc0e4058-c996-4ed1-af0d-0b37b0bf2a51","resolution":{"observed_at":"2026-07-03T17:08:43.512720Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T04:34:24.520652Z","title":"Quillen,Homotopy properties of the poset of nontrivialp-subgroups of a groupAd- vances in Mathematics,28.2(1978), pp.101-128","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:6065844c7e1b32a9fc7e9d3f1aa9bb050f3f9d3cffdc7df2bb70504f64922cd6","observation_id":"11573a6c-c5f0-4e77-aad4-1379933df4a0","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Stanley,An introduction to hyperplane arrangements, Geometric Combinatorics, 13(2007), pp.389-496","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:0adfe3abb81fec011dde6b9af1bf932ddd09de569858222d6e2927d3c290692a","observation_id":"6105b2bb-1b88-4613-8d63-f65d8741169d","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Stanley,Enumerative Combinatorics: Volume 1, Cambridge Studies in Advanced Mathematician,2nd edition(2011), Cambridge University Press","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:4d384ed770f5f62f24256175e7c06a9943c09ccb2d1ccc66d8892a948fc90d66","observation_id":"1b408e74-d2d4-4b41-828a-12eccb429445","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Tajima, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:c3ed82edc8a0c7e6e6f372fd66d74672f5c312c40a3d6e545bc042a922fb2914","observation_id":"1e69ca1b-c59d-4577-a7da-f8105cedf3e7","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Wachs,Poset topology: tools and applications, Geometric combinatorics,13(2007), pp.497-615","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:f7f2919cfefb22de24ef2e24038821187dfbb00617398f776852a81e679904ed","observation_id":"1cc58662-1497-482c-a9b5-93d3cb3954bb","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"Wachs, J.W","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:cbae31b62bc7c48950b786130afed76f75256b863a617bd2e9d5db1f6a400c55","observation_id":"4fe3811b-3496-4db5-abab-4052f7c7322f","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","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":"2026-06-27T04:34:24.520652Z","title":"White, ed.Matroid applications, Encyclopedia of Mathematics and its Applications, 40(1992), Cambridge University Press","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-27T04:34:24.520652Z"},"links":{"citing_paper":"/paper/2606.15241"},"observation_digest":"sha256:5db9c5c77392354b43f136e9dde9a75536d1f88efc72841751cc7a72a079002b","observation_id":"0bb2a47c-57e2-4f3b-998a-3950f350b3de","resolution":{"observed_at":"2026-06-27T04:34:24.520652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.15241","last_updated":"2026-06-24T06:41:42Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-02T02:53:17.411459Z","submitted_at":"2026-06-13T10:44:16Z","title":"Filtered order complexes and magnitude homology of finite graded posets"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":6,"verified_fuzzy":0},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2606.15241."}