{"as_of":"2026-08-12T06:53:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:83a4b59add688c62e1db414e6b6d208a423ad0c5cccd89eeb60750c5a96377b4","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T04:54:55.152892Z","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":"2026-08-12T06:34:41.77262+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/2604.17775/citation-record","integrity":"/paper/2604.17775/integrity","json":"/paper/2604.17775/citation-record.json","paper":"/paper/2604.17775"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9cc045aa-8765-4eb8-b3c7-5532515765a7","year":null},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:55b0bbc3ac317bbddc2837096a6c97a392678b9575915f2ae9687687ffc39b3b","observation_id":"05c896a0-12a3-46c2-9204-79ca616932cf","resolution":{"observed_at":"2026-05-22T01:25:53.126854Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3800404f-627f-4644-af72-c8ef5c8bd3a2","year":1941},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:e6ad4dd399fed16e77fa9b3322d7ab9f842d414043a692dd81b5f6e81860ec7e","observation_id":"971f43b0-b57e-47bc-850c-4bd3300e02f7","resolution":{"observed_at":"2026-05-22T01:25:53.137198Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Eckmann, Comment","venue":null,"work_id":"212f0a07-eeb7-4bab-9cb1-0d4697731f98","year":1944},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:f4e4091df3b3eb2b77dc056df3e6279568d386ce552ef4624b2e997b501d9755","observation_id":"5ea33f15-90c8-48de-b434-7c80f8371218","resolution":{"observed_at":"2026-05-22T01:25:53.133392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Dodziuk and V","venue":null,"work_id":"f9acdbd7-3cf0-4c5e-bf8e-41a20c47089d","year":1976},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:ef9e634ef34bd5f7420607d30482b596fc59ef6e90ee8436c9dee96881ccb7ac","observation_id":"75fb3f06-3440-4f85-89d3-bc0be8bdf2fc","resolution":{"observed_at":"2026-05-22T01:25:53.177097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Dodziuk, Amer","venue":null,"work_id":"e151b1f8-47d6-4448-ac3c-a1d7b1d01fb9","year":1976},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:092462c6a193dfc4fde2a1fe77619d7eb4566f5b13a5948582fe0a9601f6985e","observation_id":"0b0730d9-bda4-48e1-9e7a-2723b5baf1ad","resolution":{"observed_at":"2026-05-22T01:25:53.163238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Friedman, Algorithmica21, 331 (1998)","venue":null,"work_id":"bf16475a-c31b-4ac7-8a57-0c71906622bd","year":1998},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:95354b74614090173fa78b0f960809fd5cc8779924a59bb591b09c728118be4e","observation_id":"466e5a56-8c70-47b3-a662-72bdc158e7f1","resolution":{"observed_at":"2026-05-22T01:25:53.130042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"73a3df68-1f6d-4da8-9a5f-e03261a478be","year":1997},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:7ec93be611bac692747a77a36240b222df8d2877215a1460981e4cfc11bea582","observation_id":"28d30101-2981-4a92-8713-1dfefaa5817f","resolution":{"observed_at":"2026-05-22T01:25:53.197150Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Horak and J","venue":null,"work_id":"cfd35de2-c9f3-45d9-97c6-346cd7b52acc","year":2013},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:e18f9da50acd769917ef0bb7d6553c2c4d0b46fb6c4f1bae31d2f07a0e6c34f7","observation_id":"37301eb7-b0d4-4d0f-a981-c522f3f5ba1c","resolution":{"observed_at":"2026-05-22T01:25:53.169878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0d5831ef-774f-4cc0-8d9a-1075826fd937","year":2010},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:fea6005cdf3bd890fec7d141e9e431755932e15111096cd002be40d65651e056","observation_id":"1a0f261d-984a-405f-b57b-6719333d67b0","resolution":{"observed_at":"2026-05-22T01:25:53.190016Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Kozlov,Combinatorial Algebraic Topology, Algorithms and Computation in Mathematics, Vol","venue":null,"work_id":"cb1c8e7d-4f8d-4c79-a27d-b53d46117896","year":2008},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:d4dd7f43cd3b870a853cf40360ed0a93e551cb9bfb9958b1a36a7fe83c4e0d25","observation_id":"4750f688-d1c6-469e-87f8-e4f594c0a9e4","resolution":{"observed_at":"2026-05-22T01:25:53.156798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Lim, SIAM Rev.62, 685 (2020)","venue":null,"work_id":"dc1f7344-4c22-40cb-a7db-655366e45216","year":2020},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:8c791aca5b9b37925f435dbd1f96a953bfa7aba0781d48797976aa3668213ab6","observation_id":"b6327d1b-2672-47ea-8357-2b5a43d54aa4","resolution":{"observed_at":"2026-05-22T01:25:53.160019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Jiang, L.-H","venue":null,"work_id":"f6dac942-9064-4c8c-94d9-61bd2aa8c2f1","year":2011},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:8dc6a340f096cd1dea68a7ab04e59777eed8ab02837f251a24b7bf963017aa21","observation_id":"fac53686-b836-44af-a6f2-1db0734c0c02","resolution":{"observed_at":"2026-05-22T01:25:53.148154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"13dc4660-a8f9-49eb-9b3f-f473a9a880ab","year":2020},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:e6b5208cdce8480f095a6fa9b85f9b75af7d2bf745ffffd2c320fbce3b7db1ae","observation_id":"864d2d82-ec8f-4317-90b3-1a473c262b19","resolution":{"observed_at":"2026-05-22T01:25:53.180602Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Washburn and M","venue":null,"work_id":"0e33c558-3424-4f8c-810e-44836b4b1548","year":2026},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:cdac37f73a34e42d132561c3d100f7295cfb50ab639d1efaa379ef0288923e5b","observation_id":"7d57c602-4ac2-4fb9-aafa-d093a64ce22e","resolution":{"observed_at":"2026-05-22T01:25:53.144689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2601.12194","last_updated":"2026-01-17T23:31:51Z","snapshot_observed_at":"2026-08-05T02:45:44.806233Z","submitted_at":"2026-01-17T23:31:51Z","title":"Coherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics","version":1},"cited_work":{"arxiv_id":"2601.12194","doi":null,"metadata_source":"pith","pith_arxiv_id":"2601.12194","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Coherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics","venue":"cs.IT","work_id":"3cf5c98c-dcb2-4641-b500-ca4aa833ecf2","year":2026},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"cited_paper":"/paper/2601.12194","citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:e22f94160a7edb836eb622b4424ca118b898aeeef46fb11865ca2a67560183d3","observation_id":"cc550533-284a-4f48-a51f-d8a458f98007","resolution":{"observed_at":"2026-05-10T11:10:09.746919Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Husimi, J","venue":null,"work_id":"1b8e6fbf-54a1-407a-bb61-62e41935217f","year":1950},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:38f8ccad5ba00e0c4287932b27b2ce1883a324c2e368d2c680c0dc7defefe209","observation_id":"b1f23ca6-c326-4c0c-ad1d-66dcab84ded2","resolution":{"observed_at":"2026-05-22T01:25:53.183658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Harary and G","venue":null,"work_id":"ae1f7ad8-a7ce-415a-9149-8782913eff44","year":1953},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:a4439fd34272d8dca0294f4a51470b6481517fc5e44f094dcbc55b7578d47f9d","observation_id":"05ded03c-fa49-4e1e-9fcc-8c242edf0773","resolution":{"observed_at":"2026-05-22T01:25:53.140764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Diestel,Graph Theory, 5th ed., Graduate Texts in Mathematics, Vol","venue":null,"work_id":"2530385c-478d-469c-b735-143bb530c650","year":2017},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:dbe58b19a5ade625b9b639a0680d8e75ff98aad60d2b4a42679a3992982ff9b4","observation_id":"7cfb20f2-9d19-4912-ba21-86ab973b8b92","resolution":{"observed_at":"2026-05-22T01:25:53.152647Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Nesterov and A","venue":null,"work_id":"6f55212e-f2bb-45ab-a6d3-744cb2bdfc34","year":1994},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:6c5dff625b9d353b92f9e8e4aac2540cdc2805990db5d6113e0a14b75d278015","observation_id":"02ad0f03-41a0-43c5-924a-a4afb7317c8e","resolution":{"observed_at":"2026-05-22T01:25:53.186736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":"Nesterov,Lectures on Convex Optimization, 2nd ed., Springer Optimization and Its Applications, Vol","venue":null,"work_id":"211c9309-50ba-4069-afb5-bfd52404bdd7","year":2018},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:7e6ca0dfc941490ee70d55c0ca73249e06511f56aca4c7dd22f1ad88a1aefe23","observation_id":"f965054d-5bb4-469e-b2d9-55f2f88506a3","resolution":{"observed_at":"2026-05-22T01:25:53.166746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-07-10T00:56:40.952546Z","title":"Boyd and L","venue":null,"work_id":"f76d1b23-7471-4176-9be7-8370b119a29b","year":2004},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:843080daedce4be153ab59c225284bbb1e3c05ceca82e580a4ed30487269b26d","observation_id":"bb0cc449-e005-4808-a3f7-ebc371053fa9","resolution":{"observed_at":"2026-05-22T01:25:53.193561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"daac7930-ebc9-4ba7-82eb-fcc262f57da4","year":2003},"citing_paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-10T04:54:55.152892Z"},"links":{"citing_paper":"/paper/2604.17775"},"observation_digest":"sha256:8398e72f35eb77c0c56ffaddf8dc7ef26fe97bd68e7bc4cc9d19a91652c1da2a","observation_id":"2e8bfb71-8374-40a3-b8b4-dd6bd8f10429","resolution":{"observed_at":"2026-05-22T01:25:53.173086Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.17775","last_updated":"2026-04-20T03:53:24Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-08T10:03:13.929063Z","submitted_at":"2026-04-20T03:53:24Z","title":"The Cactus Criterion: When Nonlinear Hodge Theory Reduces to Linear on Graphs"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":1,"verified_fuzzy":15},"total_outbound_references":22},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2604.17775."}