{"as_of":"2026-08-14T14:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2cedde50023f0e21bbf599929557d4eff748bdb520613f093ead4840fefcdc3d","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T18:59:18.021527Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2501.10876/citation-record","integrity":"/paper/2501.10876/integrity","json":"/paper/2501.10876/citation-record.json","paper":"/paper/2501.10876"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T18:59:18.357744Z","title":"The Alpha complex Aα at a scale parameter α is constructed by first considering the union of balls centered at the points in P with radius α","venue":null,"work_id":"b0128583-4863-422f-b69c-fb9add22de92","year":2020},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:18.009998Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:5c9b017c8c1cb4f5d6f9504b989701da5b14e6c4e6c9ced65c1a42de14da5601","observation_id":"89c66484-666e-4097-9983-31e239aea67c","resolution":{"observed_at":"2026-08-10T18:59:18.363267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.402295Z","title":"Persistence weighted gaussian kernel for topological data analysis","venue":null,"work_id":"d5cbdddf-2515-4692-b724-f341ce5ec11e","year":2004},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.980497Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:bda703d70d8e4449e7799959597e5d497dea4c9b1e3bc8e7cef2f571ffaad94b","observation_id":"7a41e4cf-0d07-48f7-a73d-6742132907c0","resolution":{"observed_at":"2026-08-10T18:59:18.408489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T18:59:17.986517Z","title":"URL https://doi","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.986517Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:a817330adecf21ed75e8e3a2df63e67fb16cedbd1233590830cb331c6a3b502b","observation_id":"195ebfa2-41b4-4782-bead-b6c10c02295b","resolution":{"observed_at":"2026-08-10T18:59:17.986517Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.16824","last_updated":"2025-07-10T07:26:30Z","snapshot_observed_at":"2026-08-14T10:37:36.691188Z","submitted_at":"2020-06-30T14:01:05Z","title":"Wasserstein Stability for Persistence Diagrams","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.16824","snapshot_observed_at":"2026-08-10T18:59:17.991743Z","title":"Wasserstein stability for persistence diagrams","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.991743Z"},"links":{"cited_paper":"/paper/2006.16824","citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:c124a261411d8055ec51903e5b2b63d20ab7b08d59213fd6c34ea3fb2426911f","observation_id":"dbcadef1-195f-481a-91df-f20aa9b4f59c","resolution":{"observed_at":"2026-08-10T18:59:17.991743Z","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":"2026-08-10T18:59:18.372703Z","title":"By construction (see (Agerberg et al., 2023, Sect","venue":null,"work_id":"176ab071-ab4f-499b-81c9-b473c45aaec6","year":2020},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:18.005104Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:e7927d968f2ae055bc26417c2dbae5d58b2787036e05acf99056e2401418cd09","observation_id":"3ea38709-9a45-402a-9282-e9b734baedec","resolution":{"observed_at":"2026-08-10T18:59:18.377548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.344097Z","title":"In order to test the robustness of Perslay in PyTorch we reimplement it with the following DeepSet (Zaheer et al.,","venue":null,"work_id":"2f9e348e-5bcb-462f-b7ec-f4c078db1f3e","year":2018},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:18.015095Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:fddd492688fe4ff89a8cee3712cc6f475441d6d6e66052649ae703a50f6f7b63","observation_id":"1fa2bd56-f30f-4236-944d-42a3a7bbb87f","resolution":{"observed_at":"2026-08-10T18:59:18.348763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.328489Z","title":"(2020): each point in the persistence diagram is upsampled from 2 dimensions to 25 13 Agerberg Guidolin Martinelli Hoefgeest Eklund Scolamiero through 2 layers","venue":null,"work_id":"4b7fc73d-1b2a-4273-9c77-5f7056e32cfe","year":2020},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:18.021527Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:d42009378a2a6c8820be9ef5b1966ef33984fcbb5c0f1a3530d974cad92e2dd9","observation_id":"7b53a0c6-132f-43fd-abf0-a0d2e5528d64","resolution":{"observed_at":"2026-08-10T18:59:18.333986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.419208Z","title":"Reluplex: An efficient smt solver for verifying deep neural networks","venue":null,"work_id":"623afff5-89d0-4172-874d-0b8a8cffa2ca","year":2017},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":1995,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.975472Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:28f48a1e4a1321a34c337082ec2cb6c18abf25ff6c0ae78092bc2dee2764294c","observation_id":"faba38d4-b9bc-48d6-b5a7-e926216103b1","resolution":{"observed_at":"2026-08-10T18:59:18.424182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T18:59:17.963785Z","title":"ISBN 9781450325943","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.963785Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:6003ec82c8c0fa83ce518e4dc173b93e1222fca3d74f35d23149c7a244a1811e","observation_id":"1adece68-076a-4000-a050-80626135f703","resolution":{"observed_at":"2026-08-10T18:59:17.963785Z","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":"2026-08-10T18:59:18.456220Z","title":"Nicholas Carlini and David Wagner","venue":null,"work_id":"5f8e1fff-9118-4c96-aee2-e2895b93e4aa","year":2017},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.959148Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:0a00839b6c1114fefbac8da90b70d1d5e572c01e5fa0b8509949165bf19c3fe8","observation_id":"d630c03d-b9e3-4516-81a1-c644fea6766a","resolution":{"observed_at":"2026-08-10T18:59:18.463274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.06484","last_updated":"2024-08-22T14:51:26Z","snapshot_observed_at":"2026-08-13T13:03:42.471528Z","submitted_at":"2023-01-16T15:42:46Z","title":"Algebraic Wasserstein distances and stable homological invariants of data","version":3},"cited_work":{"arxiv_id":"2301.06484","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.06484","snapshot_observed_at":"2026-08-10T18:59:18.309264Z","title":"Algebraic Wasserstein distances and stable homological invariants of data","venue":"math.AT","work_id":"299e6fe2-4abf-4544-ab72-80411f435fe8","year":2023},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.949604Z"},"links":{"cited_paper":"/paper/2301.06484","citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:8918969e87681947a23bbbd3983ea169f0bdd95cc49e2411df9a67b27e539037","observation_id":"005ae828-a829-4dc8-832a-abb7fc7d5002","resolution":{"observed_at":"2026-08-10T18:59:18.316762Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.388656Z","title":"Persistent homology and distances A.1","venue":null,"work_id":"f558c0ea-b414-4d63-b9d3-7304c25c3c93","year":2017},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.999731Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:67657d8ef2e8f02e75de11755332d3d061f00ed093c1f8bfe57149b1ddc3b7ad","observation_id":"5c2f3d53-4376-4054-822b-1439548995d0","resolution":{"observed_at":"2026-08-10T18:59:18.392819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T18:59:18.433524Z","title":"Topological data analysis for arrhythmia detection through modular neural networks","venue":null,"work_id":"4a0102ed-f229-46b9-87ef-17b492a6f3aa","year":2020},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.970188Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:4141eb725d0704ad95390c55044ad28bf07e849eedafa2c05a3dea2e5793db66","observation_id":"4765d8fc-4fc1-421d-8761-4c87b872eb64","resolution":{"observed_at":"2026-08-10T18:59:18.438452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T18:59:17.954642Z","title":"doi: 10.1109/tpami.2023.3308391","venue":null,"work_id":null,"year":1939},"citing_paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-10T18:59:17.954642Z"},"links":{"citing_paper":"/paper/2501.10876"},"observation_digest":"sha256:43a0c592ee6045de20e88e033a8a7ca45958ed8d874109508783c7c7bacb56e8","observation_id":"24cfc7be-f9fa-4845-b8fc-a3680481fc45","resolution":{"observed_at":"2026-08-10T18:59:17.954642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2501.10876","last_updated":"2025-01-18T20:57:20Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-14T10:38:36.813792Z","submitted_at":"2025-01-18T20:57:20Z","title":"Certifying Robustness via Topological Representations"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":1,"verified_fuzzy":9},"total_outbound_references":14},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2501.10876."}