{"as_of":"2026-08-10T12:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5605c75a8a44e0255d5eb795cb3fd83254bcae0631dd36b3995b084eaf2f89fe","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T10:32:45.952876Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"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/2507.23762/citation-record","integrity":"/paper/2507.23762/integrity","json":"/paper/2507.23762/citation-record.json","paper":"/paper/2507.23762"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.600073Z","title":"Computing the interleaving distance is NP-hard","venue":null,"work_id":"9b39ebb7-1e66-4ee5-b238-792329c7e41b","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.776447Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:5810069ad43344f2c3313a2753c8d95ad3e9fb175b376a0bd6fc52903e60af85","observation_id":"5f84952d-15cf-4bdb-8220-3a388f75a81d","resolution":{"observed_at":"2026-08-06T10:32:46.603747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2106.13589","last_updated":"2021-11-11T15:59:32Z","snapshot_observed_at":"2026-07-06T11:23:05.896928Z","submitted_at":"2021-06-25T12:40:19Z","title":"$\\ell^p$-Distances on Multiparameter Persistence Modules","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.13589","snapshot_observed_at":"2026-08-06T10:32:45.781253Z","title":"ℓ𝑝-distances on multiparameter persistence modules","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.781253Z"},"links":{"cited_paper":"/paper/2106.13589","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:5f2a061bae6fbcdb5a68944f4cfdecf2204b8c21b32ecc852f619236d92a70e7","observation_id":"a7b55cf8-76de-4482-b1c1-1474e2d838df","resolution":{"observed_at":"2026-08-06T10:32:45.781253Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.14289","last_updated":"2023-03-13T13:14:26Z","snapshot_observed_at":"2026-08-10T01:49:42.233479Z","submitted_at":"2022-03-27T12:35:41Z","title":"An Introduction to Multiparameter Persistence","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.14289","snapshot_observed_at":"2026-08-06T10:32:45.785059Z","title":"An introduc- tion to multiparameter persistence","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.785059Z"},"links":{"cited_paper":"/paper/2203.14289","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:8a4db02975b2297dac0a2a426b5f135b2018e3b5f382b33185ac102a457127b7","observation_id":"d5fce9bf-1d79-455a-915f-71235b9ba0fe","resolution":{"observed_at":"2026-08-06T10:32:45.785059Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1809.09654","last_updated":"2022-08-26T13:55:41Z","snapshot_observed_at":"2026-08-10T02:13:11.876481Z","submitted_at":"2018-09-25T18:48:24Z","title":"Exact weights, path metrics, and algebraic Wasserstein distances","version":4},"cited_work":{"arxiv_id":"1809.09654","doi":null,"metadata_source":"pith","pith_arxiv_id":"1809.09654","snapshot_observed_at":"2026-08-06T10:32:46.221976Z","title":"Exact weights, path metrics, and algebraic Wasserstein distances","venue":"math.RA","work_id":"35a441b4-50bd-476a-a1cf-db1f1e6d45ab","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.788814Z"},"links":{"cited_paper":"/paper/1809.09654","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:1cef52825c8bfce08f42c52b8bb4e3be50d7d0737070a04119d25988f3a9fe44","observation_id":"750849d9-a816-409c-9a5b-41e8db99fcbe","resolution":{"observed_at":"2026-08-06T10:32:46.226291Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.588917Z","title":"Embeddings of per- sistence diagrams into Hilbert spaces","venue":null,"work_id":"e7335152-158d-4ccf-b46d-1a2e6403b003","year":2020},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.792768Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:2196ea2a846e17137b3e1ed18062e022dc33e1a7b75c3f4b027e60090252d41a","observation_id":"89f3cffc-6e21-4723-83cf-d1408ccb6ffe","resolution":{"observed_at":"2026-08-06T10:32:46.592114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.578926Z","title":"The theory of mul- tidimensional persistence","venue":null,"work_id":"71efc832-938c-4563-a279-f398aad37f97","year":2009},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.796278Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:ed4d2badb161be2289a36d1b4586f4d73b059a758ab6a7ec70171936aaf69731","observation_id":"183e1501-3e86-410e-86e4-97e0541955b2","resolution":{"observed_at":"2026-08-06T10:32:46.582088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1806.06924","last_updated":"2019-08-07T22:01:55Z","snapshot_observed_at":"2026-08-10T02:13:10.912550Z","submitted_at":"2018-06-19T02:49:08Z","title":"On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces","version":3},"cited_work":{"arxiv_id":"1806.06924","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.06924","snapshot_observed_at":"2026-08-06T10:32:46.205304Z","title":"On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces","venue":"cs.LG","work_id":"8eb8327e-cbd9-4e05-93ce-52d5038c7338","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.800037Z"},"links":{"cited_paper":"/paper/1806.06924","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:254481760def57e759f500d57baa7528e127761edb45dffed67a02a67d57ad9b","observation_id":"d9c6418a-d022-43d8-a916-2e7debac7794","resolution":{"observed_at":"2026-08-06T10:32:46.209145Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.568808Z","title":"Multiparameter persistence image for topological machine learning","venue":null,"work_id":"26b9e948-bda6-4a98-8ad2-eef02176ef34","year":2020},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.805222Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:80f330ccb8f3a7cf4b16e3813df6fa5a2dde89c934045a5e067dcfa44b713475","observation_id":"d949dbd3-d551-4b89-8e12-1c596c47ac08","resolution":{"observed_at":"2026-08-06T10:32:46.572315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.556900Z","title":"Sliced Wasserstein kernel for persistence diagrams","venue":null,"work_id":"bfb385f4-81a7-46e5-b2f1-5496fafec5b2","year":2017},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.808881Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:e8d79c2af81cad84090cd6b7e429ca3c951b8054b5c4f9f953d001a4447c8237","observation_id":"09383ea0-05d4-4615-9794-d2d8d4f63b2b","resolution":{"observed_at":"2026-08-06T10:32:46.560767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.544292Z","title":"On the ge- ometrical properties of the coherent matching distance in 2D persistent homology","venue":null,"work_id":"dbdc5a50-181d-4cfe-85db-d00b51c3ecd3","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.813432Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:98afbe2b2f2659e7ba5d25e9352b6751e19383446138bfd5e90aa8e1e9c00389","observation_id":"dc87d5dc-0c84-486c-af24-c3c884ee89e0","resolution":{"observed_at":"2026-08-06T10:32:46.548463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.532835Z","title":"Betti numbers in multidimensional per- sistent homology are stable functions","venue":null,"work_id":"25848a4f-9751-47e0-a097-c0eaee874619","year":2013},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.817494Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:4f76f91a1c4fb65c8ca25062e87201cff5037cf4eb55e5ff80f35fd89b61c786","observation_id":"d26d7eed-83af-4106-aa2f-0f37fa25dede","resolution":{"observed_at":"2026-08-06T10:32:46.536346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2112.06509","last_updated":"2024-03-19T07:30:46Z","snapshot_observed_at":"2026-08-10T09:22:58.669417Z","submitted_at":"2021-12-13T09:41:32Z","title":"The Shift-Dimension of Multipersistence Modules","version":4},"cited_work":{"arxiv_id":"2112.06509","doi":"10.48550/arxiv.2112.06509","metadata_source":"pith","pith_arxiv_id":"2112.06509","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"The Shift-Dimension of Multipersistence Modules","venue":"math.AC","work_id":"c9cc0e11-2fab-4a11-8b32-75967de7cf5d","year":2021},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.820879Z"},"links":{"cited_paper":"/paper/2112.06509","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:bf1d7f6625b17da1bfc81c2caab0986739457545abcbdbc0b8159bdfe315b9ec","observation_id":"b3cbca07-276b-4ee2-811d-c82d802f50c4","resolution":{"observed_at":"2026-08-06T10:32:46.001981Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.523031Z","title":"Geometric Inference for Probability Measures","venue":null,"work_id":"ec28f04d-d891-41f7-8db1-f4fa9942417f","year":2011},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.824956Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:d0cb952efe286dda04cdcda1e24c55ad863eeda4688100988e6b3b9981170ca0","observation_id":"4d6e5c26-0fa7-46ab-9e50-8a932f74b837","resolution":{"observed_at":"2026-08-06T10:32:46.526243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.511232Z","title":"Proximity of Persistence Modules and Their Diagrams","venue":null,"work_id":"31c99ab2-e80c-4456-b502-54cacc1d405b","year":2009},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.828166Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:9771815d8c34f3e802e1b0a65349009190d6bbabbf8da9333ec7f56b520b3b25","observation_id":"565dbd27-bf76-4f56-bbee-2b377fab71d1","resolution":{"observed_at":"2026-08-06T10:32:46.515367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.500032Z","title":"Stability of Persistence Diagrams","venue":null,"work_id":"5679d8da-beee-42c4-ac3c-84356448fa40","year":2007},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.831208Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:33b6fbc745b45e9d133f84d2fc08dbbb8fd577bf9e38bf843732e6fe52f466bb","observation_id":"693b4cb8-2a47-46dc-8e30-11c0a7be3122","resolution":{"observed_at":"2026-08-06T10:32:46.504216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"10.1007/s41468-018-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:45.977082Z","title":"The representation the- orem of persistence revisited and generalized","venue":null,"work_id":"4832120b-63c7-48f0-91f5-158eb6a272a8","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.835230Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:d6f987a9cd30db397e015df35ace447ff1178ccff8396b426e78513b23dfcded","observation_id":"01125a9c-d860-4360-a7c9-89311be7355a","resolution":{"observed_at":"2026-08-06T10:32:45.982850Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.489396Z","title":"A kernel for multi-parameter persistent homology","venue":null,"work_id":"bd531cc6-6e0f-4247-b55d-377eff7f8df8","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.838537Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:4b4a915159f38e616fd7634b82f6b21e7749150d5da9c00331e2036c1a3f8fd2","observation_id":"7fbabcb3-463e-4284-9aab-eeb1c7a1b51c","resolution":{"observed_at":"2026-08-06T10:32:46.493283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.478882Z","title":"Computing the Multicover Bifiltration","venue":null,"work_id":"ad8d81b8-2b62-478f-9f01-f2ae2944527a","year":2021},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.841505Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:e05af63c7d4c34b69f502293717bf2a2eac90b34b1c3dd778a9bf2b7ed59bcc3","observation_id":"6c21b3ad-4dbf-46e4-968d-108cdf9f5c61","resolution":{"observed_at":"2026-08-06T10:32:46.482283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.469005Z","title":"ToDD: Topological compound finger- printing in computer-aided drug discovery","venue":null,"work_id":"400bd67b-c821-447e-b8fd-4f541eff0085","year":2022},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.846026Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:3f1a09def881b896043211b318062016c5f997d6923ed8c15426fb7918111207","observation_id":"57f0d3b7-0268-427e-8373-9600c24ff17d","resolution":{"observed_at":"2026-08-06T10:32:46.472591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.458940Z","title":"Commutative Algebra: With a View Toward Algebraic Geometry","venue":null,"work_id":"008ac589-4c30-4275-81f8-acc1673721b9","year":1995},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.849503Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:50f1ec4e88a843a4f393df2f7fd25be6f91d1651be73a59b15bcf881a2330cf9","observation_id":"e87b166d-eeae-4854-b0b3-e195e09431a8","resolution":{"observed_at":"2026-08-06T10:32:46.462683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.449636Z","title":"Unzerlegbare Darstellungen I","venue":null,"work_id":"57080edd-c760-4849-96d1-be8afe01742c","year":1972},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.853513Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:f3d0a6817030bac28bf979f0c0197eba983e5e53d6ca8edc703ea84d29b9e354","observation_id":"0f68d8b7-dc2b-4840-86fe-9956b77b4f72","resolution":{"observed_at":"2026-08-06T10:32:46.452746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1703.03632","last_updated":"2021-04-14T13:52:09Z","snapshot_observed_at":"2026-08-07T21:10:55.973982Z","submitted_at":"2017-03-10T11:28:39Z","title":"Stable Invariants for Multiparameter Persistence","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1703.03632","snapshot_observed_at":"2026-08-06T10:32:45.857059Z","title":"Stable Invariants for Multidimensional Persistence","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.857059Z"},"links":{"cited_paper":"/paper/1703.03632","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:a944f75ddd3c0721eebf442152553b5e634f7fd5f26d574ffc7dd035c6fb5d85","observation_id":"f656ee0b-ec17-408c-9565-8a0d836cbc32","resolution":{"observed_at":"2026-08-06T10:32:45.857059Z","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":"2026-08-06T10:32:46.439114Z","title":"Barcodes: the persistent topology of data","venue":null,"work_id":"7ea02ed3-2ad9-4601-8aec-61b7dc22c7b7","year":2008},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.863676Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:e681356fbe9f717c128af850172c04617508143eb53195653a2bfe29d56f646b","observation_id":"1e7b7b83-87f9-4699-9944-0bd5a64a63a9","resolution":{"observed_at":"2026-08-06T10:32:46.443358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1708.07390","last_updated":"2019-06-18T14:10:14Z","snapshot_observed_at":"2026-07-06T05:56:32.711115Z","submitted_at":"2017-08-24T13:22:59Z","title":"Stratifying multiparameter persistent homology","version":2},"cited_work":{"arxiv_id":"1708.07390","doi":null,"metadata_source":"pith","pith_arxiv_id":"1708.07390","snapshot_observed_at":"2026-08-06T10:32:46.176030Z","title":"Stratifying multiparameter persistent homology","venue":"math.AT","work_id":"195a19b8-88f1-4cc3-bab0-d11936d6d159","year":2017},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.866817Z"},"links":{"cited_paper":"/paper/1708.07390","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:a4f2f8cf885bd608ca5aba085931653974b241e8b8b1425fa7591d0698776c7c","observation_id":"549934d3-e228-4958-b60a-3cd31bddcf63","resolution":{"observed_at":"2026-08-06T10:32:46.181481Z","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":"screening/6969260","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.157691Z","title":"Per- sistent Homology for Virtual Screening","venue":null,"work_id":"99c1b6a4-7c5f-4b1b-b9dd-91be50939d42","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.870303Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:b7d4b14f9ae7ea0c4382a1d6753e62d8b1fa236a885f62392269898cda5a1453","observation_id":"afb99f4b-976c-43e6-9784-5129b409b1ea","resolution":{"observed_at":"2026-08-06T10:32:46.163588Z","resolver_source":"raw_fallback","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.427637Z","title":"Exact Computation of the Matching Distance on 2-Parameter Per- sistence Modules","venue":null,"work_id":"8eee46f3-ac3d-4366-8afa-660a9db666b7","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.873785Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:6be126e143c40c47d14ccc117c55a4a56697705caa849cdc55a555fe22d628f1","observation_id":"5f9a4447-3abc-4809-b284-36e9dade8a25","resolution":{"observed_at":"2026-08-06T10:32:46.432104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.417496Z","title":"Ge- ometry Helps to Compare Persistence Diagrams","venue":null,"work_id":"3856785d-3dc9-4108-a2cd-8152d86fcb01","year":2016},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.876748Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:fe05c79cbfc4d5c6ae9d7c5cb98ec324734311ffb1f269e8d6c5a3dc06f39599","observation_id":"66ec2d8b-4417-4546-9dd2-7d6740fe36af","resolution":{"observed_at":"2026-08-06T10:32:46.421634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.406786Z","title":"Efficient Approxima- tion of the Matching Distance for 2-Parameter Persistence","venue":null,"work_id":"657d2e89-810a-4305-aa3d-278533af165c","year":2020},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.881182Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:607fd7bcc1fbdfa9ef6b4a8ab573368f9c4064b6c31658091087d63359990da3","observation_id":"f51a2402-5f66-4807-8037-9427dfc0dcfd","resolution":{"observed_at":"2026-08-06T10:32:46.410463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.395493Z","title":"Per- sistence weighted Gaussian kernel for topological data anal- ysis","venue":null,"work_id":"61786439-6698-4068-97a9-e3a9b5e74345","year":2016},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.885769Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:78cdf041e9dc52590a5be754a069735df0665160e7c27671cf6a8273cbaefeef","observation_id":"7fc88528-c0fb-402f-94f6-945b542148c7","resolution":{"observed_at":"2026-08-06T10:32:46.399552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1412.3374","last_updated":"2014-12-10T17:19:30Z","snapshot_observed_at":"2026-07-06T04:03:11.003049Z","submitted_at":"2014-12-10T17:19:30Z","title":"The rank invariant stability via interleavings","version":1},"cited_work":{"arxiv_id":"1412.3374","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.3374","snapshot_observed_at":"2026-08-06T10:32:46.091142Z","title":"The rank invariant stability via interleavings","venue":"cs.CG","work_id":"f6f15761-849a-4472-bb62-910459410a55","year":2014},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.889405Z"},"links":{"cited_paper":"/paper/1412.3374","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:b24d3d7065982928d0ddab2709ad681d0e0bb934c32a638bc061cc2c6c1f5d32","observation_id":"0ef2d119-12ce-479e-8304-1d9997799311","resolution":{"observed_at":"2026-08-06T10:32:46.096791Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.383018Z","title":"The theory of the interleaving distance on multidimensional persistence modules","venue":null,"work_id":"e9cedea4-8712-4cc1-a9af-48ad30853703","year":2015},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.893061Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:9cb946602f5f9ff1aa617eaeaaaac9e612f0612ebbab4b2441a6a1fa7b0f8724","observation_id":"3dc2d307-eaa1-439d-bcec-acdabd59c92a","resolution":{"observed_at":"2026-08-06T10:32:46.387542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1902.05708","last_updated":"2022-05-19T23:05:34Z","snapshot_observed_at":"2026-08-10T03:10:59.818239Z","submitted_at":"2019-02-15T07:19:16Z","title":"Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology","version":6},"cited_work":{"arxiv_id":"1902.05708","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.05708","snapshot_observed_at":"2026-08-06T10:32:46.074254Z","title":"Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology","venue":"math.AT","work_id":"fff1a904-b05b-4add-aca8-94798150164b","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.896628Z"},"links":{"cited_paper":"/paper/1902.05708","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:d32309225283d043f0fd317ca59d0c8c6da025ca9c850138ba517facdb8c6ce2","observation_id":"cec4ff9b-4f4e-497e-a193-91c086acccaf","resolution":{"observed_at":"2026-08-06T10:32:46.078012Z","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":"1512.00180","last_updated":"2015-12-01T09:12:26Z","snapshot_observed_at":"2026-08-08T21:12:57.668804Z","submitted_at":"2015-12-01T09:12:26Z","title":"Interactive Visualization of 2-D Persistence Modules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.00180","snapshot_observed_at":"2026-08-06T10:32:45.900452Z","title":"Interactive visualiza- tion of 2-D persistence modules","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.900452Z"},"links":{"cited_paper":"/paper/1512.00180","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:81f48bb31e5b9c89df64bc0fa7ab63df5f4796c48c4feafa3a1a7efe898e088e","observation_id":"6242606e-cc92-4f6b-aecd-c88ab7fd27f5","resolution":{"observed_at":"2026-08-06T10:32:45.900452Z","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":"2026-08-06T10:32:46.370783Z","title":"Proba- bility measures on the space of persistence diagrams","venue":null,"work_id":"a3b86c5f-b24b-493e-9d33-0794f4708098","year":2011},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.904188Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:9abe50e01b94b81319c95b2087bb70ea02e474b09cdb2d64e9ac94c285c377e2","observation_id":"be1b432d-7c6d-4a49-b029-088bd1c0ace0","resolution":{"observed_at":"2026-08-06T10:32:46.374348Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1709.08155","last_updated":"2020-08-12T02:56:11Z","snapshot_observed_at":"2026-07-06T06:01:03.421749Z","submitted_at":"2017-09-24T06:50:44Z","title":"Data structures for real multiparameter persistence modules","version":2},"cited_work":{"arxiv_id":"1709.08155","doi":null,"metadata_source":"pith","pith_arxiv_id":"1709.08155","snapshot_observed_at":"2026-08-06T10:32:46.047664Z","title":"Data structures for real multiparameter persistence modules","venue":"math.AT","work_id":"a4a335f0-5b87-45e2-8485-fe69bd8f4169","year":2017},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.908828Z"},"links":{"cited_paper":"/paper/1709.08155","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:efadce831682b5ebd0bf810452f59127322096ced9c5dc026c9f5b9bd86393bd","observation_id":"d2cd58ae-db1e-42e6-abed-7df2ab68cdae","resolution":{"observed_at":"2026-08-06T10:32:46.052232Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.360774Z","title":null,"venue":null,"work_id":"d4f6de60-c29c-4967-9b4e-c1836b488bd5","year":2005},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.912383Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:bea84bc5a2b5986b28024429e999c523870d81d6871f6f5e46f5af56cafffd55","observation_id":"26805ba3-bb17-4bd7-b7bd-d4838803ecf1","resolution":{"observed_at":"2026-08-06T10:32:46.364014Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.349842Z","title":"Topological autoencoders","venue":null,"work_id":"aa52b9ba-19c2-4f98-8130-65011eb5c8bd","year":2020},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.916170Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:86b29f59dd9fc04075eb3c4d57021b72c7245cb9fbab58b4e2cabbac5c6d4ccc","observation_id":"9f1d9c6f-e10f-4782-8f9f-ddc4608a1f90","resolution":{"observed_at":"2026-08-06T10:32:46.353812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.338535Z","title":"A stable multi-scale kernel for topo- logical machine learning","venue":null,"work_id":"0e41ed0a-43c0-4292-a7e4-3fce31623edf","year":2015},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.919400Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:dad696c6b65ea083809ab916974334a64bb11dc03b1f34c739fbe3f5748b0d59","observation_id":"dccd9b4b-0c60-4347-95cc-101d7abe9c7c","resolution":{"observed_at":"2026-08-06T10:32:46.342329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1807.01217","last_updated":"2018-06-13T14:21:26Z","snapshot_observed_at":"2026-07-06T06:48:10.937945Z","submitted_at":"2018-06-13T14:21:26Z","title":"Generalized persistence analysis based on stable rank invariant","version":1},"cited_work":{"arxiv_id":"1807.01217","doi":null,"metadata_source":"pith","pith_arxiv_id":"1807.01217","snapshot_observed_at":"2026-08-06T10:32:46.029639Z","title":"Generalized persistence analysis based on stable rank invariant","venue":"cs.CG","work_id":"650e6732-af13-44f3-842c-e9436dbb688f","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.923140Z"},"links":{"cited_paper":"/paper/1807.01217","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:d546e859dca86d5c4ef29134733576e99bcd6e605cf20fc489a2e43f440d7cf5","observation_id":"201291e4-6ea9-4cf3-a487-61697b33334b","resolution":{"observed_at":"2026-08-06T10:32:46.033970Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.326758Z","title":"Multidimensional persistence and noise","venue":null,"work_id":"c7a79ac6-612c-464f-bcef-1e2b72fd8fe8","year":2017},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.926311Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:c4a8c1b8a98d6415a0683a8090744eeddc7ffeaa46bc72a5942c6869f62d7ab5","observation_id":"3d887650-df1c-4383-b7ef-e5fab43b712a","resolution":{"observed_at":"2026-08-06T10:32:46.330779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.313637Z","title":"A Multicover Nerve for Geometric In- ference","venue":null,"work_id":"9571827d-69be-479b-8966-2118f9e8f6ae","year":2012},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.930190Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:93c12dc0e36d1fe430a2bd960f0d01f904e629bff5e6bcffcb6e203d962e4aee","observation_id":"9ba0ace9-c70c-4562-8f5b-e94bef3e33c7","resolution":{"observed_at":"2026-08-06T10:32:46.317374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.300145Z","title":"ReinBo: Machine learning pipeline conditional hierarchy search and configu- ration with Bayesian optimization embedded reinforcement learning","venue":null,"work_id":"2d196166-12c0-48c6-bcb5-f0ee5136b5a4","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.933854Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:dc03346ff0423ff22d1fa11f8a46b1a97c993f112a8e7271352da10c3a74c2ab","observation_id":"8180f292-04ab-4daa-b1a2-925dd7d46a88","resolution":{"observed_at":"2026-08-06T10:32:46.304629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.287423Z","title":"Reinforcement learning","venue":null,"work_id":"a1c75472-b2fa-4816-a200-4e2e5f259863","year":1999},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.936842Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:fe751f63df824539215253c627ab98cf52be92008c9e4af736ac96c15420b0e6","observation_id":"0cfb27dd-2bf0-4e27-bf36-8bee6f5944c8","resolution":{"observed_at":"2026-08-06T10:32:46.290749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.277181Z","title":"Invariants and Metrics for Multiparame- ter Persistent Homology","venue":null,"work_id":"fa90f79b-16a9-47f3-ae69-004d29b87692","year":2019},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.941004Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:14b54a83c0e1f0a53ba28d80ee00f9b2a5580eb3eb5a369e91c499f68edfe3bf","observation_id":"e721d49f-68fd-4f10-b538-481ddb82ef35","resolution":{"observed_at":"2026-08-06T10:32:46.280799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.265337Z","title":"Fréchet means for distributions of persistence diagrams","venue":null,"work_id":"8864012d-568a-4468-8934-a1fa66b5f7d2","year":2014},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.944962Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:9814ecc45cf097126c450edea9d0988f3aced368b26b9396050307ec42df8d6f","observation_id":"f8893048-2bdd-4dae-92f7-db5216198420","resolution":{"observed_at":"2026-08-06T10:32:46.269222Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"1812.09935","last_updated":"2018-12-24T15:22:46Z","snapshot_observed_at":"2026-07-06T07:23:18.087801Z","submitted_at":"2018-12-24T15:22:46Z","title":"Multiparameter Persistence Landscapes","version":1},"cited_work":{"arxiv_id":"1812.09935","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.09935","snapshot_observed_at":"2026-08-06T10:32:46.014366Z","title":"Multiparameter Persistence Landscapes","venue":"math.AT","work_id":"8da08b84-a895-4884-bdb5-c98111c02bee","year":2018},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.948661Z"},"links":{"cited_paper":"/paper/1812.09935","citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:a00b01e59604cfdb98fc90bbebf469299ca328051c457ca194516733f7b969b2","observation_id":"864c687e-c07e-4d3e-bb68-012d2343d4e4","resolution":{"observed_at":"2026-08-06T10:32:46.018741Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:32:46.253647Z","title":"Nonembeddability of persistence dia- grams with p> 2 Wasserstein metric","venue":null,"work_id":"11d8f802-d561-4d83-a286-cffa3e82d8bc","year":2021},"citing_paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T10:32:45.952876Z"},"links":{"citing_paper":"/paper/2507.23762"},"observation_digest":"sha256:b88a6b32490dc13a05533b9cedebe0c1288d1840bf21785e03e64f86f5329dee","observation_id":"d3a76b37-2d40-4cd9-9974-85d0918ea299","resolution":{"observed_at":"2026-08-06T10:32:46.257181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2507.23762","last_updated":"2025-07-31T17:50:48Z","latest_version":1,"primary_category":"math.AT","snapshot_observed_at":"2026-08-10T02:12:56.731816Z","submitted_at":"2025-07-31T17:50:48Z","title":"Path representations in multiparameter persistent homology"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":10,"verified_fuzzy":31},"total_outbound_references":47},"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 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2507.23762."}