{"as_of":"2026-08-12T11:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8443bce0f05b66797b333c664c8f09c26c1e81d45c5f8235b13fe8c1f173c2fe","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T11:46:33.399563Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"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/2509.02347/citation-record","integrity":"/paper/2509.02347/integrity","json":"/paper/2509.02347/citation-record.json","paper":"/paper/2509.02347"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:46:33.924838Z","title":"Persistence Probabilities and Exponents","venue":null,"work_id":"571eb9e2-60e8-4826-a7b6-addd03d2711e","year":null},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.352080Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:c5b5df81150ac9150b795a5e38a0f66282064437f41dad09c7b54936191fd622","observation_id":"764646f2-274e-443b-84b1-9135028ec071","resolution":{"observed_at":"2026-08-05T11:46:33.928546Z","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":"2026-08-05T11:46:33.900674Z","title":"Balakrishnan","venue":null,"work_id":"f04f0d1d-16eb-4d7e-ae9e-3bfb6253782e","year":2005},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.560805Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:4c745a57a1f8d3d628865dba486c7df3a3d3e61a14d30557923a9aab9e2261bd","observation_id":"fc8fb08e-50d7-4e41-a569-8becbbd8a2bf","resolution":{"observed_at":"2026-08-05T11:46:33.904373Z","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":"2026-08-05T11:46:33.888393Z","title":"Bray, Satya N","venue":null,"work_id":"dc324d80-dfca-4e68-802c-b43ef3789e7c","year":2013},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.660739Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:cadcbf743e9987491c776234b2c79be5b251e6d88f4c7b2c50c5a8004453723a","observation_id":"0701afde-8dc8-4c04-95b3-3b8addb802d2","resolution":{"observed_at":"2026-08-05T11:46:33.892239Z","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":"2026-08-05T11:46:33.875815Z","title":"Interest rate models: theory and practice: with smile, inflation, and credit","venue":null,"work_id":"676cc283-267e-401d-8f46-70e4a3a03693","year":2006},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.768290Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2d41155c3a52a473a42bc7ab747f23479ca44bbc7f84cd9a96b0df433e00c7f9","observation_id":"6f8ef8cd-5450-4bc4-84bb-b3afab83e984","resolution":{"observed_at":"2026-08-05T11:46:33.879711Z","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":"2026-08-05T11:46:33.863193Z","title":"First Passage Time Distribution of a Two- Dimensional Wiener Process with Drift","venue":null,"work_id":"1edde72a-fff0-4ca5-95cc-5aa8eb2736e3","year":1993},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.896088Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2e32e22843f4932df34d0dc2c8aecfae4d7da6f3f7912c9741ba64d9558f7101","observation_id":"f0d966fe-56f5-4a8b-987b-a234208ffcbb","resolution":{"observed_at":"2026-08-05T11:46:33.867083Z","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":"2026-08-05T11:46:33.850867Z","title":"A Simple Exponential Model for Dependent Defaults","venue":null,"work_id":"3b86209e-2b75-4323-a1be-84e06d8fdfe4","year":2003},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.011230Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2dfaca3c7d221028b6638cf59186f5a50c7bb7298d7f1d29af69c53c92899d80","observation_id":"9bd30778-0a1e-41c3-8408-28c6802f9109","resolution":{"observed_at":"2026-08-05T11:46:33.854782Z","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":"2026-08-05T11:46:33.839257Z","title":"Monte Carlo methods in financial engineering","venue":null,"work_id":"42cb1416-d36e-4aae-bbbe-94589c498b2e","year":2003},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.111165Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:0d5a39f865e145b875e1212ec0e9fff27b5ddeb58dd00a1445851f31cbc2bc1e","observation_id":"331dbee4-fdf1-454d-b742-9d8c16ef632a","resolution":{"observed_at":"2026-08-05T11:46:33.842812Z","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":"2026-08-05T11:46:33.827553Z","title":null,"venue":null,"work_id":"e694ab4b-c3d5-4fe5-9b08-2e5f53f233ee","year":2007},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.190608Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:0a14ab7bfeb3d9bb7f78adac56ec104ce4db7a753c9e23f47c04cd4c393eeea7","observation_id":"07789a25-9557-4199-a491-d05897a33e91","resolution":{"observed_at":"2026-08-05T11:46:33.831184Z","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":"2026-08-05T11:46:33.815080Z","title":"Dependent Default Modeling through Multi- variate Generalized Cox Processes, 2025","venue":null,"work_id":"dbfd1bed-f74e-4b56-8c37-6549b15a4c1c","year":2025},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.269121Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:b0bfef3a6475f2f187a85ee3dc5044a7febdb752ff27056f10391614004cad62","observation_id":"77ae76a8-ddc7-496b-a8f9-852923071ee7","resolution":{"observed_at":"2026-08-05T11:46:33.818831Z","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":"2026-08-05T11:46:33.803365Z","title":"Mean-field limit of particle systems with absorp- tion, 2023","venue":null,"work_id":"a5f119e6-3757-4b39-889e-9c9439b25d17","year":2023},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.425397Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:040de3a8ad7b657877d912ecc899670dd4c36e8085061e35f422577e9f1c5311","observation_id":"6eb23283-9951-42e5-bd11-622b3de626c8","resolution":{"observed_at":"2026-08-05T11:46:33.807137Z","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":"2026-08-05T11:46:33.791882Z","title":"collisions","venue":null,"work_id":"aae0f7b7-f2fc-4389-ba04-af010145709d","year":1965},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.577115Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:5c306076dd56f7340540373c3575afb8284c391f96b520023c167715af784951","observation_id":"8b4c1ce0-4fec-40a7-9378-8b9dbf9e4afa","resolution":{"observed_at":"2026-08-05T11:46:33.795577Z","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":"2026-08-05T11:46:33.779837Z","title":null,"venue":null,"work_id":"467cca12-4a88-4911-a1b9-6eec48cb3254","year":1964},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.722861Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:4a910c24c72b4edbdbcac92291dae3b85127f3276d8a2454bbbfbbe67ced06c0","observation_id":"dc29cb15-c504-4397-824c-f03493e5a9c2","resolution":{"observed_at":"2026-08-05T11:46:33.783564Z","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":"2026-08-05T11:46:33.767852Z","title":"Valuation of a CDO and an n -th to Default CDS Without Monte Carlo Simulation","venue":null,"work_id":"c2284355-8de4-4d25-9280-4bab534ecb4e","year":2004},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.809828Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:9d38d30a75cc750c48cb900432293be5c566b6850993050e7fb8906ec195ef12","observation_id":"b1983c0a-e9a6-41d9-acb2-541f6d02e2c6","resolution":{"observed_at":"2026-08-05T11:46:33.771598Z","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":"2026-08-05T11:46:33.754955Z","title":"Hummer, J","venue":null,"work_id":"63ced4c7-d68b-4f79-a308-77442e3755d7","year":2001},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:31.917635Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:cfd4077378ea059aa495ddcf7efad6b47c4bc563dcff024d007d61699b0f265b","observation_id":"7589716e-f441-4f17-ae01-81cb017a9c4b","resolution":{"observed_at":"2026-08-05T11:46:33.758983Z","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":"2026-08-05T11:46:33.742743Z","title":null,"venue":null,"work_id":"08bcfd78-f891-4e8c-8ab6-20709b5ddabc","year":1965},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.012422Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:9c35dbff5b066cccad9875f59f84506a3b02a5253fd2351ec9269761428b705e","observation_id":"96f7cad3-7c37-4431-a4d4-d644135cba25","resolution":{"observed_at":"2026-08-05T11:46:33.746383Z","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":"2026-08-05T11:46:33.730782Z","title":"Analysis of sports data by using bivariate Poisson models","venue":null,"work_id":"ffcca47e-9ed4-4e6a-a5a2-b527e717f2a4","year":2003},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.119675Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:6e1ecf9a8212b12c2ac1a0efc2a6c974aca88d4c2110542c79f308b7b39e9da0","observation_id":"ea0fa5b7-52ea-47d4-8947-62a9df3409d0","resolution":{"observed_at":"2026-08-05T11:46:33.734627Z","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":"2026-08-05T11:46:33.718093Z","title":"The structure of trivariate Poisson distribution","venue":null,"work_id":"c4d3c566-9dbc-4cec-9a56-8d14932740a0","year":1976},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.213622Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:ee1678e0771839375840a25d769f2cf34eef3514680928dc7e144cff78a72ec6","observation_id":"f568bba5-46f9-4a92-9797-c5e9105097f3","resolution":{"observed_at":"2026-08-05T11:46:33.722165Z","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":"2026-08-05T11:46:33.704703Z","title":"The structure of multivariate Poisson distribution","venue":null,"work_id":"8f9ed941-0fce-488f-bc95-932c52419a10","year":1979},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.307683Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:e2d8beb2eaa2cfbfdb540bd9ca7f8ac7d96f5602498b7281917b831f0fc7acc3","observation_id":"aad354f7-1f4e-4601-aec9-6558b18cfcff","resolution":{"observed_at":"2026-08-05T11:46:33.709265Z","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":"2026-08-05T11:46:33.692402Z","title":"Kloeden and Eckhard Platen","venue":null,"work_id":"2d119977-465f-4107-a899-5b529ecbcbe7","year":1992},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.356629Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:7d250d6f14de30343d6ca17b1655c9ccaa061cc2983b657d69222c940abc1855","observation_id":"0f7616b6-7b4b-4484-ba3c-b85399422d5f","resolution":{"observed_at":"2026-08-05T11:46:33.696150Z","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":"2026-08-05T11:46:33.679734Z","title":"First-passage times of two-dimensional Brownian motion","venue":null,"work_id":"fb95be6a-f1df-461f-96e2-9670b89cf4d2","year":2016},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.444250Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:d705ee6eff46e8618e4f4311ce01515327f35f6c45edd27561bff42258ab340d","observation_id":"cd1b15aa-3794-404d-9b29-a6560e86b5cc","resolution":{"observed_at":"2026-08-05T11:46:33.683831Z","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":"2026-08-05T11:46:33.666788Z","title":"The First Exit Time Statistics and the Entropic Forces in Single File Diffusion, 2022","venue":null,"work_id":"d5d19e34-6599-42e7-8535-b08e1b720796","year":2022},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.546270Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:68dedcd18edd2fee83603295dbc92379a8deba2293fbac367afe66e05e3dff9e","observation_id":"d7e806d1-7ac8-4f15-8feb-b498acf077dd","resolution":{"observed_at":"2026-08-05T11:46:33.670778Z","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":"2026-08-05T11:46:33.653635Z","title":"BetheSF: Efficient computation of the exact tagged- particle propagator in single-file systems via the Bethe eigenspectrum","venue":null,"work_id":"75fb590b-ec83-4ca2-a2ab-62022326b97f","year":2020},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.653321Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:82022cd2740338dfa48868983533f27778e412feddc6fe33ac688157b964adb6","observation_id":"d06b812c-fc5e-4f8c-acab-f6bff137c3f3","resolution":{"observed_at":"2026-08-05T11:46:33.657781Z","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":"2026-08-05T11:46:33.641368Z","title":"Basket default swaps, CDOs and factor copulas","venue":null,"work_id":"87b526d2-44ee-415b-ba38-f09c8092f413","year":2005},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.772747Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:759cef2291d9fe8e3c683852585e6aa7b22eeb0d806f34a3879bf8696aa841d2","observation_id":"e6e7d4c2-8599-4baf-978c-da5141940db4","resolution":{"observed_at":"2026-08-05T11:46:33.645226Z","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":"2026-08-05T11:46:33.629216Z","title":null,"venue":null,"work_id":"99a479b6-08cd-475c-b6e9-2b5f5b096583","year":2020},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:32.896858Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:e8134c5fe6c4b4c0efe6650051e158dfbbba21e4b5bfa95f049fe162016b872f","observation_id":"ce65f0a9-338f-4a2a-a333-7b8facf2f396","resolution":{"observed_at":"2026-08-05T11:46:33.632908Z","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":"2026-08-05T11:46:33.616984Z","title":null,"venue":null,"work_id":"d1251e9f-56d0-472c-9d32-dc6e99b2868a","year":2000},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.033182Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:087d16cd4feb7d16d81d091d8a8fac0807ea6ffe98941eed979618d47c463109","observation_id":"11a13b56-43fd-4c67-a761-c9e2f5b27345","resolution":{"observed_at":"2026-08-05T11:46:33.620527Z","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":"2026-08-05T11:46:33.605228Z","title":"Berg, and Johan Elf","venue":null,"work_id":"9915061b-6530-41c4-9646-8599bc22456c","year":2009},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.189557Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:76addf5ecaa0828e0ddcc48c1071ca5655a190826991d6c6ff6ed2ff4ea5d1bd","observation_id":"c102f450-6602-4157-b333-378a8415c80e","resolution":{"observed_at":"2026-08-05T11:46:33.608649Z","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":"2026-08-05T11:46:33.594176Z","title":"Active Brownian particles escaping a channel in single file","venue":null,"work_id":"22eae7aa-4177-4ffb-a196-b5d66503f945","year":2015},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.351657Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:660e68e9f76234abbd8aaffc4cfaa6fc3727fadccfc13ed7382ae486a1b109c3","observation_id":"43de326d-90eb-439a-b8d4-dcbd885236e4","resolution":{"observed_at":"2026-08-05T11:46:33.597670Z","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":"2026-08-05T11:46:33.581987Z","title":"Single-File Escape of Colloidal Particles from Microfluidic Channels","venue":null,"work_id":"571abe5d-846a-4706-bf21-f5dd247460e4","year":2016},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.356032Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:1f930dba2619398781f29e5d2d2f879367d7e8012fbc0108f0e62e5724266cb0","observation_id":"e99b4bc0-ff0b-4f12-b7f0-1b56076d60fb","resolution":{"observed_at":"2026-08-05T11:46:33.585619Z","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":"2026-08-05T11:46:33.570227Z","title":"Credit and basket default swaps","venue":null,"work_id":"4088a5f5-ec7a-4ab3-96e7-2ec679a9d9d4","year":2006},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.360390Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:652d939b0c5aa8ee809ca09c778eaa259cf46e368a1a5d5be127c4cf008fb618","observation_id":"cdfe6ba5-13f2-4487-89be-c6933ec570eb","resolution":{"observed_at":"2026-08-05T11:46:33.573838Z","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":"2026-08-05T11:46:33.557739Z","title":"Majumdar, Arnab Pal, and Gr´ egory Schehr","venue":null,"work_id":"6e045b13-b503-44b6-8988-9f9a9d2f51d1","year":2020},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.363875Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:94a2d66b374a30fe9388633a8da7a696e37de48b35f7cd5005c5b3f4cf5d3b5b","observation_id":"c63a3a4d-2e3c-4ae1-9053-54bac7f8c15e","resolution":{"observed_at":"2026-08-05T11:46:33.561762Z","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":"2026-08-05T11:46:33.545347Z","title":"Marshall and Ingram Olkin","venue":null,"work_id":"72d6bd9d-8dbb-495c-9e7d-61d3e699ac53","year":1967},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.367431Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:cce887d1ff3e6d44291e307d65c039e07a49733b35f6e32644b921c2b93df95a","observation_id":"613b4acd-50b1-414d-8e82-607365ea9f63","resolution":{"observed_at":"2026-08-05T11:46:33.549308Z","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":"2026-08-05T11:46:33.533611Z","title":"Semi-Analytical Valuation of Basket Credit Derivatives in Intensity- Based Models","venue":null,"work_id":"f463be34-300e-45e3-bc1e-1fa2bb1ff2b9","year":2006},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.371022Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:8ee2b88ee940ca54e03379520d164b34f17170ca956280cc05c17c45865b9ffe","observation_id":"3998ca88-f331-46a8-bbd3-634dedb167ff","resolution":{"observed_at":"2026-08-05T11:46:33.537253Z","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":"2026-08-05T11:46:33.521949Z","title":"Navarro and Ian G","venue":null,"work_id":"a04bdac8-4328-4d0e-aaea-72c0edfe979f","year":2009},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.374502Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:a335a0b62b0e9e677f18a3936a9266a01305d7d9d20944b40a939c99e575eab0","observation_id":"7ba2433a-477d-49d8-a85e-0f9cd921d70f","resolution":{"observed_at":"2026-08-05T11:46:33.525349Z","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":"2026-08-05T11:46:33.509493Z","title":"Stopping times occurring simultaneously","venue":null,"work_id":"09a6cdad-9a24-4c1f-8d31-811dbfb6dd80","year":2024},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.377951Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2271ada49b67ed7edd271dbcfdd72b538100203d005b9c6816231603661ae835","observation_id":"e98be8d8-cf7e-414e-8213-1c0080056ed7","resolution":{"observed_at":"2026-08-05T11:46:33.513701Z","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":"2026-08-05T11:46:33.496124Z","title":"A guide to first-passage processes","venue":null,"work_id":"018eeb3b-1d3c-49f4-8692-33c02b15755b","year":2007},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.381521Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:81c889e302950530f9240ce66f00a55752db232a3106826ee411f12860b9e970","observation_id":"82f5e717-fdd9-47c8-ad6c-cb4de8d33fb3","resolution":{"observed_at":"2026-08-05T11:46:33.500493Z","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":"2026-08-05T11:46:33.482593Z","title":"Single-file diffusion in an interval: First passage properties","venue":null,"work_id":"6285705b-a68b-433e-ac59-7242a76cb668","year":2013},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.385226Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2dcec5d9f4718da89de274057606bb295e0c8763cc292c8a62ab363e14419b18","observation_id":"4f4c3015-9a24-40db-80f5-bc71d5098a75","resolution":{"observed_at":"2026-08-05T11:46:33.486495Z","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":"2026-08-05T11:46:33.469885Z","title":"Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications","venue":null,"work_id":"8014f02e-e84a-4ea8-9725-cde8b8bd2e9f","year":2058},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.389105Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:c5c7ce710ab892877f8e60173d23514418ef4a20f7dd4dd0c54c51a2172f73f2","observation_id":"1c82524c-775e-4b6a-a14a-fab368c37390","resolution":{"observed_at":"2026-08-05T11:46:33.473902Z","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":"2026-08-05T11:46:33.457237Z","title":"First passage times of two-dimensional correlated processes: Analytical results for the Wiener process and a numerical method for diffusion processes","venue":null,"work_id":"73ee7a7f-f5d2-4bb4-8ec6-e9198f1fff1e","year":2016},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.392668Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:167d1ab9c10c8b46276b54b5b154453be4f5b57c0899fc23564e1d5ac660cc6f","observation_id":"ba118f9d-8eaf-47fe-8999-56b5b7b01580","resolution":{"observed_at":"2026-08-05T11:46:33.461506Z","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":"2026-08-05T11:46:33.444649Z","title":null,"venue":null,"work_id":"bffa06e0-e68b-4137-a8e9-b40fd10e026d","year":1982},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.396085Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:2711db82c151612ac521663c05b188fec4baf2466a49d47fd7943f33df565989","observation_id":"9caedfba-2d78-43d3-917b-acdeeae6bbc2","resolution":{"observed_at":"2026-08-05T11:46:33.448422Z","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":"2026-08-05T11:46:33.428831Z","title":"An Analysis of Default Correlations and Multiple Defaults","venue":null,"work_id":"d274fb5b-fdae-4405-8bf7-7a7858d33673","year":2001},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:33.399563Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:3c9a017ad98fe82d23a80967523d14d884e1ae517d935c024901508973eced43","observation_id":"ef2ef5e4-bac3-4a6c-98c4-43ec007aaf54","resolution":{"observed_at":"2026-08-05T11:46:33.435125Z","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":"2026-08-05T11:46:33.912453Z","title":null,"venue":null,"work_id":"a7c22c7e-9ac3-432e-aadd-d1d1e126c11f","year":null},"citing_paper":{"arxiv_id":"2509.02347","last_updated":"2025-09-10T04:10:06Z","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS","version":2},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-05T11:46:30.458635Z"},"links":{"citing_paper":"/paper/2509.02347"},"observation_digest":"sha256:fd93ca9cc293586d113cb410caaead9f726ab3aad4c4bc9ee20639f28873fadc","observation_id":"29daacad-0f83-40fd-97a4-7f6cd4305fc1","resolution":{"observed_at":"2026-08-05T11:46:33.916275Z","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":"2509.02347","last_updated":"2025-09-10T04:10:06Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-08T06:43:24.975408Z","submitted_at":"2025-09-02T14:14:30Z","title":"A recursive formula for the $n^\\text{th}$ survival function and the $n^\\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\\text{th}$-to-default CDS"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":34},"total_outbound_references":41},"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 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2509.02347."}