{"as_of":"2026-08-22T06:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3880e1142094ece43239e906aa98386e2cdb208f00541672a1d4efe1b562e802","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":"2026-08-06T15:15:09.582540Z","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":"2026-08-21T06:32:19.484+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/2507.16644/citation-record","integrity":"/paper/2507.16644/integrity","json":"/paper/2507.16644/citation-record.json","paper":"/paper/2507.16644"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:15:10.200536Z","title":"Vanishing coefficients in the expansion of products of Rogers-Ramanujan type","venue":null,"work_id":"a1d6baa5-2f52-4f12-8189-20620a189edf","year":1994},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.394193Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:f4243cb04072d9ae856f805adc0a88ffa06564c922482fa5bb39aafeceb3aeb0","observation_id":"56334af3-abda-4eea-b81d-dd294a2fb72e","resolution":{"observed_at":"2026-08-06T15:15:10.204936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.185368Z","title":"On a Conjecture of Peter Borwein , Journal of Symbolic Computation, Volume 20, Issues 5–6, 1995","venue":null,"work_id":"6b111342-e807-4e3b-81e4-2c3f4fde0429","year":1995},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.399166Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:2a2cc95588ce4dfed6bad3db8343c7281d889ab706bbab757b3689bd7c58ebbe","observation_id":"b3eceb4c-7f49-4b21-a814-3c2080feaa3f","resolution":{"observed_at":"2026-08-06T15:15:10.190782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.171577Z","title":null,"venue":null,"work_id":"f51dd989-2d27-4a8b-a091-3e360fc93edb","year":1981},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.403877Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:3e351554b38a9d22ba54897fd844744a987c5929715f0ee952817676c2e13235","observation_id":"baa8f9d0-ae21-4348-b20e-a126cef66510","resolution":{"observed_at":"2026-08-06T15:15:10.176132Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.157890Z","title":"E.; Bressoud, D","venue":null,"work_id":"b8b20130-ac1f-4db2-a27e-623fa1a47570","year":1979},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.408731Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:39ab0a9394cd21ef218d235760916c598e7e8d771b3a5644d43341436a0c87e3","observation_id":"169c8f38-77a4-4421-b93b-ab5a065982a9","resolution":{"observed_at":"2026-08-06T15:15:10.162434Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.144301Z","title":"Baruah and M","venue":null,"work_id":"0a2fdb59-c2f6-4ced-88b7-f5e8188bd04e","year":2020},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.413826Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:85a1f864b8515bbdec4c9faa67a9a2ec04998185acc3f6635e9fa77a987d3315","observation_id":"b781c50b-3415-4cba-bd43-7509945f181a","resolution":{"observed_at":"2026-08-06T15:15:10.148819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.130670Z","title":null,"venue":null,"work_id":"6b6b2853-e74a-479c-9000-e53efdd6ebe9","year":2025},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.418124Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:b321cdf51f0faf6920fccf28fad4fc26e94c12370c5feffe191eb455444f07f4","observation_id":"893d4ca5-e65a-4735-924e-50e81d6a4f24","resolution":{"observed_at":"2026-08-06T15:15:10.135011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.115000Z","title":"Sign changes of Fourier coefficients for holomorphic eta-quotients , preprint","venue":null,"work_id":"523d4ab2-8b3f-41b0-8a70-b78164643de6","year":null},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.423957Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:ecb51192fb3be9bd0356fa34ea00d56c6b3bd8ba9f181dcadfb430bb8dbc81ea","observation_id":"ec762399-fbc1-4b7b-80ff-59e202545fde","resolution":{"observed_at":"2026-08-06T15:15:10.120578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.100523Z","title":"Vanishing properties of Fourier coefficients of holomorphic η- quotients, preprint","venue":null,"work_id":"9d32a1ef-33f3-4ffb-b5c2-581409a9d81c","year":null},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.428817Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:6ab77a68a9291261ca18c6192d4a1a70b12c80193060b89b7f4c11f1118c7832","observation_id":"a6913e7f-701b-4790-b6c7-6b92fa76276e","resolution":{"observed_at":"2026-08-06T15:15:10.105078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.086583Z","title":"Periodic sign changes of weakly holomorphic η-quotients, preprint","venue":null,"work_id":"edd5a833-b279-4fe6-a776-1f9b8c545253","year":null},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.433253Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:c81a8d280a31bb129913b1f7d1ffd15330a2e7ab8ca6eccf40e36d9f659435ad","observation_id":"6d3bfd28-8eef-44b4-9d8b-114f8ea7d5a5","resolution":{"observed_at":"2026-08-06T15:15:10.091146Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.072355Z","title":"On a generalization of vanishing coefficients in two q-series expansions","venue":null,"work_id":"dbe23dc2-ab19-4005-a63b-e5a693ac6197","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.438217Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:a5d39a095a6bb02eb54eb3b85bcbd58a7228100debd79e9036e1af61505ecb7d","observation_id":"fa8c1192-d452-46a5-a43f-902489ff9f85","resolution":{"observed_at":"2026-08-06T15:15:10.076965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.057871Z","title":"K.; Dasappa, R","venue":null,"work_id":"3a032c8b-bf56-48bd-b5cc-66365d9cfb20","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.443380Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:a7482900d3068c8acf0701bd490832452be1836809b1bb4445a951466bebb7ea","observation_id":"71838225-b40a-4800-8f36-b9878d7cc742","resolution":{"observed_at":"2026-08-06T15:15:10.062780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.042049Z","title":"Vanishing coefficients in quotients of theta functions of modulus five","venue":null,"work_id":"d146814c-6eb3-4278-ad09-98839a1a1795","year":2020},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.447882Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:362f2c6034b0f2f6964c2c1287a1f25715e527345667a42a4f123d2c7ec25722","observation_id":"e2ea9c61-5eec-44ae-a248-58e0c5ab3c1e","resolution":{"observed_at":"2026-08-06T15:15:10.047520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.026352Z","title":"5-dissections and sign patterns of Ramanujan ’s parameter and its companion","venue":null,"work_id":"4ff2e145-c272-4bca-9a25-fed7e330bb26","year":2021},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.452838Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:d31a7bd84ef6720e969eafecae49b010eb751e9bfb37d612525691438df2730d","observation_id":"97cdcdeb-98f5-4a1d-ab50-3c1abc4be090","resolution":{"observed_at":"2026-08-06T15:15:10.031635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:10.011387Z","title":"General coefficient-vanishing results associated with theta series","venue":null,"work_id":"0c74b80d-0604-4e0c-b71a-c807116d43b7","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.457305Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:ea8eeaec3dab5f23fc2d3b08249d1b90c8dd14c101e90334ca7798c87e17b542","observation_id":"b0af9e3b-598d-4526-bab5-f5d9aabdcf3d","resolution":{"observed_at":"2026-08-06T15:15:10.016321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.995606Z","title":"Modular forms: A classical approach , Graduate Studies in Mathematics, Vol 179, Amer","venue":null,"work_id":"414216f1-3dd4-4309-b18e-895b27935735","year":2017},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.461861Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:785a15bb708413369b0b9e2bcdacc5f0cfe4c54c5b4ea508f36249e5f18fcc34","observation_id":"7971ff14-e7e2-4e19-97f1-b48f92fff679","resolution":{"observed_at":"2026-08-06T15:15:10.000363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.980651Z","title":"Ramanujan ’s theta functions, Springer, Cham, 2017","venue":null,"work_id":"938bccc1-b3cc-4e19-a689-9253becb0cf7","year":2017},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.466239Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:8f67e93e8e2de27f850dab47a8d868eeafc64e0cd063126ba447790fb011a52d","observation_id":"244a7b91-1c7e-4286-9609-c1dd5331b1e7","resolution":{"observed_at":"2026-08-06T15:15:09.986059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.965321Z","title":"Vanishing coefficients in two q-series related to Legendre-signed partitions","venue":null,"work_id":"2cc5c64d-65bb-45d4-acc1-30bdb2a056ea","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.471233Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:1cad4a1bab8eebeab67b6e00c71afc675b2e84f877618269a6c4564c2600f15a","observation_id":"418ccccf-cf0e-47dd-b5aa-a9c5bd131733","resolution":{"observed_at":"2026-08-06T15:15:09.970870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.951106Z","title":null,"venue":null,"work_id":"6e74ed87-bbed-4d9d-a61e-ff69a8e53ccd","year":2021},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.476272Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:9ddcccef64789a574efb444a06b7daf5667338a86999cf8cb1d64af874866884","observation_id":"e6f4d955-5938-45a3-a6d5-aeeec4c96a14","resolution":{"observed_at":"2026-08-06T15:15:09.955353Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.936830Z","title":"Collected Papers of Srinivasa Ramanujan (AMS Chelsea, Provi- dence, 2000)","venue":null,"work_id":"d91bbba8-d33f-4d21-b777-6dbbfb17bdc1","year":2000},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.481014Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:93a2024c47e1b5a926f8beeedfe61a515334c80733e2a2a31292cdda9dd48052","observation_id":"fc82330c-18ad-48e4-9121-801e3f74e52e","resolution":{"observed_at":"2026-08-06T15:15:09.941455Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.922560Z","title":null,"venue":null,"work_id":"35ff74c7-9d91-49a4-b331-656c20ce805a","year":1998},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.485588Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:d0c630f8c8baebf4043d6bf36152b956dd63da9880304bb23b06e9561cbeb5e9","observation_id":"8f274f12-90ae-4df1-914b-9c31f25f7239","resolution":{"observed_at":"2026-08-06T15:15:09.927307Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.907272Z","title":null,"venue":null,"work_id":"12ea49fd-7f2a-4686-a515-8e4b215a65b7","year":2019},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.490292Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:443ae00b65619a93f88370f9e5ec1312c92b1ebd8dddc353af2fe86defc6e80f","observation_id":"c5989111-6f90-4929-b74c-7a4a54640041","resolution":{"observed_at":"2026-08-06T15:15:09.912752Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.891793Z","title":"Dissection of the quintuple product, with applications , preprint","venue":null,"work_id":"6fd1596d-f5fe-45f4-a2ce-465848a1dc8f","year":null},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.494968Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:b12c4f40339bb804351e3123575ffea3e4fdd877ec5aa7fee21f3b6e3a5a26c1","observation_id":"5e67d540-0a4c-425e-b6a5-f6a694afdaaf","resolution":{"observed_at":"2026-08-06T15:15:09.896590Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.877384Z","title":"Results on vanishing coefficients in infinite q-series expansions for certain arithmetic progres- sions mod7","venue":null,"work_id":"f8f5d98f-74a7-4e96-8e04-a0c0be0206e4","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.499246Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:001cad03a1c4aa495580fa7688c02f280353c797b8bdfc31fb181f5a2c9e4ff0","observation_id":"bd99e91a-a0ae-4d15-82d6-81c1967d4fc7","resolution":{"observed_at":"2026-08-06T15:15:09.881975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.863153Z","title":"On the vanishing coefficients of odd powers of Ramanujan ’s theta functions","venue":null,"work_id":"70579d14-5024-4458-94df-dc01cc03b3db","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.503969Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:38edbc93ce825f2234420d3d6331370e91591cca273ef97896de386b015ece11","observation_id":"1851f6d0-7138-46fe-917b-238bac63c5ec","resolution":{"observed_at":"2026-08-06T15:15:09.867742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.849086Z","title":"Further results on vanishing coefficients in infinite product expansions , J","venue":null,"work_id":"11e6b8e0-090c-4c32-8997-fcca438aa391","year":2015},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.508468Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:495e161f6a4628961297c38938897b7b1c754130d8039b607c2aa051d4474b76","observation_id":"4a333711-2074-476d-97c0-e00f0e4a5816","resolution":{"observed_at":"2026-08-06T15:15:09.853664Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11139-020-00275-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"New infinite q-product expansions with vanishing coefficients","venue":"The Ramanujan Journal","work_id":"4b0f11fd-2b1a-4ecd-a1da-ed37d60b08a2","year":2021},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.513024Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:e249728b15874e3acde5a5e6ade6e499e4d698f6e21fe2b429fdd7d940ef7c4b","observation_id":"a7c7f0d9-a97f-46e2-9b76-b38ea06385fc","resolution":{"observed_at":"2026-08-06T15:15:09.619527Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.834334Z","title":"m-Dissections of some infinite products and related identities , The Ramanujan Journal (2022) 59:313–350","venue":null,"work_id":"b926a200-eaa4-45e6-aa1a-7a328794f32a","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.517496Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:a2748159d51003a761cf9478f784c64b9510ce1fb606b1ca165decd625e6531d","observation_id":"e7cada93-74b7-4580-8844-d0bae37e709d","resolution":{"observed_at":"2026-08-06T15:15:09.839362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.820563Z","title":"Further results on Vanishing Coefficients in infinite products of the form (qb, qp−b; qp)3 ∞(qjb, q2p−jb; q2p)∞ Int","venue":null,"work_id":"3fa2ee3d-ddc8-464f-8d2b-14adacfee7cb","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.522336Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:43817176e9f6b67f429fda6ca16c5535f2df4732cfac12c6b5e181e127e5e190","observation_id":"2aa05ffa-9560-4ded-9014-2c63fd41bd6b","resolution":{"observed_at":"2026-08-06T15:15:09.825033Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.806128Z","title":"Theta-function identities of Ramanujan ’s continued fractions of order fourteen and twenty-eight, partition identities and vanishing coefficients","venue":null,"work_id":"f0c61715-e7a6-4254-bff2-79031faee592","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.527213Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:fa2c4c4c7c9efffd52de68ca49ea1bc1027b425c80ff177950feba0abc0972f0","observation_id":"1e5dae6d-c262-4fb7-91e3-1bb1ae992689","resolution":{"observed_at":"2026-08-06T15:15:09.811340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.791072Z","title":"The Taylor coefficients of certain infinite products","venue":null,"work_id":"a0e9e504-bf8f-43ab-bcc6-2cc5ab2c54b2","year":1978},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.532173Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:ea41b19546bd9f211a023e271738cf6508fbb1b009870918d2e9bf0647de0d29","observation_id":"bcc5ea96-1195-4843-89de-7bad46d6b711","resolution":{"observed_at":"2026-08-06T15:15:09.796367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.777125Z","title":"J.; Zhou, N","venue":null,"work_id":"93cc90c2-2be2-4160-ba45-f6c10ff5f44b","year":2023},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.536563Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:a66e0e44a9680d9b9a0244113f3da3012775fe637504e7947b4483df1fb07704","observation_id":"7216e285-939a-418e-a57a-719723bb6997","resolution":{"observed_at":"2026-08-06T15:15:09.781860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.763551Z","title":"D.; Thulasi, M","venue":null,"work_id":"8c5d0ad3-6a1b-4ad1-a9fb-2725e83c011d","year":2023},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.541285Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:60a5c57dc700636a904cb46b2544a00bc3dba984e9e32967ee018b73ce8b8955","observation_id":"d0fd15be-2d61-4624-9f8f-ea34813bd4f9","resolution":{"observed_at":"2026-08-06T15:15:09.767889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.749501Z","title":"Vanishing coefficients in some q-series expansions","venue":null,"work_id":"90a010b6-8496-4408-878d-53ffb5043df0","year":2019},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.546269Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:511c4f89bc1c2df07b9d03ce46c87b860f5e2cf6d97f998964c920ac9a31a9ae","observation_id":"84e31e78-9a29-4aa7-a33d-57af1c7c4324","resolution":{"observed_at":"2026-08-06T15:15:09.753967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.734817Z","title":"Vanishing coefficients on four quotients of infinite product expansions","venue":null,"work_id":"06bfdf82-6bce-4042-8538-b94892ed70b4","year":2019},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.550651Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:ec1bb97072a33cd5b1ee032678835216a66f6286e0285ec8987b6c7db8f64924","observation_id":"aceaa51d-5779-4ed3-8e2f-8891627ef629","resolution":{"observed_at":"2026-08-06T15:15:09.739791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.719358Z","title":"On 5- and 10-dissections for some infinite products","venue":null,"work_id":"b58dce4a-ddd5-408c-bebe-ad6fde169bf2","year":2021},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.555189Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:671495f1d13d3f613595435adba4a8aeca61b55033af0711db540ca5a2ca2013","observation_id":"c560c997-55e7-4739-a314-77ff31c8d2d1","resolution":{"observed_at":"2026-08-06T15:15:09.724647Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.705399Z","title":"Vanishing coefficients in three families of products of theta functions","venue":null,"work_id":"a56c5a45-519b-4c5a-be8f-1f206cd57926","year":2023},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.559596Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:8a5f33f1a485bc87927873b416c79adf11355899229f858b2c0361caf44eadee","observation_id":"867f3ab1-e9bf-4fb6-b18e-1509bb935591","resolution":{"observed_at":"2026-08-06T15:15:09.709849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.688816Z","title":"Vanishing coefficients in three families of products of theta functions","venue":null,"work_id":"98570254-7e62-4a8d-a5a3-12dd8d7e83a3","year":2023},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.564960Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:188aea28d0b4c2a246a8a25f6a8ef00a7530718afd606f5338bf7fb02ef275d6","observation_id":"9138ba3b-07fe-4260-89b5-81c7af695691","resolution":{"observed_at":"2026-08-06T15:15:09.694331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.673018Z","title":"Vanishing coefficients in powers of theta functions with odd moduli","venue":null,"work_id":"3d583713-eef3-4ea6-a561-06c53cfe6dcb","year":2024},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.569273Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:a37c39b97c16200916cc11b435650f01d2a588cf6f0991924e467f6b197f7850","observation_id":"53c9112a-1a58-4386-b6c8-261d2fa9694d","resolution":{"observed_at":"2026-08-06T15:15:09.677529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.658864Z","title":"Vanishing coefficients of q5n+r and q11n+r in certain infinite q-product expansions","venue":null,"work_id":"d3ec57d7-cfc6-44d5-a10a-8a492cfdf4f4","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.573964Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:27263cff4fae64e2822c617e05d1a49f2faa2170be5f3147fccc3bc1e2bdead4","observation_id":"415e4e8d-cb86-4b12-8b41-a8b36f09685f","resolution":{"observed_at":"2026-08-06T15:15:09.663382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.644185Z","title":"Sign changes of coefficients of powers of the infinite Borwein product","venue":null,"work_id":"6775cdac-3de6-41a5-882b-cbbfe006e0a6","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.578147Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:7035d32ad397f3bc74cb5a1b21a0ee6265c0ac6a9a6868926ce923930950b49d","observation_id":"a6672218-8454-4859-abbd-3c74eaa1e06b","resolution":{"observed_at":"2026-08-06T15:15:09.648880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T15:15:09.629782Z","title":null,"venue":null,"work_id":"b0e8bf21-bf59-4951-a95e-e38774ee1b98","year":2022},"citing_paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T15:15:09.582540Z"},"links":{"citing_paper":"/paper/2507.16644"},"observation_digest":"sha256:608b68f651b29e0ff5d41c53bfe637831a578c0303ba92014d143269e3fcda60","observation_id":"4b0728e5-27d1-4a3e-9ccb-4808dca8251b","resolution":{"observed_at":"2026-08-06T15:15:09.634215Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.16644","last_updated":"2025-07-22T14:42:04Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-14T01:41:01.982874Z","submitted_at":"2025-07-22T14:42:04Z","title":"Sign-patterns of Certain Infinite Products"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":1,"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2507.16644."}