{"as_of":"2026-08-11T17:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5797e8085d647ec13eafa865e0c99a1efb450ab2cacc58c91ddf276f34614b19","coverage":[{"denominator":75,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":75,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:55:39.535855Z","state":"measured"},{"denominator":75,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":75,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2507.07055/citation-record","integrity":"/paper/2507.07055/integrity","json":"/paper/2507.07055/citation-record.json","paper":"/paper/2507.07055"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:55:40.332101Z","title":null,"venue":null,"work_id":"5ed25382-aab9-4387-91f3-0fdf4a07a52a","year":1993},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.281702Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:9159cb5b8e1ed8c4747bcf9da9c867aeaf12e3965fbff05f3bc749d28d6b5efd","observation_id":"4f2d2f93-6aaa-40b3-91d6-52fa55a7e59b","resolution":{"observed_at":"2026-08-06T18:55:40.335398Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.322692Z","title":"I., Ariffin, M","venue":null,"work_id":"a2d8196c-305a-49ef-aa51-ae85d5deadec","year":2019},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.285529Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:ccd512493af699ac0649a2a1b8edea8947c7508db522b76d758b739d219f3f73","observation_id":"15fd9221-d04d-4997-9d6f-7963e4e00181","resolution":{"observed_at":"2026-08-06T18:55:40.326167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.312193Z","title":"and Saxena N","venue":null,"work_id":"3e386e14-319a-4465-99ca-a52b7b9ed5d0","year":2004},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.289309Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:47722171a94e664faefa289aa4807217ade1b877f20281e3cd63ef7c1c642b40","observation_id":"f961777b-58ad-4ac1-8542-7cdb7df83973","resolution":{"observed_at":"2026-08-06T18:55:40.316062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.301501Z","title":"A comparison with the Gaussian Integer Method, Mathematics of Computation, Volume 72, Number 242, Pages 953–967","venue":null,"work_id":"8495a4dd-1764-40fc-989c-a939eaa402be","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.293163Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:55ebd1e848e31da3487e2e3d3cc56a9b592e46efa226409d04c9531db5444f6e","observation_id":"8b0b8b0a-428b-4313-9bdb-49dd63379c0a","resolution":{"observed_at":"2026-08-06T18:55:40.305217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.291622Z","title":"Lenstra and H","venue":null,"work_id":"2262b164-0e80-4264-8475-ae7bfd2fbf0d","year":1993},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.296827Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:2557e8f4bbe615e4e2c49ef8b0769efa6f129903bbb97ed9fdcf0a7d097fba9f","observation_id":"119ec394-8dbe-4f0c-9979-384ac222ef14","resolution":{"observed_at":"2026-08-06T18:55:40.295054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.280964Z","title":"Sugli integrali multipli","venue":null,"work_id":"b317ea8b-cd1d-4c9b-bdd2-0875dac4936d","year":1907},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.300406Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:d92dc0474f28e584f722e02179135aea64ed5b3abc6834b39a87cbb278652fa0","observation_id":"36853b76-fd8c-4bcc-b43c-00103d481e04","resolution":{"observed_at":"2026-08-06T18:55:40.285074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.270865Z","title":null,"venue":null,"work_id":"2e93aad2-a1c3-4b71-ac48-904c9ed1a1eb","year":1977},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.303881Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:bf32f02ee0daa4294d200fe228ae95429015487b4df5771dcb5f23686df66377","observation_id":"4fea4dc4-77e8-4215-85c1-1974c2efa838","resolution":{"observed_at":"2026-08-06T18:55:40.274602Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.259327Z","title":"Coppersmith, Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities, Journal of Cryptology, 10(4), 1997, pp","venue":null,"work_id":"386705ee-5993-483b-b9a8-9a4bc2d96008","year":1997},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.307147Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:f010b656949c09977289babf9ef2bcad022e6c286e96cec8843f43780dbccef6","observation_id":"33d1ef8a-f9ce-4512-a8c3-5cc45e2844bf","resolution":{"observed_at":"2026-08-06T18:55:40.263912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.248449Z","title":"(2007) Faster Addition and Doubling on Elliptic Curves","venue":null,"work_id":"4f8824cd-5e9a-4c6c-9cec-af8a9fb1dde6","year":2007},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.310351Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:8bde0ecd147051806686c93493b71a6a878ad7ae6fc98772b07be7fac40e93b5","observation_id":"ec98ce48-4300-453d-860f-bca1fdb54c34","resolution":{"observed_at":"2026-08-06T18:55:40.252197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.228177Z","title":"In: Boztaş, S., Lu, H.-F","venue":null,"work_id":"3f415055-e244-404b-8cb2-233da6b6e707","year":2007},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.317275Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:e5b18df84be2a7410d6c51e40864fa6bce81fd39051d77e22de7f91c47446f91","observation_id":"0dd3558a-0577-44c6-ad27-5d64b6056e13","resolution":{"observed_at":"2026-08-06T18:55:40.231591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.217408Z","title":"In: Vaudenay, S","venue":null,"work_id":"dcb94bba-fe50-445a-9f88-9533d08e26a6","year":2008},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.320412Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:96f2666fa0f3db5e526a51743d9d043ba3fbc8f5f3dcd530522d37bfe2776473","observation_id":"3b16b779-4c5d-4dee-8ff8-4ed12306e166","resolution":{"observed_at":"2026-08-06T18:55:40.220960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.206942Z","title":"In: Fossorier, M.P.C., Hoholdt, T., Poli, A","venue":null,"work_id":"398e3e88-76b0-4ed6-b18e-aafee2abb1c7","year":2003},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.323746Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:40efdf42fe4d4bf93cfea8f0a7d873cf4b30ae2f807fecf5c55e78bf07055e7e","observation_id":"ff4d5cc5-71c7-4761-89aa-b3cb8a99cbe3","resolution":{"observed_at":"2026-08-06T18:55:40.210609Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.196865Z","title":"and Tonien, J","venue":null,"work_id":"ce73f83f-34fb-4d1e-9f1e-b272dce3c2f6","year":2017},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.327152Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:41bdb060347dc04515d3ddb79dcd0b663e9352a5ad897cb1057548302262cc57","observation_id":"95172b10-e23d-4270-95d9-6d9d040d2c3b","resolution":{"observed_at":"2026-08-06T18:55:40.200394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-1-4939-7560-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":null,"venue":null,"work_id":"4815bfd9-319b-4eb3-bff8-9e74d1bb9304","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.330452Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:0a93e019763422d3e6ecac7d8583e0cae9f6c9b35ba571f8ffdb373c9eedb3bc","observation_id":"ea8cd5c6-d86d-4f2f-a9ba-a1c3b277d30d","resolution":{"observed_at":"2026-08-06T18:55:39.606370Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.187367Z","title":"EUROCRYPT ’84’, LNCS 209, pp.169-182, 1985","venue":null,"work_id":"0228b7f4-10b2-4f71-b9eb-890e43ccb77f","year":1985},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.334072Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:2a1a38bc454a07c593cbdb776e3e9d821f73e9d1e8612d71e4d658968434185a","observation_id":"0955031a-cedd-4654-a4ab-fd9f10bb6be9","resolution":{"observed_at":"2026-08-06T18:55:40.190971Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.176702Z","title":"proceedings of Symposia in Applied Mathematics, Volume 48, 1994","venue":null,"work_id":"24df9e16-7c27-43f9-88d2-ff209e8c3d89","year":1994},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.337452Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:afdaa69421e2894b4a80e1564d5170580ffbde81cb3396789d3aa6a2117f1fac","observation_id":"1846121b-887d-4b35-99d4-6c542a276d7d","resolution":{"observed_at":"2026-08-06T18:55:40.180743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.165696Z","title":null,"venue":null,"work_id":"d97294db-803f-4f16-b1e9-e7906fb22d23","year":2012},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.340812Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:d3caa8f6306af6bf77d232dc54dd36615ae40af969aa9d9c74fea946e750330c","observation_id":"5ee622bc-611e-4667-ac30-ae7d7a273bac","resolution":{"observed_at":"2026-08-06T18:55:40.169636Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.154698Z","title":"In: Ohta, K., Pei, D","venue":null,"work_id":"6ef33c06-aaa1-40c9-8815-9f29ffc257ee","year":1998},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.344169Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:eaf8808d04dfdad0ac52dffe9bc4a26bbf9462f8a3372bbfab711387d83219a8","observation_id":"91d50421-59da-4d7e-90f6-e4be4f75f18d","resolution":{"observed_at":"2026-08-06T18:55:40.158307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.144051Z","title":"Montréal, CA: McGill University","venue":null,"work_id":"c6f18856-b696-45f0-84ea-97218871c6e3","year":1999},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.347936Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:483fdedbc1fcf9a876da022fa662cfc17f58d470e3f2119b71937d986dd94e2b","observation_id":"f235f425-cb7b-4ced-a643-047acaca9dfb","resolution":{"observed_at":"2026-08-06T18:55:40.148145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.132756Z","title":"Gilat, Gauss’s Lemma and the Irrationality of Roots , Revisited, Math","venue":null,"work_id":"f3a76a43-67d4-4f4e-a651-3b9cdb242398","year":2012},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.352223Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:f006e58e2dd24b0e1ba2f46e50e1d5c3272882986565a445b97117282bb60733","observation_id":"bca9a65e-d0ac-4528-b176-63a051266f90","resolution":{"observed_at":"2026-08-06T18:55:40.136542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.122273Z","title":null,"venue":null,"work_id":"ae9725c3-810c-49f2-b762-0dd5456a2ecb","year":2010},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.355555Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:f144fbbe12e18cc453c23e5fd74843848fcca9dad3a6cdefa9dbba8f7c63ed04","observation_id":"f6512dae-f473-492e-977b-fbc42f60d314","resolution":{"observed_at":"2026-08-06T18:55:40.126022Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.111076Z","title":"Gordon, Asurvey of fast exponentiation methods , Journal of Algorithms 27 (1998), no","venue":null,"work_id":"966a69cf-ede9-4f5b-9f09-4ae0739764c8","year":1998},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.359831Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:1721a2852dfe6b31cb7304fbe04c741393acd90ccbf7e6597b0b07b5a08329f2","observation_id":"124beb92-9cbc-4023-bc38-6f4b27d17639","resolution":{"observed_at":"2026-08-06T18:55:40.115064Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.101697Z","title":null,"venue":null,"work_id":"32be3035-b5ea-47d3-88ef-5c4ecccad3d4","year":2004},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.363094Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:56128dd2820c2c27e951bc624a7c64282131892ffd211144015d415cd5e6df1c","observation_id":"2d56ab41-3b3f-49a8-913f-c000338ec860","resolution":{"observed_at":"2026-08-06T18:55:40.104896Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.091755Z","title":"Bernstein, Peter BIRKNER, Tanja LANGE and Christiane","venue":null,"work_id":"64e8e44d-1365-4049-84ef-4b456046174b","year":2013},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.366313Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:92c81457782ccd0c4ffb4587736c963a869cb74b35f49e25f9e77d37de0773be","observation_id":"9c6bc516-12fe-423e-b307-5d3ac7d11e95","resolution":{"observed_at":"2026-08-06T18:55:40.095559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.080664Z","title":"Johannis Pellii; & speciatim de Problematis imperfecte determinatis (On Algebra by Dr","venue":null,"work_id":"81c517f3-aa5a-48a2-a5dc-263ffc792751","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.369986Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:412e071643ee2c503ce85cf4455aad55f21e711c6c10b48218de78c78ad9059e","observation_id":"f15921c2-9e94-4559-a022-9feba7d9bcc4","resolution":{"observed_at":"2026-08-06T18:55:40.084828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.070876Z","title":null,"venue":null,"work_id":"38d42fd8-46ff-4fce-8a95-96e033288641","year":2002},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.373432Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:e49aba64b93c1c4469015ff38955dbdbd3c14ec4f2995d429c7233c9735c4bb2","observation_id":"2114465b-9e98-48cd-9998-1dd1aef781d4","resolution":{"observed_at":"2026-08-06T18:55:40.074358Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.060987Z","title":"Théorie génerale des équations algébriques","venue":null,"work_id":"d0b9ab26-fa27-4770-8e53-58ccbfb67ec9","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.376784Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:28a5377811c6c31ef825789e14c99a15c8bf3fcabb981d5bbba251a7c54a5110","observation_id":"d0990ed2-2b6f-4aa9-bbc3-a2aee42b5ed1","resolution":{"observed_at":"2026-08-06T18:55:40.064909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.051044Z","title":null,"venue":null,"work_id":"5ee2f75e-df09-4ff0-8834-246035ab2460","year":2017},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.380635Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:cec6acd16c45b3acc369cd54e16889122b21a128d357a3f734d9728a60fd1db6","observation_id":"c0430535-3f85-44cb-a0d9-9bbc27002d6c","resolution":{"observed_at":"2026-08-06T18:55:40.054512Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.041147Z","title":null,"venue":null,"work_id":"425dfb30-047e-468f-8172-20552ba3b0ec","year":1985},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.384008Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:1fe2c903dce8ff10df048319b849d71732e89a40d3041a784d2b8561764f5083","observation_id":"a89cbadd-d9b2-4cd9-a0ca-8d8f527eea4e","resolution":{"observed_at":"2026-08-06T18:55:40.044850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.030020Z","title":"Lemmermeyer, Residue Class Rings Lecture Notes, https://www.mathi.uni- heidelberg.de/ flemmermeyer/pell/bfc03.pdf","venue":null,"work_id":"84fbfa28-3f35-47a1-bcd4-5f955ba57bdc","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.387250Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:24684020f07b7b07cbdcb49465fbdd585ed645ec97883c50c416c355c13de58e","observation_id":"fa7c01b0-a458-4a86-8e71-abbba1b64c57","resolution":{"observed_at":"2026-08-06T18:55:40.034539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.019513Z","title":null,"venue":null,"work_id":"6582288a-70f2-4fd8-82f3-d9c5b5b696b1","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.390831Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:1591c2bdcc5bfee0bc3107dcafbbdcd5c3df78ae102995dab83f9551eeadfb98","observation_id":"90c942bb-e53c-47f7-bfe1-bcbca487fbd9","resolution":{"observed_at":"2026-08-06T18:55:40.023250Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.008530Z","title":"Bansimba, Régis F","venue":null,"work_id":"2adb1830-51b7-4034-b6bd-96a364dc4544","year":2019},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.394148Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:71acb561f7f4ab8c46c146414f14a8c6712e3fed6cd2df96fe64cca0e0ec6529","observation_id":"0d148228-ff70-4d1f-a508-b4b57249e7b2","resolution":{"observed_at":"2026-08-06T18:55:40.012198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.342425Z","title":"Bansimba, Regis F","venue":null,"work_id":"a4778728-5cce-4b96-817e-6b880b4b8c59","year":2021},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.397930Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:38f902bf25d47b9ec6fdf4bc6f0ba90fd037c402700de0701e12518b0bb28bf4","observation_id":"0d89d238-d5e7-4996-927b-912bbe6e4950","resolution":{"observed_at":"2026-08-06T18:55:40.346227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.997519Z","title":"Lattice Points on the Fermat Factoriza- tion Method","venue":null,"work_id":"a48cdeeb-a889-4fda-ac2c-e8445b36644a","year":2022},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.401223Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:debd3402507d22fdee484232bc20d0168529a8fc6068fa03ea6546faca8a93b8","observation_id":"5b9f9d07-43de-48b3-bdfc-7ad1571932f9","resolution":{"observed_at":"2026-08-06T18:55:40.001331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.07474","last_updated":"2023-04-15T05:21:37Z","snapshot_observed_at":"2026-08-10T22:23:14.497122Z","submitted_at":"2023-04-15T05:21:37Z","title":"A New Hyperbola based Approach to factoring Integers","version":1},"cited_work":{"arxiv_id":"2304.07474","doi":"10.48550/arxiv.2304.07474","metadata_source":"pith","pith_arxiv_id":"2304.07474","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"A New Hyperbola based Approach to factoring Integers","venue":"math.NT","work_id":"d51bd19f-692a-4509-9d1d-96c72491e97d","year":2023},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.407619Z"},"links":{"cited_paper":"/paper/2304.07474","citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:e9b8661c8b212c45b203b3f5bd91bfc39c0bdccd4adc91cc58c6cf3777001a11","observation_id":"83641edc-2f82-43a2-8ba9-cd8ac46fc411","resolution":{"observed_at":"2026-08-06T18:55:39.596197Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.03957","last_updated":"2023-05-09T08:30:29Z","snapshot_observed_at":"2026-07-06T15:13:33.023550Z","submitted_at":"2023-04-08T08:46:19Z","title":"A Continued Fraction-Hyperbola based Attack on RSA cryptosystem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.03957","snapshot_observed_at":"2026-08-06T18:55:39.411524Z","title":"Babindamana, Basile Guy R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.411524Z"},"links":{"cited_paper":"/paper/2304.03957","citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:616093437614515129fa8694d42fa9151d455d51b50f78ab8b0b0c7e8897c066","observation_id":"ee5ad347-d257-42c5-861b-15a3f00fdf5e","resolution":{"observed_at":"2026-08-06T18:55:39.411524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:55:39.985792Z","title":"Bansimba,PytLoc: a python tool that locks and obfuscate python source files using a one time pad lock , Python Package Index https://pypi.org/project/pytLoc/","venue":null,"work_id":"9da35cf5-8fcf-41a0-bb4d-1c5ec57e45f8","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.415484Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:ad66a179517f3ace13387cca864176146763f6f418d476315f644d94ea5908e3","observation_id":"71aff32a-cc07-482e-b7a1-47a13814d534","resolution":{"observed_at":"2026-08-06T18:55:39.990161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.975309Z","title":null,"venue":null,"work_id":"d9f93e61-f94f-42bb-843e-174bb1018154","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.419613Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:d8a7a1beb7ca8ac418a91932db59daf9033236320bc68c27e5627ec9b56e9c13","observation_id":"7c5c9653-c53c-4a33-845c-6b55d7211774","resolution":{"observed_at":"2026-08-06T18:55:39.978978Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.964289Z","title":"Edwards, A Normal Form for Elliptic Curves, Bulletin of the American Mathematical Society, Volume 44, Number 3, July 2007, Pages 393–422","venue":null,"work_id":"b990776a-871e-47a0-825b-3e7bc506267a","year":2007},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.422846Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:b9454c9898c85360847c7752652e29582a75d1e073e689459107a7bd2e52ce9a","observation_id":"c56da640-871c-48de-b989-1e99fc508097","resolution":{"observed_at":"2026-08-06T18:55:39.967896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.954446Z","title":null,"venue":null,"work_id":"1a22f683-edc3-4c9d-8c27-0bd4c8d51992","year":2020},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.427134Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:a90a045528ca621611fe3da5df89416d65f71b43d4a5efd6e5eeb58e225e1906","observation_id":"fee0ea90-374e-4c05-8e88-52d5c052e025","resolution":{"observed_at":"2026-08-06T18:55:39.958213Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.944449Z","title":null,"venue":null,"work_id":"02e03f77-4dbc-4dd0-ab87-fb64c568b32f","year":2008},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.430431Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:b047352421119875700f71e2c9140c173325cbf0f13f22866500aa7f8076e6dc","observation_id":"a055cba4-00df-4c7e-8f66-46dabf862c27","resolution":{"observed_at":"2026-08-06T18:55:39.948139Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.935245Z","title":"Matplotlib: A 2D Graphics Environment","venue":null,"work_id":"9588b586-c4ee-46a8-8086-1d80e78c5dcb","year":2007},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.433663Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:3928502446a4bcdc6e82103780a38f8f953e84b3a6c18bf69b407e264d5d9be7","observation_id":"547890a6-5e73-42c2-8f24-42f4c921e2e5","resolution":{"observed_at":"2026-08-06T18:55:39.938794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.925948Z","title":null,"venue":null,"work_id":"9d6193f3-63a7-4ee8-9c5d-701fb0cb34d6","year":1974},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.437379Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:b524d270d0a80171700c2dba395099ca53e5c72c5581dd635480d251ba40cce4","observation_id":"8f06ca74-15dc-42e5-bff7-6d07ad2a66e7","resolution":{"observed_at":"2026-08-06T18:55:39.929191Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.916020Z","title":"Computational aspects of the Aryabhata algorithm","venue":null,"work_id":"9d9e30b8-1d2f-4581-ab1a-ee69278f2352","year":1986},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.440703Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:64ac4f47060ad5d4a0ac0e633c9e7244937390f5c7e761ed2dc5637b8896c3ea","observation_id":"5b20546f-4536-407e-8291-153e3b74679e","resolution":{"observed_at":"2026-08-06T18:55:39.919456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.906423Z","title":"Two Simple Lower Bounds for Euler’s Function , vol","venue":null,"work_id":"ca177818-833a-4dfa-aa63-cc22103a8548","year":1965},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.444110Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:a11734ff66ce352d5500f04185adc6ab717c93612720dc33eb0b2ce3e91999ef","observation_id":"9f4940d3-2aa0-402c-bc2e-5211d648ecf1","resolution":{"observed_at":"2026-08-06T18:55:39.910002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.896069Z","title":null,"venue":null,"work_id":"1cfc7342-4b4a-42e1-9d31-b3d3f7a0f403","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.447323Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:f84f5d35d2f03cd6d8b2613599ba751b5edea26457b3a8730c2d75830f2adf98","observation_id":"e2f7478c-229f-472f-8e35-a75282628a85","resolution":{"observed_at":"2026-08-06T18:55:39.899659Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.885747Z","title":"75 (256): 2037–2047","venue":null,"work_id":"20f65173-71cc-41da-89ed-116745312f15","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.450405Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:94c728308142d59c52cfde5ee1737d4b74caea28ff86d99977897be68fd5b722","observation_id":"650c6618-4483-4a82-b718-58d1b65c4a26","resolution":{"observed_at":"2026-08-06T18:55:39.889369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.875714Z","title":"Suite des réflexions sur la résolution algébrique des équations. Section troisieme. De la résolution des équations du cinquieme degré & des degrés ultérieurs","venue":null,"work_id":"8a3cd470-8171-4b3b-80f1-0a5f9b937713","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.453880Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:3fdfc98bb577d6002f71b26fdc9f5508eb00412e3e7cbec70a9ddb89ac068cb4","observation_id":"06959f18-0dc1-4540-8137-92209e050d16","resolution":{"observed_at":"2026-08-06T18:55:39.879632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.865345Z","title":null,"venue":null,"work_id":"b9517d26-ab18-4b37-a375-48d1fba81fa2","year":1920},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.457169Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:d6579a3273eba9d23324457bf7e1448feb0b37da3f8e33b8c664e01909d08a4f","observation_id":"f073cc76-bb8f-45b9-bb0b-98e3b3ab4acc","resolution":{"observed_at":"2026-08-06T18:55:39.869267Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.855405Z","title":"and Pomerance, C.:Primality testing with Gaussian periods","venue":null,"work_id":"a2809d31-edd8-40bf-b952-6fe2ada84a57","year":2011},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.460387Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:d4add91c31b7965a93de9c3602cc1a36957fb8916a641ef94b1908c906fbf98a","observation_id":"6bfcdea3-f2b6-4215-af3c-61d90f31d018","resolution":{"observed_at":"2026-08-06T18:55:39.859088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/2310010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Another proof of Cauchy’s group Theorem","venue":"American Mathematical Monthly","work_id":"c87ec004-3952-482b-987e-b1803537b1c8","year":1959},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.463488Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:4be5d36b9e0b6c9d2c0eb5c7615403329c650809b975f3030e30721cb04f6e08","observation_id":"8f41dbe4-7309-41c0-85b5-3e4a392184c4","resolution":{"observed_at":"2026-08-06T18:55:39.570217Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.845043Z","title":"Speeding Fermat’s factoring method","venue":null,"work_id":"4f8aaf70-cef2-4cbd-aa91-2425f8d511d1","year":1999},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.466804Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:8b5826923e624a2ed3a52571cc2fc19cbb4229251f8ce0bab6f69447b418b7d1","observation_id":"bc7ad0a6-46ca-4b29-a62e-fa3af5f4c585","resolution":{"observed_at":"2026-08-06T18:55:39.848641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.834761Z","title":null,"venue":null,"work_id":"8bf69042-dad5-4c50-859e-dbc3c1346da7","year":1999},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.470031Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:82c51e70d2d253771569e538d84102397fa445c47e985a67bb8e35a7a7a2203e","observation_id":"6597c0c9-8cff-49d9-9862-33a22d120db8","resolution":{"observed_at":"2026-08-06T18:55:39.838207Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.825139Z","title":"Koblitz, Elliptic curve cryptosystems","venue":null,"work_id":"d08b4901-f441-404b-a710-a14b4cefae77","year":1987},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.473217Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:06b736641aa991b5de09e83b8c40173b6d60bce6ae35337a4ba841f4e04a2bcb","observation_id":"5c0e14cc-df3d-48c5-b117-442ee8bacec2","resolution":{"observed_at":"2026-08-06T18:55:39.828643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.815074Z","title":null,"venue":null,"work_id":"5af784c6-0e52-4a32-8b5f-698d30d4799e","year":2013},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.476511Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:48f626236cb9bc23d85911b783d232d5e78d9cd62753e3dacf2e2346709852dc","observation_id":"2bad90f4-e306-45eb-80d0-d5969e22d843","resolution":{"observed_at":"2026-08-06T18:55:39.818643Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.803479Z","title":"(2014) Fast Point Multi- plication Algorithms for Binary Elliptic Curves with and without Precomputation","venue":null,"work_id":"47f80ca5-4f92-4b4a-86ff-a50de5403f6d","year":2014},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.479882Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:6078708349aef4d02fe57cd865876db30ed735615220eb923c46adfdd8fe8029","observation_id":"f49c0594-ac27-470a-b79f-89f7bcd030e5","resolution":{"observed_at":"2026-08-06T18:55:39.808246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.779510Z","title":"Zimmermann et al","venue":null,"work_id":"f7e17a70-d838-42fe-8ce7-71fdbb65a112","year":2012},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.486315Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:30187f698d93d5297009bbdc24757b1b34cacb669f8c676726e8f4e54f3e13fe","observation_id":"9fa74a46-be77-4b99-be97-ed3b8ed38b3f","resolution":{"observed_at":"2026-08-06T18:55:39.785522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.769563Z","title":"Summing up the Euler Φ function","venue":null,"work_id":"d7a2dd9b-c997-4ed4-a66e-bc900e676888","year":2008},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.489246Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:6fc46b857f6e9786df59fe116fc1b18ac98c50a0e4eb257ec39fa7656d6ed03e","observation_id":"7e7fb4b7-c5bf-4ef6-ab6f-6c296e7af36f","resolution":{"observed_at":"2026-08-06T18:55:39.773129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.759326Z","title":null,"venue":null,"work_id":"c91a3524-fd2e-4088-a250-f5c30051750e","year":2020},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.492472Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:b7e29b22d1233b97736bac6ccfa0f6adb286cdcaaa99a10d63f700875c729e18","observation_id":"e8e09afe-fe2b-4b73-82dd-1d81f8b4751b","resolution":{"observed_at":"2026-08-06T18:55:39.763035Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.748860Z","title":"Speeding the Pollard and elliptic curve methods of factor- ization,Mathematics of computation, 48(177):243–264, 1987","venue":null,"work_id":"aea7d5c5-0fbf-4313-be0f-5420f28b2cc0","year":1987},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.495465Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:130d835bcd1d59cd237b44b91fb08e6de6813e9add34c330b7bed7f03a7fb66d","observation_id":"69b674ce-8c50-4ea8-bfee-f4803e53aae0","resolution":{"observed_at":"2026-08-06T18:55:39.752420Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.739130Z","title":null,"venue":null,"work_id":"34a8b4c1-9d5a-4ff1-94a4-d99c45da43f8","year":1978},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.498441Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:9469f2ced50b1f4d3f7f30562395607fdf9f6a51144b69198d4294a206e0ded4","observation_id":"bf490cb5-efbd-4e3c-85b4-f3294904ab9f","resolution":{"observed_at":"2026-08-06T18:55:39.742506Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.729459Z","title":"Finding ECM-friendly curves through a study of Galois properties","venue":null,"work_id":"e2ef1e44-df7c-446c-a85f-0ad8ffaf38eb","year":2012},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.501498Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:24ddc3405b3e0bce85f227a92375b2252228647e942397da364267aec3b75cfc","observation_id":"fa9d236e-4405-4cf6-ada5-2cbf9f086379","resolution":{"observed_at":"2026-08-06T18:55:39.732850Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.719511Z","title":"Brent, Recent Progress and Prospects for Integer Factorization Algo- rithms, Oxford University Computing Laboratory , Wolfson Building, Parks Road, http://www.comlab.ox.ac.uk","venue":null,"work_id":"996e3b7d-9fac-407c-8f50-e20365794c47","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.505296Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:5ce92c9549548866f4be0ac13eb5f0a97e1453ec9d3c2f6962a61590fcec89f4","observation_id":"9bd7190f-d50b-4608-ada3-20879237b9ed","resolution":{"observed_at":"2026-08-06T18:55:39.723183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.709899Z","title":"Goldwasser, J","venue":null,"work_id":"c159dd33-8333-4716-8e16-f299bec5ef07","year":1986},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.508559Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:10fbb5e2d08eed15333f8297c9e7046634d8d057fa3a30a0203f666cea99c3bf","observation_id":"00b996ea-4cae-47cb-bd76-8b29755c5b77","resolution":{"observed_at":"2026-08-06T18:55:39.713331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.699072Z","title":"Goldwasser, J","venue":null,"work_id":"7ca086a6-3c98-4e88-a095-53454a15cff3","year":1986},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.511756Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:49fabfd568c5007959f7df94fea885109305d2248babae2eb317199057aa6e56","observation_id":"50408dd3-ab57-406f-b657-3553ad71cb7d","resolution":{"observed_at":"2026-08-06T18:55:39.703477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.689340Z","title":"Lang (1966), Introduction to Diophantine Approximations, Addison-Wesley Pub","venue":null,"work_id":"eb638744-6cf7-44ff-abca-fd83dece4f67","year":1966},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.515036Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:249d522393520e7adfbbdd7e7dbc993f8421aef2f940e4a1f16372c2455f0434","observation_id":"0045e5da-4175-473c-ada6-4ebd43512b31","resolution":{"observed_at":"2026-08-06T18:55:39.692937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.678740Z","title":"An arithmetic function arising from the Φ function","venue":null,"work_id":"b80beae9-9deb-4643-8ea8-d416a1ddca5f","year":1943},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.518144Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:a48e058a012d35a350d5d6f271e17d90009b535720c84a62312011831fe39938","observation_id":"c093e64b-596b-43e9-9f44-b56ab26473ff","resolution":{"observed_at":"2026-08-06T18:55:39.682415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.668833Z","title":null,"venue":null,"work_id":"6c02d77a-3066-4391-82e0-a4a72b396372","year":2011},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.521998Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:447dfe796f534943858b641d6f25027578ea69c43754828f8c0bbf984c1a7c30","observation_id":"e97186af-59c0-4b9d-9560-23ec58173633","resolution":{"observed_at":"2026-08-06T18:55:39.672226Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.658444Z","title":"CADO-NFS, An Implementation of the Num- ber Field Sieve Algorithm , Release 2.3.0, 2017,http://cado-nfs.gforge.inria.fr/","venue":null,"work_id":"adfd22be-5a6b-4eb3-bdd4-b3dd92aee9f9","year":2017},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.525333Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:1abdd91c6aec9a3a08de1a3586fe4d4a542578db68d77142a43ed37a43b148ed","observation_id":"fea32218-9271-4a03-9cf3-7954f2532281","resolution":{"observed_at":"2026-08-06T18:55:39.662366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.647602Z","title":"Miller, Use of elliptic curves in cryptography","venue":null,"work_id":"fbf4f705-3e5d-4711-98c9-ce61e882a764","year":1985},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.528661Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:b9e9f2e8b3da2c69e85323689bba9bccf4292e33672a089ee3f178d9eb77b1b8","observation_id":"6db74611-3de0-4221-8ebe-433e99dae554","resolution":{"observed_at":"2026-08-06T18:55:39.651392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.10486","last_updated":"2018-02-28T15:46:25Z","snapshot_observed_at":"2026-07-06T06:25:52.160703Z","submitted_at":"2018-02-28T15:46:25Z","title":"On quadratic curves over finite fields","version":1},"cited_work":{"arxiv_id":"1802.10486","doi":null,"metadata_source":"pith","pith_arxiv_id":"1802.10486","snapshot_observed_at":"2026-08-06T18:55:39.626694Z","title":"On quadratic curves over finite fields","venue":"math.NT","work_id":"453a2e41-96ef-44ee-b884-2abd653b82d7","year":2018},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.532096Z"},"links":{"cited_paper":"/paper/1802.10486","citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:8d822d682dfec49ccf4557753d1b9f146b4473b95774be5d82ace132487e167f","observation_id":"c8ded2c0-0bf5-4712-a8ca-c13c2f237320","resolution":{"observed_at":"2026-08-06T18:55:39.630418Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.637485Z","title":null,"venue":null,"work_id":"a83eb48c-97ba-45d8-852f-90b05c2d8342","year":1990},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.535855Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:dd2f34a763fb17934842439864b3be322eb5f5b79b9f93643b768888e76149cf","observation_id":"12d3b2f2-c225-43d5-a21d-3a4026dc2401","resolution":{"observed_at":"2026-08-06T18:55:39.640966Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:40.237768Z","title":"Springer, Berlin, Heidelberg","venue":null,"work_id":"7a562adc-f704-4754-9573-c3e53840cd60","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.313987Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:5a6f8dea04692a6cad86890fdcee2c4debdcf8a30b6343a5fa94c7dc200ca6bd","observation_id":"649df8f3-840c-4ce4-89e2-afa178cbcb89","resolution":{"observed_at":"2026-08-06T18:55:40.241246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T18:55:39.793340Z","title":"Springer","venue":null,"work_id":"3bfed29b-bb42-4d4b-bb41-f12cae9c302e","year":null},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.483339Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:a02f94cb1a70f24eca5876a9afd3f84550fb4a80093c23c866ccd2de5bc09d8e","observation_id":"2684f86b-38d3-4120-9ba8-8a8968950f49","resolution":{"observed_at":"2026-08-06T18:55:39.796968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1155/2022/6360264","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Journal of Mathematics","work_id":"a125ade1-e77e-4117-8c40-a9cf13284d68","year":2022},"citing_paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-06T18:55:39.404579Z"},"links":{"citing_paper":"/paper/2507.07055"},"observation_digest":"sha256:ab9a254fae2138e51bb01146d609714d4258e1aa18dc96f607f64db2f3b9fa35","observation_id":"eaaa0e7e-e4b5-409c-bce1-9f5a1741734b","resolution":{"observed_at":"2026-08-06T18:55:39.616135Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.07055","last_updated":"2025-07-09T17:20:49Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-06T18:46:05.280727Z","submitted_at":"2025-07-09T17:20:49Z","title":"Integer Factorization: Another perspective"},"reference_resolution":{"displayed":75,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":22,"verified_exact":4,"verified_fuzzy":48},"total_outbound_references":75},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 75 of 75 outbound references and 0 inbound Pith citation observations for arXiv:2507.07055."}