{"as_of":"2026-08-08T08:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d118e6dece119f2b191852d1de6853b09d0d37f5b8d201f8e2122f2563a7a964","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T06:00:45.844723Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2506.06736/citation-record","integrity":"/paper/2506.06736/integrity","json":"/paper/2506.06736/citation-record.json","paper":"/paper/2506.06736"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T06:00:46.175946Z","title":"Acta Appl.Math.109, 973-1033 (2010)","venue":null,"work_id":"2ab12237-3b1a-473a-b52f-eff8e38b5bf5","year":2010},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:44.613814Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:7008b562dd77172c63b42e374215903ff56318646767ebb512647ae24be52751","observation_id":"6d9daa69-9811-46ee-8509-b2188d112902","resolution":{"observed_at":"2026-08-07T06:00:46.178762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.167355Z","title":null,"venue":null,"work_id":"25bc46d3-b9f3-44da-8197-273b10494441","year":2002},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:44.723820Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:f786a0622d61f0e00fd66a8ba56e606ecae06a71ff4f1cc3e18c18b4e61f47b9","observation_id":"25f5bd7d-aa3d-489c-98d8-b4814fc53a5b","resolution":{"observed_at":"2026-08-07T06:00:46.170082Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.159178Z","title":"Fract.Dynam.Contr","venue":null,"work_id":"080302d4-19e5-4c9b-9e0e-58e8875f33b6","year":2012},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:44.879273Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:99d1b94648b45a4f8eba45b3f80824092e22cd076b59957432e86339c1b1de16","observation_id":"7b05e62e-bbec-4dd6-971c-7d9e287c620b","resolution":{"observed_at":"2026-08-07T06:00:46.161859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.150845Z","title":null,"venue":null,"work_id":"e3e8d53f-a3cb-477a-bfcb-be8c175d138d","year":2008},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:44.988072Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:b14d29c02b046644e73ee85756097d81f84c93729c15e1161b83beac868daba2","observation_id":"89e525c0-61c3-4971-a0eb-af790ca0bf37","resolution":{"observed_at":"2026-08-07T06:00:46.153519Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.142457Z","title":"Nonlin.Dynam","venue":null,"work_id":"46489e0e-6ba1-46b6-b14b-e860b9905bd7","year":2008},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.130567Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:13b8d7cc7f2f192ac053a3e29c5e29aa9e38654ba755ccbca69c0d025a488d31","observation_id":"e6d4a367-d761-4264-86c8-81653838546b","resolution":{"observed_at":"2026-08-07T06:00:46.145261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.133419Z","title":"Discrete Contin","venue":null,"work_id":"e684a699-fd7c-41bd-9db6-327dbe4fbff6","year":2011},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.253148Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:a76535aba52b7ddda994179e61e295febdd4e3bd6c26f7b5c1fccdeabf07dd9c","observation_id":"49b41738-e5ae-4731-91e4-2cf4cad022b4","resolution":{"observed_at":"2026-08-07T06:00:46.136762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.124959Z","title":"ESAIM Con- trol Optim","venue":null,"work_id":"bf6af60b-ebe5-40eb-b653-87a79ad2c3da","year":2020},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.397307Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:63d0ddbfdbf1ac283e0e09038479c03882465a7c9aa2a209daeff4711b78bd98","observation_id":"9f95a742-3562-44b1-924f-363b885bf458","resolution":{"observed_at":"2026-08-07T06:00:46.127819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.116373Z","title":null,"venue":null,"work_id":"3294f48a-0aa1-46ae-8eef-b17c900e4aca","year":2013},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.561877Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:e7d59a64e3a9f36132a06a03a5e89e119e7490a941c3511a77d6c6f3cb868bb1","observation_id":"a787b95b-b6d1-42b8-842a-8362f97b4224","resolution":{"observed_at":"2026-08-07T06:00:46.119132Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.107710Z","title":null,"venue":null,"work_id":"c677a132-f0ab-48be-87a2-a56a24e8c889","year":2021},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.611567Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:a7b3836f72775649b30a7ca1abb0ae2dc5cf220a107910583083e3196fadc323","observation_id":"f4495a64-a99b-4874-b02c-80362d309a63","resolution":{"observed_at":"2026-08-07T06:00:46.110427Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.098950Z","title":"1-183 (2020)","venue":null,"work_id":"b56a0f03-16e1-4a06-9d88-974910cb7c5e","year":2020},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.739375Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:97ed54c7cfd25b9911052e5f6e5c410a21ad969480db815880d13948d00d5068","observation_id":"f3298255-e248-499a-a4f4-f10a2a16a7d7","resolution":{"observed_at":"2026-08-07T06:00:46.101983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.090485Z","title":"Prepublication MAP5, (2001)","venue":null,"work_id":"58adaa7a-466b-4406-b131-0f624fc3c345","year":2001},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.742610Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:c1ae7030bc780d2e51f0d47f5a968827725e4b7c84cda97475a12254d6973949","observation_id":"89482fb0-b170-4e30-9fca-b318b5593541","resolution":{"observed_at":"2026-08-07T06:00:46.093246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.080938Z","title":null,"venue":null,"work_id":"84984af8-4416-45b9-a2ea-c66ca39e12eb","year":1974},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.775650Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:36c49e14ba0c26bd66c1116587b8e6ee6b8cd319cf57493a127b582f88ebf131","observation_id":"dfdfb428-8e8b-4a23-941a-8a23a99fc132","resolution":{"observed_at":"2026-08-07T06:00:46.083887Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.072206Z","title":null,"venue":null,"work_id":"0c182aff-7179-428d-a3ab-2b5f67bc03f6","year":2019},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.779545Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:050390333490278f115a329ce38474ab5fbdcd6b85caf1d3fb4ecf5a95e4132b","observation_id":"26a21d33-4db4-47a5-b3db-da7277902bfe","resolution":{"observed_at":"2026-08-07T06:00:46.074936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.062666Z","title":"Rev ised English edition translated and edited by Richard A","venue":null,"work_id":"59921e80-2983-4794-9291-844de5fb155c","year":1963},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.782750Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:2d8128009c5881817ebf2470f8cd764e8ac8203276446360006076cf063ba31e","observation_id":"06018e43-73d8-453b-a2fd-bc6cbb80ae2d","resolution":{"observed_at":"2026-08-07T06:00:46.066019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.054255Z","title":null,"venue":null,"work_id":"132dc5cb-9346-4e13-b1e8-6c555b8917b4","year":2013},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.785859Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:c22ca6937ba5f52bf02465b51dfb3bc9fc34d9b514d258aa719323c2cd5b22c7","observation_id":"6a451aae-ab1f-4909-9e1a-28918831aa53","resolution":{"observed_at":"2026-08-07T06:00:46.057050Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.045960Z","title":"Robert E","venue":null,"work_id":"2fcafa7e-043c-4070-bd30-f7c36a9c613c","year":1980},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.789050Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:ba46280527a48e0b94581610ce98e579ff9f2eec1e2c83bc1aa098274b281136","observation_id":"7f32f08b-9875-4f46-af99-bc1bf5b4f65b","resolution":{"observed_at":"2026-08-07T06:00:46.048783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.036267Z","title":"W orld Scientiﬁc, River Edge, New Jersey (2000)","venue":null,"work_id":"092d7414-ffbf-4945-9260-535d50870697","year":2000},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.791777Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:b4d1bfe86f0ba696e9445d3cb6d73075de3a2f8df65bc456e4425044ece0c0a7","observation_id":"72818621-3fee-4ed6-bc5e-15d65b163973","resolution":{"observed_at":"2026-08-07T06:00:46.039262Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.027769Z","title":"In Applications of fractional calculus in physics, 429-463","venue":null,"work_id":"c38529fb-0833-4f8b-8c52-00cb0e98948c","year":2000},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.794785Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:95c4e2e2a4502e0a4c2ca561e70317cf9ea2849c5664c844039a04aeaca58f53","observation_id":"e790cc48-fdfe-4735-a8fc-b5f2148d8d39","resolution":{"observed_at":"2026-08-07T06:00:46.030744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.019292Z","title":"volume 204 of North-Holland Mathemat ics Studies","venue":null,"work_id":"8340261f-5ef9-4347-aa1a-81f45bc8f6dd","year":2006},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.797859Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:f5c62d0115aaed58719e859b8a08707c774b8b89f09afa9ca324bf68ca4ac324","observation_id":"3cc21db8-4ede-4e24-b26b-73283ca5cc82","resolution":{"observed_at":"2026-08-07T06:00:46.022067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.010528Z","title":"In XXVI W orkshop on Geometrical Methods in Physics, volume 956 of AI P Conf","venue":null,"work_id":"1a77a579-cc84-4406-b71f-62ea2d855013","year":2007},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.800615Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:bbf9a165d0d42495d5941c31b138bd5d190abd2ff1fec9761580d71f9fab9336","observation_id":"bb825e91-f2aa-4949-b563-0d9fd074ec49","resolution":{"observed_at":"2026-08-07T06:00:46.013485Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:46.001924Z","title":"197, 798-816 (2023)","venue":null,"work_id":"5c96a732-27bb-404c-a02e-050bec44ff97","year":2023},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.803348Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:d79d5e27042a43914f477178daf3247778cf0a628c3aaaa97ee539b960d60026","observation_id":"3e2cd197-88d4-4d85-bcb6-c175ae8c619c","resolution":{"observed_at":"2026-08-07T06:00:46.004674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.993073Z","title":null,"venue":null,"work_id":"6178bfee-92d2-4ce3-96ef-d0fe46ee89d4","year":2019},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.806410Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:0baa4f1464294eeeb8cca55bab5dbe0b5c1986489daa0ffff4e836f9bbec3d23","observation_id":"cea0d7d7-54a4-43cb-9f85-fd216baec4b5","resolution":{"observed_at":"2026-08-07T06:00:45.996176Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.984944Z","title":null,"venue":null,"work_id":"63ad3d21-4bb6-47ff-8a9a-4aeca68c2a39","year":2011},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.809179Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:edb158f118f4afb2f6d504c5487443d01f887ffa48d0dda114f427ce6e6e7fa1","observation_id":"8bdc6478-f260-4c02-a058-618ef6d6ac5d","resolution":{"observed_at":"2026-08-07T06:00:45.987668Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.976831Z","title":null,"venue":null,"work_id":"891932a3-559d-40e5-9030-3c62ce01b648","year":2022},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.811939Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:90aca72590467bc8c369f117f70f234c783155c0160406793480db5c49374ed5","observation_id":"1bb4c281-aa69-44de-be2d-bb6b429259ba","resolution":{"observed_at":"2026-08-07T06:00:45.979573Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.967871Z","title":"11, 85-96 (2010) 30 Shikhi Sh","venue":null,"work_id":"43025e0f-d9a2-4bcc-9812-ec0034beffd3","year":2010},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.815122Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:f992f72ff4dac439e3685fa97d82c9703c81dcfb2d254944b277c06f1951008e","observation_id":"226f0fcf-dbb8-4384-936d-535304f92701","resolution":{"observed_at":"2026-08-07T06:00:45.970815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.958759Z","title":null,"venue":null,"work_id":"73710384-5ef6-4bc5-ae52-8143448c2bfc","year":2016},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.818049Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:b85e6c3d5faac84e10b13839aadf8ca84494c5d8364f4277b87c666868a83e29","observation_id":"fcad50e2-2615-47f0-9ce6-1354bdc30924","resolution":{"observed_at":"2026-08-07T06:00:45.961705Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.949161Z","title":null,"venue":null,"work_id":"a1aa76c5-7fb8-4441-af82-bfea4df8321a","year":1996},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.821057Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:3392d53c360d5ec98022d563e6ad7e698b2b2b44a87f2551fbc4df98afa80f7e","observation_id":"0588f17c-c02f-4af0-bdd6-58ea56a9d92f","resolution":{"observed_at":"2026-08-07T06:00:45.952474Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.940466Z","title":"Advances i n fractional calculus","venue":null,"work_id":"5435f486-1117-4574-8e12-7076bdfceda6","year":2007},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.824157Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:377a39c84afef418d291e896d96fc0f64ad6d1cef629ca0bfa35c4998ee8c259","observation_id":"e348801c-b3f4-44a2-878e-e06e62be3ed1","resolution":{"observed_at":"2026-08-07T06:00:45.943217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.930586Z","title":"Gordon and Breach Science Publishers, Yverdon (1993)","venue":null,"work_id":"5281a602-3141-42f2-ba8c-3c4a2595a35f","year":1993},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.826930Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:a6ece8066d504098cb67e816090ecac2c7a9ddb050add5ede99a8796bfa7b701","observation_id":"de4b65fd-ac97-4d1d-a594-49caddd5cf9e","resolution":{"observed_at":"2026-08-07T06:00:45.934297Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.920774Z","title":null,"venue":null,"work_id":"a2b59a3f-6ebe-4967-a4ab-c1f3f16f03a4","year":2018},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.830085Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:dcb6ec7df8e1e9ad0cfff4f22449f9985c6f9f8ba9849c00fa06413c8b056da5","observation_id":"60202f31-c134-4192-be2b-e816325de685","resolution":{"observed_at":"2026-08-07T06:00:45.924061Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.911628Z","title":"Universitext","venue":null,"work_id":"30fed690-205b-450c-b6fd-75f60ad41e8c","year":2004},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.832926Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:3130a33d81f2c390a0123823d322e879b1b5041fb5b693d0016743e615b42a0d","observation_id":"5c34738b-c374-4808-8c66-73bd402ddb6a","resolution":{"observed_at":"2026-08-07T06:00:45.914363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.902817Z","title":null,"venue":null,"work_id":"f697f2e2-d57e-460a-b830-dbf9697d102c","year":2022},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.835968Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:6b9134a75877813aa5db7f7bb13425540c81c583b81b7aefbf7856f4ecf3245e","observation_id":"4cb7afb0-529c-425e-802a-d38c560e6d25","resolution":{"observed_at":"2026-08-07T06:00:45.905797Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.893040Z","title":null,"venue":null,"work_id":"96fe2978-4902-48e5-949b-8937ab516c99","year":2023},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.839054Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:44da39bccb436cd9a498fb5ff090c14a564327cb444a37fa58b50d1bc53f8f5a","observation_id":"ea4b6e8f-16cc-4df3-bee0-060e1b898e92","resolution":{"observed_at":"2026-08-07T06:00:45.896282Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.883344Z","title":null,"venue":null,"work_id":"78f5901d-63d2-449b-abf9-daad7442d15c","year":2023},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.841985Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:7815fba37869f4f33384e5028f8ed48bb4d80bf6f57c56a3937542b5536aa09f","observation_id":"e4dfc619-e0d7-4374-926e-b710e0dd657b","resolution":{"observed_at":"2026-08-07T06:00:45.886498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T06:00:45.870934Z","title":null,"venue":null,"work_id":"74410c61-d442-483e-b14e-139f47b539f8","year":2023},"citing_paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T06:00:45.844723Z"},"links":{"citing_paper":"/paper/2506.06736"},"observation_digest":"sha256:783af87239d9b5564eea56d6cd2f80ff0c46938f9e53594e523f0819980b4403","observation_id":"1fd31ee5-1a62-4b3e-ace2-569464ce1b8d","resolution":{"observed_at":"2026-08-07T06:00:45.875991Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.06736","last_updated":"2025-06-07T09:44:37Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-07T05:48:17.399696Z","submitted_at":"2025-06-07T09:44:37Z","title":"The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":35},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.06736."}