{"as_of":"2026-08-22T04:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ff11b5fe629ae9b1a8e69fc35e7cb1e69f1500bef9084bbf13ad7f05ce95b45f","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T19:37:39.977027Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-10T09:43:53.079617Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-10T09:47:00.529325Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"cited_work":{"arxiv_id":"2605.15925","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.15925","snapshot_observed_at":"2026-07-10T09:47:00.529325Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","venue":"cs.IT","work_id":"93998e52-0979-4286-9a40-7ce9234e4028","year":2026},"citing_paper":{"arxiv_id":"2607.08304","last_updated":"2026-07-09T09:46:32Z","snapshot_observed_at":"2026-08-17T14:02:21.084186Z","submitted_at":"2026-07-09T09:46:32Z","title":"A Study Of Skew-Polycyclic Codes Over A Non-Chain Ring","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-10T09:43:53.079617Z"},"links":{"cited_paper":"/paper/2605.15925","citing_paper":"/paper/2607.08304"},"observation_digest":"sha256:f6152db20096050d266e7da303e45a9497da7082397a8ed93b514281762ad835","observation_id":"e99889ac-e085-4b47-9c56-7cc7f312118f","resolution":{"observed_at":"2026-07-10T09:47:00.531181Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2605.15925/citation-record","integrity":"/paper/2605.15925/integrity","json":"/paper/2605.15925/citation-record.json","paper":"/paper/2605.15925"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.822107Z","title":null,"venue":null,"work_id":"1021b8f0-f116-4835-bbef-fd6725d24c3c","year":null},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:3483a15d0b3efb635328d8d8699eac4ab77f0abfefeea8168568d0800c3b614e","observation_id":"7eea1d90-0060-40a4-8cfe-26ff61dd02d5","resolution":{"observed_at":"2026-05-19T19:37:43.860601Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.825738Z","title":null,"venue":null,"work_id":"930c9b5b-8061-4aa6-b691-8a33e6251078","year":null},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:75ed6cf315d7007750a10db7ff3880a7713fc87a5e172c321f95c26fce4842c0","observation_id":"0d43539f-140b-4210-a642-3f04a38301dd","resolution":{"observed_at":"2026-05-19T19:37:43.846089Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.824032Z","title":"and Maheshwary, S","venue":null,"work_id":"91eced11-dd9c-4b0c-afcd-8b3aa64d9ed6","year":2025},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:a9adbef980d4079b07fb935ca285ef92cb249e6912387649f0a4007c9bf11ee9","observation_id":"3456fb8d-d28d-417a-b0dc-a5e4bd75fbf3","resolution":{"observed_at":"2026-05-19T19:37:43.838756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.827449Z","title":"and Samei, K","venue":null,"work_id":"d81fd101-4ae0-41a0-869f-76412fa5942d","year":2023},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:adcd01a2dcba79da8c910eb28854391548d71b0b58e314ff36862dc799951d58","observation_id":"662a43f3-2386-4f7d-892f-f0f1d1a92fcb","resolution":{"observed_at":"2026-05-19T19:37:43.855069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.829107Z","title":"TITLE =","venue":null,"work_id":"b40fcb64-2efd-4f30-b7a9-63a04090c5f6","year":2010},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:80338f3c0e1b8c657c839f0a0c5454d69296a32f28899a5d909c5522da32c1d4","observation_id":"bc58e2cd-690d-407f-9a71-8afda05dfa4b","resolution":{"observed_at":"2026-05-19T19:37:43.825535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.816511Z","title":"and Geiselmann, W","venue":null,"work_id":"b465254f-4bdb-4041-9851-cbd0fb8c3eed","year":2007},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:c365310836ee5f0f66a5c43acd32247662bd0a006dfc337c0b04b09c9dd02c7a","observation_id":"73b8eb84-d70f-42d0-abab-8278612db33e","resolution":{"observed_at":"2026-05-19T19:37:43.862388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.813019Z","title":"and Dinh, H.Q","venue":null,"work_id":"e14e9b2a-d521-456c-9592-2f6facc39f3c","year":2016},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:bcf866da5849f48910fba25e389f24f9dcaa2299365b0f7aa26ac9a258e38dd2","observation_id":"b4c0bf81-093a-4479-883a-201731f0dd0b","resolution":{"observed_at":"2026-05-19T19:37:43.807050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.820226Z","title":"and Dhompongsa, S","venue":null,"work_id":"dff1421d-abe3-435e-a20d-f248c274001b","year":2017},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:a0bd53de65d0fe7624ec35a02dae25c35b37827dda6fca0f3bc34b2bd10209d8","observation_id":"09dab9e4-b393-4f93-9693-51e70a8198ae","resolution":{"observed_at":"2026-05-19T19:37:43.844182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.798235Z","title":"TITLE =","venue":null,"work_id":"81f18d24-b9e1-4a9f-a454-d892f01b5b95","year":2013},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:8f48a54b7013c6a89238a73af6dadf28828c6afb82209de6d28e807df255e804","observation_id":"eb73b8f8-b560-485e-96dd-fa04156d8967","resolution":{"observed_at":"2026-05-19T19:37:43.842393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.803447Z","title":"TITLE =","venue":null,"work_id":"f8773232-cef2-4756-add8-4928ad1ff6f8","year":2014},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:2d6bffa4026727df106b8e030661216fc017e8a703fc4a0e609ce0a8645919b2","observation_id":"04eb6505-9998-4361-acf3-8d8e26ed5758","resolution":{"observed_at":"2026-05-19T19:37:43.829270Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.799963Z","title":"2025 , eprint=","venue":null,"work_id":"1cb4edd8-9675-4cb3-8eb5-05417f165fc4","year":2025},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:a2e32813fea75ab79264a67054652a6449d0786eb1d78a891fe51a559969bf40","observation_id":"a8fccc82-e5d6-453b-9cc9-a3db5e080ccd","resolution":{"observed_at":"2026-05-19T19:37:43.815607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.818406Z","title":"2026 , eprint=","venue":null,"work_id":"6a9aea5b-3ce1-423f-a8b6-45959c23fcac","year":2026},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:1b65fee4a4e1260ddaaac68c7a09e0c4c8e4119e1575fc40683f8111d18a946c","observation_id":"39e2a5b0-6cd9-47ed-b63a-805d12546220","resolution":{"observed_at":"2026-05-19T19:37:43.853298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.807782Z","title":"and Mohebbei, M","venue":null,"work_id":"ef668940-d0ee-414f-9e29-430926bf3ba6","year":2024},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:737052f7b514f23e77575dce36cbafd4d1a506a0f7229394190a37bb4c02f047","observation_id":"03bdb4fd-9201-42d5-bb87-b493b43ae7ec","resolution":{"observed_at":"2026-05-19T19:37:43.836849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.796496Z","title":"and Ling, S","venue":null,"work_id":"ab257d2d-2294-4543-aaeb-06e54759464c","year":2012},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:37d9fe644c97d8299b862f8c125cf006d754a2dd155f73babd5c36932fd2997d","observation_id":"530d5de9-ce39-4c03-a900-d568914b4f6d","resolution":{"observed_at":"2026-05-19T19:37:43.809258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"TITLE =","venue":null,"work_id":"22f5ac75-dd6d-42b5-bdeb-9edf6248c7fd","year":1974},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:9cf3745b38e64b7812cb181ba3444335ba3b7f8baa48a0cca22ee5a110ef1ccb","observation_id":"a7f9f2c0-ca08-44da-ae82-e39de7975d10","resolution":{"observed_at":"2026-05-19T19:37:43.817477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.811325Z","title":"TITLE =","venue":null,"work_id":"769bcca4-6a69-45a6-b1f5-27a1c6cbcb83","year":1991},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:6c25db054cb52e55459a49ed75f97593e07968c5563e22319dce4f29da448b80","observation_id":"dfd992f4-be00-42ef-b201-b5ea0a743d8c","resolution":{"observed_at":"2026-05-19T19:37:43.813550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.791025Z","title":"and Raj, R","venue":null,"work_id":"61ee4693-f72c-4296-9a37-67c2aa4df2cb","year":2025},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:721cdbdbebfcfe56a475394d252c6de4e9da39c5acad0e47f7bed0d9aa49b863","observation_id":"b2f32caf-764d-4f72-88af-6c00608377ed","resolution":{"observed_at":"2026-05-19T19:37:43.865893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.814702Z","title":"and Tang, X","venue":null,"work_id":"f9404e78-aa73-4795-9918-c18427c4ec33","year":2018},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:5e25d0cb9def5a02950ef29cd0a79e5d970df16ca12031102bec820e964dd90b","observation_id":"4f8e5356-8a9a-44b1-bfa8-6a67868f328e","resolution":{"observed_at":"2026-05-19T19:37:43.801229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Hesari, R.M.and Rezaei, H","venue":null,"work_id":"35c7e33c-8718-4cbd-b39d-2bfa91a582ac","year":2022},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:ed6a8e107d4f4607b758d8445bf4bdd9400dbd084fe6fcfa1dba96f9846e143f","observation_id":"d86ee202-d2a5-4dcf-8773-dbe501928c76","resolution":{"observed_at":"2026-05-19T19:37:43.811220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.808051Z","title":"and Samei, K","venue":null,"work_id":"5fef3d9b-a45b-4803-ae2b-e54f5d9c0bdd","year":2026},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:7e488bdc93db23cf809ba71ac248f2c9ff022b3ded60d971e05e87c97dda123a","observation_id":"47f68e89-4714-4e3a-9995-fbdcafe78018","resolution":{"observed_at":"2026-05-19T19:37:43.867556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.801899Z","title":"and Cao, Y","venue":null,"work_id":"3dfcf684-834f-4ac3-98eb-467a8ed14776","year":2018},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:ea67b0da3e4f1189ee187995f10b4ae48b9948b4b653aff0ca054fb883ed25b1","observation_id":"8974c1fb-ce16-4e9e-90ed-ed63ccd6b7d3","resolution":{"observed_at":"2026-05-19T19:37:43.803082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T09:47:00.798410Z","title":"and Cannon, J","venue":null,"work_id":"5de2bd42-34c7-4fde-aeb8-3f25f8257071","year":1997},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:77c1e482e3c4fcc146f9c806080835a202f0e541f3829096756a590ffbe97990","observation_id":"b1d36d45-76ff-4e5f-9cc0-a5d89ae674d4","resolution":{"observed_at":"2026-05-19T19:37:43.847873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.16563","last_updated":"2025-06-28T12:55:39Z","snapshot_observed_at":"2026-08-17T05:22:22.154368Z","submitted_at":"2024-11-25T16:48:53Z","title":"Uniformly semi-rational groups","version":2},"cited_work":{"arxiv_id":"2411.16563","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.16563","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Antil, G","venue":null,"work_id":"e9d91ece-67b3-4a40-b158-c938ac052df8","year":2025},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"cited_paper":"/paper/2411.16563","citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:78e47dc3848eea6159bb4f7e4d56f072660b2b58e43ec69142ceb1e6db54f120","observation_id":"6b13e37b-9f19-4a22-b76e-3312452373b8","resolution":{"observed_at":"2026-05-19T19:37:43.731326Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bosma, J","venue":null,"work_id":"5284d6f9-90e4-4103-9d80-ad5e24e395ba","year":1997},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:bed53591e8748df978e2951f9a20e73f7bb6dee4035ccd0965d3390eff08a00e","observation_id":"0d5ed684-1dd2-4eea-8408-589b9144eb74","resolution":{"observed_at":"2026-05-19T19:37:43.804953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Boucher, W","venue":null,"work_id":"f99735df-983b-4489-a830-8b4811b0fa21","year":2007},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:735c06a24043ea10f304cf5fb25907208a1e73999e7058c0c5e2b5f52933411c","observation_id":"41e3e897-d3d6-4771-976a-24f6b2b36e3b","resolution":{"observed_at":"2026-05-19T19:37:43.821757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bagheri, H","venue":null,"work_id":"b9381662-f530-43b5-97e2-f2770b835e0e","year":2022},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:7569a1bddf7dc122eb04f098a5d7176e10ed58f55a36851d53372f1f6b1ee78d","observation_id":"ee96bac6-da87-4a1d-9f15-2fd2e8c17cae","resolution":{"observed_at":"2026-05-19T19:37:43.864013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.03164","last_updated":"2026-05-04T21:22:14Z","snapshot_observed_at":"2026-08-14T04:31:15.832670Z","submitted_at":"2026-05-04T21:22:14Z","title":"Skew polycyclic over finite chain rings associated to trinomials","version":1},"cited_work":{"arxiv_id":"2605.03164","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.03164","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Skew polycyclic over finite chain rings associated to trinomials","venue":"cs.IT","work_id":"1d9ee35d-9a81-4555-8f38-03d4a2a4cca1","year":2026},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"cited_paper":"/paper/2605.03164","citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:622bc558c4dbe1bd5ad4b1b223e9e5a5beebef071baa25ab9920e68008517a25","observation_id":"ccb2fe0b-c539-4fb2-8a78-d12cef6b95bf","resolution":{"observed_at":"2026-05-19T19:37:43.727888Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Burton, Elementary number theory, McGraw-Hill","venue":null,"work_id":"929ea301-9ab1-4fab-a2a9-1d2bc1873a4e","year":2010},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:086c8d178d8403865ec062150a9d70cade00c2310b6dcfcc56b19180d6c574bd","observation_id":"ef8e2556-13e2-499e-b1c3-f40951f86180","resolution":{"observed_at":"2026-05-19T19:37:43.819579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"eb0aeaef-d6ae-419d-9276-4b69dfe89b3d","year":2018},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:bfcebd838a27bb32ed1df27f8d92ab7dac607b72e33bb7e12da71b57891ecf75","observation_id":"d7c76048-af77-47c2-89ae-d3dbef913fd5","resolution":{"observed_at":"2026-05-19T19:37:43.869394Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chen, H.Q","venue":null,"work_id":"c216cfe3-ee1e-4b08-84c9-103b7a183c8d","year":2016},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:44661211b93bde922cd654b6efc7934e6f20c685ca3e9bc0ad0932e981962af6","observation_id":"89f23c3e-01c4-4609-8de4-626090932df2","resolution":{"observed_at":"2026-05-19T19:37:43.834998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f9985160-bd4a-43eb-b16e-6066960f5fea","year":2017},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:2709ec170863b19fd9b22d5a0d79315f7bbb03983c04ec4d4f439643dd4582c3","observation_id":"9b728907-a11c-4fda-a966-c339ccc7e706","resolution":{"observed_at":"2026-05-19T19:37:43.871122Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Dinh, Constacyclic codes of length p^s over F_ p^m +u F_ p^m , J","venue":null,"work_id":"deee75b5-0af2-403a-bce4-a5e74d2e168c","year":2010},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:7ad7d7bf6bd19eea5164ccd88b1703862aaaf5f9ea6c25db27af17538e86490e","observation_id":"b04b7200-53ee-4478-90e0-fe3b413583a9","resolution":{"observed_at":"2026-05-19T19:37:43.857029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"313 (2013), no","venue":null,"work_id":"d08cc582-c1f4-4caa-873d-00bf3936be3d","year":2013},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:9690a7a4698c2d976f27bccd15486e23b0fb6c624f428b88783d5992bea63542","observation_id":"48cf05d4-a95b-4405-a976-78f9cfa13394","resolution":{"observed_at":"2026-05-19T19:37:43.831216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Math., vol","venue":null,"work_id":"4ee234ac-c2ae-4d4d-b0fa-1bf0a8e086da","year":2014},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:01551b40c4f020638abe2e2e4b857cbd93ffa01d9431a5cd8ebc994c51dfd731","observation_id":"4d727e73-427e-4cf6-a844-bb015ba5538f","resolution":{"observed_at":"2026-05-19T19:37:43.823749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hesari, M","venue":null,"work_id":"585a4525-34c3-4e1c-924d-589bc43a9ee0","year":2024},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:e52b6271bed265c06daa50d989d33a4c2e8b16e23d6b5db6b4f704c6d35ca158","observation_id":"58b9670e-534e-487a-82fa-799fd3fbd21d","resolution":{"observed_at":"2026-05-19T19:37:43.858839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hesari and K","venue":null,"work_id":"3bb7f36d-64c9-4569-bd12-b1cbddbf7084","year":2023},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:54d639b876099e70a04ffc450b298465c8d07323a9cbc0fd8690a3bee83b08eb","observation_id":"7ace338a-8f6f-408f-846d-9b8bd2c975af","resolution":{"observed_at":"2026-05-19T19:37:43.840630Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"737ea0f1-9f7a-434d-9523-acfd0c1d0f57","year":2026},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:5fe7b8c31b449351ff14096a2d3c63432495333d3891703ab91c070e4abce9be","observation_id":"ed7980dd-1c74-403f-a937-8cfada669cda","resolution":{"observed_at":"2026-05-19T19:37:43.851439Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Jitman, S","venue":null,"work_id":"9c59cba6-7a78-4efa-9017-e810f730851b","year":2012},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:db706823e27345154cf04e7605e9b673de027f04b8d935a94c3b5cc18bf3d675","observation_id":"753fcb72-d20c-4643-b39f-521f99d3a9ff","resolution":{"observed_at":"2026-05-19T19:37:43.827303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"11c49716-5671-4532-b632-93b4943db88b","year":1974},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:40c22f64f24ce2dd12481c498594cc2526811b93538b8ba0abc35e60d3d13f69","observation_id":"3a5c371f-eaa5-4e1d-b440-92fafbf92e41","resolution":{"observed_at":"2026-05-19T19:37:43.833214Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pathak, R","venue":null,"work_id":"3127c4ed-708a-4c65-8212-37b256174e25","year":2025},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:08e982717458b07b1195864c6cefa7b9246c2cf33cc8feb329a3c946fe8bdf4b","observation_id":"bf0b3d4f-a064-4ed3-aaf4-b84d65585a47","resolution":{"observed_at":"2026-05-19T19:37:43.849659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"62e68c90-29a7-499b-8766-d21b968a6fac","year":2018},"citing_paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-05-19T19:37:39.977027Z"},"links":{"citing_paper":"/paper/2605.15925"},"observation_digest":"sha256:4d7a189e9ba1a898b43f0df7673091da5467414c94a8bc1901e7a95cc36aeb4d","observation_id":"beb41c23-19aa-40c3-bfc3-1dcd6e13f6b2","resolution":{"observed_at":"2026-05-19T19:37:43.799201Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.15925","last_updated":"2026-05-15T13:07:37Z","latest_version":1,"primary_category":"cs.IT","snapshot_observed_at":"2026-08-16T14:59:16.823497Z","submitted_at":"2026-05-15T13:07:37Z","title":"Skew Constacyclic Codes Of Length $np^s$ over $ \\frac{\\mathbb{F}_{p^m}[u]}{\\langle u^k \\rangle}"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":2,"verified_fuzzy":32},"total_outbound_references":41},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2605.15925."}