{"as_of":"2026-08-13T23:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0151acb678051d7d9befd86450d87becb24a9944088dd9c883162ce913d55ac8","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":"2026-08-11T16:42:27.950292Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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":"2026-05-23T07:42:02.626085Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T07:42:43.340270Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"cited_work":{"arxiv_id":"2412.09923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.09923","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Jose and A","venue":null,"work_id":"ef0bf035-3faf-4a6f-af01-28c57a8b3aa2","year":2024},"citing_paper":{"arxiv_id":"2412.14615","last_updated":"2026-05-08T10:48:09Z","snapshot_observed_at":"2026-08-03T00:49:49.053802Z","submitted_at":"2024-12-19T08:04:34Z","title":"Additive codes attaining the Griesmer bound","version":3},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-05-23T07:42:02.626085Z"},"links":{"cited_paper":"/paper/2412.09923","citing_paper":"/paper/2412.14615"},"observation_digest":"sha256:ef68bd0ce14d5c4e1f5e2666085a67b55d7d74b2a4b0baa25da962b44abbf383","observation_id":"f0ff89a4-8969-4edc-a00d-efce158137a6","resolution":{"observed_at":"2026-05-23T07:42:43.343361Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.09923/citation-record","integrity":"/paper/2412.09923/integrity","json":"/paper/2412.09923/citation-record.json","paper":"/paper/2412.09923"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:42:28.606516Z","title":"and Siap, I.: On Z2Z2[u]-additive codes, Int","venue":null,"work_id":"f58ca064-85b2-4737-865f-e7f9cdded8a4","year":2015},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.764727Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:e1fa705b2e4215bdd5c58a9ec442772549299cc5d88cbfb69360784b90de951b","observation_id":"7c3d6df1-18e8-4fe1-9583-95ef5c900085","resolution":{"observed_at":"2026-08-11T16:42:28.611489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.589521Z","title":"and Siap, I.: The structure of Z2Z2s-additive codes: Bounds on the minimum distance, Appl","venue":null,"work_id":"b9bb9506-0552-47dd-b8de-c600bd1031e7","year":2013},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.772695Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:cbc0b3f76a8ee4d4b2e53b9f2e6976aa7c115bd07eafa3682ec8c22adeee7bdf","observation_id":"7578c1f6-c2d1-4a15-b85a-4083fe433a87","resolution":{"observed_at":"2026-08-11T16:42:28.594762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.572620Z","title":"and Siap, I.: On Zpr Zps -additive codes, Linear Multilinear Algebra 63(10), pp","venue":null,"work_id":"05d505ee-68d8-4dad-be63-3b7a301c7293","year":2015},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.778934Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:e1e2500abc9dd15ef4b4e8f27f9c9e284289a24fa8150ed765de1b31993bec26","observation_id":"5da0aa32-3c3f-4c76-a4ba-885da8e685c9","resolution":{"observed_at":"2026-08-11T16:42:28.578177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.556009Z","title":"and Samei, K.: On codes over product of ﬁn ite chain rings, Sigma J","venue":null,"work_id":"4987eedf-393e-46a6-8ec9-754fde4f4f09","year":2023},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.784580Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:c872728b7d39f9d70951163b78682946e0609830c1d0e14aebf7fda9ce5c7286","observation_id":"cca7e19b-f989-4d70-9ec5-ae2de36074bc","resolution":{"observed_at":"2026-08-11T16:42:28.561211Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.539948Z","title":"F., Kabore, J","venue":null,"work_id":"a146011f-1339-4ae8-ae18-7139800e297c","year":2023},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.791884Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:02d9fecdf7576e212812e4eebd1ada0ef8dfc9f8b3ce5dc7336335531720c6f6","observation_id":"da80dd96-8c70-4ddd-8704-b128fc7291d7","resolution":{"observed_at":"2026-08-11T16:42:28.544980Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.523411Z","title":null,"venue":null,"work_id":"972b32a2-174f-4893-a124-fe1f8e437072","year":2009},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.798933Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:f314d1618c9e29d3e497fb42594400674619431fb280ff80117cb2d3417a7082","observation_id":"ee7521f8-1371-4825-8caf-d8c87e63fe9d","resolution":{"observed_at":"2026-08-11T16:42:28.528628Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.508048Z","title":"and Edel, Y.: Quantum twisted codes, J","venue":null,"work_id":"5d9cacfc-d35c-4307-8e37-4d29257c0e73","year":2000},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.805186Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:6b5f50f11e82b3827e8cf467e50e000de95865824d3338f48b0b950638662fd3","observation_id":"d8215603-6cb7-40ce-b9a5-4406cf2708aa","resolution":{"observed_at":"2026-08-11T16:42:28.513331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.492229Z","title":"and V illanueva, M.: Z2Z4-linear codes: Generator matrices and duality, Des","venue":null,"work_id":"2b97d537-600d-4988-a6eb-5ecdf0c9dc70","year":2010},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.810135Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:b46272ae978029153eff38651be0fac9f6a7dc0a5c249e67707944bc554e6c22","observation_id":"63aa955c-2545-4772-9ac5-5067d6badd3f","resolution":{"observed_at":"2026-08-11T16:42:28.497223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.475117Z","title":"and Ten-Valls, R.: Linear and cyclic codes over direct product of ﬁnite chain rings, Math","venue":null,"work_id":"548e2449-369c-4c50-b01d-2955e5ccf859","year":2018},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.815522Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:bcf045eab1f514760780b8ec56d01fe134fdae0d1bc4edf1eb88868db179446d","observation_id":"360026a1-0e8f-4105-9ffa-d0bcd12e7b0a","resolution":{"observed_at":"2026-08-11T16:42:28.480700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.457396Z","title":"R., Rains, E","venue":null,"work_id":"133b7710-00d9-432c-81e2-af5db6f19913","year":1998},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.820127Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:53ec19f19f4786633da3bc0eb8063e39d3837cfbc3ec926dd62c76a8e106c0f4","observation_id":"1b9adb28-b87a-4c92-9d9e-860f2ca6b7f7","resolution":{"observed_at":"2026-08-11T16:42:28.462718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.441346Z","title":null,"venue":null,"work_id":"105a4f96-64e0-4429-9462-cf3fd0ca1085","year":2015},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.824644Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:5c5ece9878ba22cd516f479b777c60b4437791ebd95848ee6da14aa4bd0f3059","observation_id":"1ac03190-fdaf-4175-b28b-39a9f6cd74b4","resolution":{"observed_at":"2026-08-11T16:42:28.446263Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.424193Z","title":null,"venue":null,"work_id":"6859cdb1-1ff9-4b64-a253-91800d50535a","year":2006},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.829353Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:67496be03228a029f1d32823e3f249090813092f6e19db11c4558706854425b3","observation_id":"64ff984a-e71d-44f2-a9d1-5510b63abd5c","resolution":{"observed_at":"2026-08-11T16:42:28.429278Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.407620Z","title":"T., Kim, J","venue":null,"work_id":"be12acbe-5c4b-4608-85c3-b7d197f40113","year":2018},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.834203Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:e0ad13e54c8f144d9fd46cae8c28f502fbb70676eef91037d171c6eaa854a4cd","observation_id":"0f76d5b6-76ad-43c1-91be-118a932f8de3","resolution":{"observed_at":"2026-08-11T16:42:28.412876Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.388644Z","title":"T., Kim, J","venue":null,"work_id":"eefe118f-d461-415f-beb3-1ff21156c9f2","year":2010},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.838576Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:7bb57f918fb2aacb031331a15d8038303f7d404540827ed0025c925dba1993d4","observation_id":"2e8c55f1-ad26-4967-8735-6984b66f5f53","resolution":{"observed_at":"2026-08-11T16:42:28.394692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.368831Z","title":"T., Korban, A","venue":null,"work_id":"cc5eac1a-90da-4397-9e3b-49845349426e","year":2022},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.843093Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:863b2b8a5f8b6686c9c18def5c2c5beb2969925169396394af8d178c0b2a0d85","observation_id":"aa457548-2405-4892-b7ef-0e8eb4aae2dd","resolution":{"observed_at":"2026-08-11T16:42:28.376383Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.351233Z","title":"T., S ¸ahinkaya, S","venue":null,"work_id":"554c0160-8e8e-4274-a0fd-94777f9a5667","year":2022},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.848057Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:a35d5750573d308e37ac79aabe0b7faece31030c4c6d469a9c40c6ad96511a97","observation_id":"09bc4a4a-7c82-4e58-ab6a-4b4acf06e178","resolution":{"observed_at":"2026-08-11T16:42:28.357030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.334590Z","title":"and O’Sullivan, M","venue":null,"work_id":"c6ea53d8-1e73-4186-8aa0-45aca7b94cc1","year":2004},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.852928Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:b454354e754d19a574552195c3a1714c13e7a71698497fc1b8697e527b0c84ec","observation_id":"6b878b44-a659-4ad8-adcd-988772795ebb","resolution":{"observed_at":"2026-08-11T16:42:28.339432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.319265Z","title":"and Schmidt, S","venue":null,"work_id":"d508e59d-0530-48f7-b89c-6adad5277e70","year":1999},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.857788Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:e1612d11e86772c72d25c9d867f52f8c18f49f46292c4a3f31492130b05acc0a","observation_id":"42f2eda0-bec8-4aec-bae2-f40713ff4fdc","resolution":{"observed_at":"2026-08-11T16:42:28.324161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.301375Z","title":"R., Kumar, P","venue":null,"work_id":"02cde0ef-7fde-40a9-b6cd-3d277e59b6f1","year":1994},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.862614Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:b5a7064b9b0e7299fcd4f5805bcbc92b193e748b2b6d3ad8a61c085cf33b5f56","observation_id":"b5cce8d1-d8be-4477-beb2-864752c1d67b","resolution":{"observed_at":"2026-08-11T16:42:28.307437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.282965Z","title":"C.: Additive cyclic codes over F4, Adv","venue":null,"work_id":"e90f00e0-8f21-43fa-8339-9c5393993a6e","year":2007},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.867667Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:4e24ba78ca793fe0ab6864570e7909329ba6dbc540733690893eecb2f85f3dcf","observation_id":"4d4cc6de-f44c-4a15-8fb1-b026bd628d27","resolution":{"observed_at":"2026-08-11T16:42:28.288960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.261541Z","title":"C.: Cyclic Fq-linear Fqt -codes, Int","venue":null,"work_id":"18b4a9fd-ecc9-4975-a2b2-2a993f495d91","year":2010},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.874186Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:5034011e5c590898e44fa4da1e0c0d54bc660c026f7c1cfa8b1c66cdd3d5fdae","observation_id":"44057ab3-ec75-4e5d-99c6-26e337bdcfbb","resolution":{"observed_at":"2026-08-11T16:42:28.266963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.240630Z","title":"C.: On the theory of Fq-linear Fqt -codes, Adv","venue":null,"work_id":"adde4ee5-7a87-4e01-a8d8-28a2ad6d8825","year":2013},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.879399Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:037167513cc3925064cd25957269196ce0ffa9385c8fca4a8ac433ed828e7091","observation_id":"dd725cab-5676-4b94-93a9-f03961247af5","resolution":{"observed_at":"2026-08-11T16:42:28.246759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.224672Z","title":null,"venue":null,"work_id":"ec2c70b3-7f93-4455-8702-127690bac53c","year":1998},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.884804Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:8f3b6cd9905c3623f7c7d6cc2a651bfcbe832c173e3b1adea76ed84e02ebd356","observation_id":"0b59cf53-8bf3-494e-99de-7cbb576ded4f","resolution":{"observed_at":"2026-08-11T16:42:28.229654Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.207146Z","title":"and Sharma, A.: Enumeration formulae for self-ortho gonal, self-dual and complementary-dual additive cyclic codes over ﬁnite commutative chain rings, Cryptogr","venue":null,"work_id":"4118f8e2-71ea-472d-97f3-278d49757ce5","year":2024},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.890550Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:5456086893bed25e52451fd8ae4d9e2796254cbbe3abd3e9fb2eb3e0bbbe221d","observation_id":"f41ff845-2231-4dd1-925b-9e126516c54b","resolution":{"observed_at":"2026-08-11T16:42:28.212638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.187939Z","title":"and Sharma, A.: On Euclidean and Hermitian LCD codes ov er mixed alphabets, Under review","venue":null,"work_id":"4c457e6d-597f-4587-9030-d2b84276c042","year":null},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.895933Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:5d2639e2a94a80171aedd83051f66cc762008748c9dd07baf189124a831f2296","observation_id":"7939c307-ce95-4cdd-ba94-66b9b91b2799","resolution":{"observed_at":"2026-08-11T16:42:28.194018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.169676Z","title":"and Samei, K.: Additive codes over Galois rings, Finite Fields Appl","venue":null,"work_id":"fd1377fb-ca9f-4eec-80d9-63411af7e9cc","year":2019},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.901338Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:35365a860126eea740dfb57fc0513eba5848b22c9f78639aa9b74f3f9ecab6e9","observation_id":"b1caa896-2642-498a-bbb8-ec64e70cb1ad","resolution":{"observed_at":"2026-08-11T16:42:28.175504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.148092Z","title":"and ¨Ozbudak, F.: Additive cyclic codes over ﬁnite commutative chain rings , Discrete Math","venue":null,"work_id":"f040ecfe-96ff-4c24-8fc7-3744e573878f","year":2018},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.906765Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:599e164c6dcee5ba94f9a39d6a500d9104259288a7e186bfab5a1185a4721f64","observation_id":"805c45cd-626c-473b-8257-dcba5826decb","resolution":{"observed_at":"2026-08-11T16:42:28.153567Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.130565Z","title":"R.: Finite rings with identity , Marcel Dekker, New York (1974)","venue":null,"work_id":"c5dcb497-a571-44a7-ac46-1e9972e0470d","year":1974},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.912622Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:1789415f7794164f8bc640429a6ab214b24b29bc4036548b2950d1e2fb7b4f9b","observation_id":"948ee36b-4e9c-491f-a48d-cbe5bf837d39","resolution":{"observed_at":"2026-08-11T16:42:28.136090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.112191Z","title":"H., and S˘ al˘ agean, A.: On the structure of linear an d cyclic codes over a ﬁnite chain ring, Appl","venue":null,"work_id":"93487bc6-39ea-430b-8609-102a112a513e","year":2000},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.918695Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:58e97d075c2795dd6446a4179058c8b8f18bf97d3e9f2a78b35cdf7675b2b443","observation_id":"07a0914a-1c41-4da9-9b4d-c440448b7a50","resolution":{"observed_at":"2026-08-11T16:42:28.117709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.081487Z","title":null,"venue":null,"work_id":"36d1ad24-4803-43aa-834e-98a258f38bb7","year":1968},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.924558Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:41d2bc88932dd6715653737ddd193a34f2a22a98d37cb2170ac8f7b23b9f78fa","observation_id":"d8a657a7-411e-4a79-8628-25975eb8f0d2","resolution":{"observed_at":"2026-08-11T16:42:28.092465Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.062672Z","title":"and Pujol, J.: Translation-invariant propelinear codes , IEEE Trans","venue":null,"work_id":"7e06e60d-7684-41e2-a7a7-e687ed674e97","year":1997},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.930127Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:a17f34f6cd03ddfe45389c2f81849d3eeb386ccd4c642cb4bdf210a83a3b909e","observation_id":"8342c3db-2eb7-4729-98d9-ece0c3e83379","resolution":{"observed_at":"2026-08-11T16:42:28.068047Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.045622Z","title":"X.: Lectures on ﬁnite ﬁelds and Galois rings , World Scientiﬁc Publishing, New Jersey (2012)","venue":null,"work_id":"f95435fd-c999-4a9c-b30a-bfd1632427c0","year":2012},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.935457Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:4331ecea078ec160a0e9609cc3ea6961522266b40f205a1176994f9650c06bb1","observation_id":"2feec286-323d-4f65-b5a3-854d7aa6d25c","resolution":{"observed_at":"2026-08-11T16:42:28.051084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.028075Z","title":"A.: Foundations of linear codes deﬁned over ﬁnite modu les: the extension theorem and the MacWilliams identities in Codes over rings, World Scientiﬁc , pp","venue":null,"work_id":"6e95d158-4a94-4ae3-95cd-8bd92575334a","year":2009},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.940348Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:80de3d0133353ec2e26fd9cc77f25c7699621559eb930c9cc0e1f6d1bf50afe7","observation_id":"551b9c8a-9b39-44c3-bf41-ddde9e709fb9","resolution":{"observed_at":"2026-08-11T16:42:28.033852Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:28.012081Z","title":"and Sharma, A.: Mass formulae for Euclidean self-ort hogonal and self-dual codes over ﬁnite commutative chain rings, Discrete Math","venue":null,"work_id":"070bee0a-5490-4630-b61e-0cbb81c9b8f3","year":2021},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.945411Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:62810275febb091586804e49efa8deae93dfd5e163990e5f7e40f856f0a60642","observation_id":"b55b07b9-70ed-4038-9d84-82e3a3a4ecdd","resolution":{"observed_at":"2026-08-11T16:42:28.017019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T16:42:27.991167Z","title":"and Sharma, A.: On the enumeration and classiﬁcation of σ-LCD codes over ﬁnite commutative chain rings, Discrete Math","venue":null,"work_id":"5595c507-2422-4df1-baaf-27e5857575c1","year":2022},"citing_paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T16:42:27.950292Z"},"links":{"citing_paper":"/paper/2412.09923"},"observation_digest":"sha256:185e997f5e81afd89ed777e31651e37219e34c7767ceb65c2384f1d2679d149e","observation_id":"e85b7e83-9d73-4acb-8836-f9284010aed0","resolution":{"observed_at":"2026-08-11T16:42:27.999390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.09923","last_updated":"2024-12-13T07:23:22Z","latest_version":1,"primary_category":"cs.IT","snapshot_observed_at":"2026-08-12T00:20:00.175073Z","submitted_at":"2024-12-13T07:23:22Z","title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":30},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2412.09923."}