{"as_of":"2026-08-14T01:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c4d3480984d6c61156fcdcdb44e0484739f8b96844fa6d874e425c4e7be5a808","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-01T16:11:11.144029Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.27312/citation-record","integrity":"/paper/2605.27312/integrity","json":"/paper/2605.27312/citation-record.json","paper":"/paper/2605.27312"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T11:02:20.458619Z","title":"Application of boolean algebra to switchi ng circuit design and to error detection,","venue":null,"work_id":"8a71bd49-633f-46c2-b9ea-bc129a0490f1","year":1954},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:0a2146f144d513eb2ca32b370df72c8436f4678452977f40e385e7700551bbf2","observation_id":"8b74c764-ed98-41f5-afae-e3e275e4127a","resolution":{"observed_at":"2026-07-06T11:02:20.460200Z","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":"2026-07-06T11:02:20.455839Z","title":"A class of multiple-error-correcting codes an d the decoding scheme,","venue":null,"work_id":"b32fa320-6336-4f25-8457-e7f5aeee0a39","year":1954},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:3f665b6e9dbb38324b3dc268b3d3533e01f40d4cdac7ffb83b9db1c74cf0d8de","observation_id":"3221ee07-fb04-4af7-aaa7-554d1b19bd81","resolution":{"observed_at":"2026-07-06T11:02:20.457834Z","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":"2026-07-06T11:02:20.453684Z","title":"Reed–muller codes achieve capacity on erasure ch annels,","venue":null,"work_id":"ec86ad42-892c-476d-b3da-d7e6630da4ad","year":2017},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:641d79732df9e92377b30c331253cf69b938685f93999157d37802950955ca50","observation_id":"c86e20cc-327c-4584-802e-d0edc7e93f54","resolution":{"observed_at":"2026-07-06T11:02:20.455026Z","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":"2026-07-06T11:02:20.451805Z","title":"Reed–muller codes on bms chan nels achieve vanishing bit-error probability for all rates belo w capacity,","venue":null,"work_id":"1ef99b4a-ea2f-406a-93ad-ce6e9e2e31f6","year":2024},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:006ef9dcd83424818959bbcf01d9a1afcbcbb5494e83440e7911c6cae79b850b","observation_id":"d0454c29-6ac1-4030-aea1-b55b46980602","resolution":{"observed_at":"2026-07-06T11:02:20.453091Z","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":"2026-07-06T11:02:20.460896Z","title":"Automorphism ensemble decoding of reed–muller codes,","venue":null,"work_id":"178792e0-9579-45d6-8ebf-17e03dc31f00","year":2021},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:e29756c48defaaa57f819724a229b7369c2d897303b3fe1dd80264f2f5e1cf45","observation_id":"e551e951-0f92-47c6-a497-436d2a97d8ab","resolution":{"observed_at":"2026-07-06T11:02:20.463602Z","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":"2026-07-06T11:02:20.441121Z","title":"Constituent au tomorphism decoding of reed-muller codes,","venue":null,"work_id":"92fb96fb-e73a-4938-abf3-39b618cb7744","year":2025},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:6f2045e255f96c2d0c3969d6efc7cb10c2e9fb8952a759dcafac9b4b0760ad85","observation_id":"158cde3a-046a-4dc9-82ed-df377697f8c5","resolution":{"observed_at":"2026-07-06T11:02:20.442272Z","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":"10.1007/bf01119999","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Semisimple cyclic and Abelian codes. II,","venue":"Cybernetics and Systems Analysis","work_id":"2d49151c-67e3-43ff-846e-9544947ee9b4","year":1967},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:e66607542fedf28b7c69a8184ed47a2c0112cac90e917bd6f9351a92b65a8b71","observation_id":"2bd53095-5741-41fb-bccf-d646cd1cd415","resolution":{"observed_at":"2026-07-01T16:15:48.709554Z","resolver_source":"doi","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T11:02:20.442890Z","title":"On a family of abelian codes a nd their state complexities,","venue":null,"work_id":"6ece492f-58e9-491b-8154-03e8acdb9f78","year":2001},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:37ec4d13c1fbfe26e6da68a7f8aa1551f670cde488c752ad636666d90778f03e","observation_id":"e1d662d4-85d6-4344-a2a8-e92747abe439","resolution":{"observed_at":"2026-07-06T11:02:20.444044Z","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":"2026-07-06T11:02:20.446595Z","title":"Berman codes: A general ization of reed–muller codes that achieve bec capacity,","venue":null,"work_id":"bd7a751a-94c0-4c0d-b097-28a2456a19bc","year":2023},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:76156c816bab8fa6100df9a78b040d12920281ea2d65f2e5dc1107f9b0215096","observation_id":"f8bfeb5d-ef59-46fe-8a93-8884ff0643fc","resolution":{"observed_at":"2026-07-06T11:02:20.448046Z","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":"2026-07-06T11:02:20.437357Z","title":"Transform domain charact erization of abelian codes,","venue":null,"work_id":"52d7441f-74cc-41a3-8378-6169f6bc36f2","year":2006},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:9fe9b5b3e3ea8fa3a5b10c7d0361ac3e8a27dae67eca393e021504783f95e246","observation_id":"ad614572-f30e-4922-8339-3eca9cebe30a","resolution":{"observed_at":"2026-07-06T11:02:20.438699Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"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":"2026-07-06T11:02:20.439277Z","title":null,"venue":null,"work_id":"9298bc0a-fc45-406b-a279-cc40723b97c3","year":1977},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:69098087302226144d96ffc196c2136f033799b1b43b289dc464c63ad71b6dd5","observation_id":"1d60e701-7980-4cc0-9f50-946e3809e05f","resolution":{"observed_at":"2026-07-06T11:02:20.440348Z","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":"2026-07-06T11:02:20.444637Z","title":"The automorphism groups of reed-solomon codes ,","venue":null,"work_id":"38435249-a1eb-48de-be6b-e84e5f080100","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:93aeb9c5261e0cede138e6e029c6bd1057719e46bd12980975ee958c66a38780","observation_id":"eaca9543-de73-4e79-8fb6-4c693b519416","resolution":{"observed_at":"2026-07-06T11:02:20.445808Z","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":"pii/0097316","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T02:49:24.595767Z","title":"Journal of Combinatorial Theory, Series A21(3), 257–298 (1976),https://www.sciencedirect.com/ science/article/pii/0097316576900017","venue":null,"work_id":"ee2f2b60-3e02-4baf-8585-3bd75f200b37","year":1979},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:17316e46276d7111cd15de44e25425866dc2035509f64c59337b09c7b9aa498f","observation_id":"e6ab83cd-71b8-402a-aa22-caa6c6c6a5fa","resolution":{"observed_at":"2026-07-01T16:15:49.075994Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T11:02:20.448635Z","title":"The automorphism group of gen eralized reed-muller codes,","venue":null,"work_id":"280668b2-0725-4f2b-8bc1-4c71d3fecb63","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:5f84ee0b2c3c89a06b5b7a0d541d92d48b5e43e72894ab8239762d9d6914bfae","observation_id":"ad07aa01-7105-4002-bdca-779f44df9e78","resolution":{"observed_at":"2026-07-06T11:02:20.450349Z","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":"pii/0012365","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T05:06:40.086149Z","title":"Upper bounds for constant weight error correcting codes,","venue":null,"work_id":"055ce48a-7eb4-4564-b525-6aa60df55a4a","year":1972},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:b9fb39aa783be10a06e3a6d528db41985057a9fdd4b34a9545c1fb73e9be4453","observation_id":"a915d1bf-38c2-4771-9358-b41aeb210aa5","resolution":{"observed_at":"2026-07-01T16:15:49.073018Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2026-07-06T11:02:20.464849Z","title":"On the automorphism group of polar codes,","venue":null,"work_id":"784d404f-70c3-4eb3-88ba-4c751033eeca","year":2021},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:915581343f5423345219fef6aa86816c9e572ddef678b4d771eb22af900fa6e7","observation_id":"35155178-596f-4c4c-a8bb-e0366acb2e52","resolution":{"observed_at":"2026-07-06T11:02:20.467005Z","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":"2026-07-06T11:12:19.574355Z","title":"A classificati on of the maximal subgroups of the finite alternating and symmetri c groups,","venue":null,"work_id":"ca706560-884f-47a0-bc5f-23aa0e7db258","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:f416035d5e4927bb3682f7a42ba419a5c9b78fb176d4849a9c43f96a17bfd453","observation_id":"63bfce4a-c279-473d-80cb-1db00465eb77","resolution":{"observed_at":"2026-07-06T11:12:19.575899Z","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":"10.1093/qmath/37.4.419","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The maximality of certain w reath products in alternating and symmetric groups,","venue":"The Quarterly Journal of Mathematics","work_id":"2cc0a351-e61f-455a-9755-c9a7d756149b","year":1986},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:e2feb97cf40e10dbe7cb199039be08b094fd6767cbcea3d3e972ad6c7efc1cb9","observation_id":"66e0b037-75d9-4884-8463-df49a2353624","resolution":{"observed_at":"2026-07-01T16:15:48.711803Z","resolver_source":"doi","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T11:12:19.572473Z","title":null,"venue":null,"work_id":"f755e077-eac8-41b0-b9b2-b5ef5a42b80b","year":1996},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:1285ece5fdec8e75fa08e62f17d6ed5c0e134ed34f46745ef0529a2892ac9043","observation_id":"bd546810-00f2-47b8-bcd1-0c242ee3696d","resolution":{"observed_at":"2026-07-06T11:12:19.573798Z","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":"2026-07-06T11:12:19.565136Z","title":"Recu rsive subprod- uct codes with reed-muller-like structure,","venue":null,"work_id":"8fde6d96-39d6-43b7-b62a-4914edac639b","year":2024},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:cb84e6b2126495332275fb08f7a0ff9e0bb121d59c304db5c3854fef5d4f9ffc","observation_id":"3ea5708a-23d8-4010-a1ce-2f70d2a67488","resolution":{"observed_at":"2026-07-06T11:12:19.567040Z","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":"2026-07-06T11:12:19.562046Z","title":"Bid codes: Algebraic codes from 3 × 3 kernel,","venue":null,"work_id":"9c44c306-0241-4043-8d16-fcff5fe70105","year":2025},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:0ffda749c29be6b3b228af33cfe51f06b98c84f11bc3de65b5839a6373f11c95","observation_id":"dd781223-2370-41cb-9b32-01cae4289689","resolution":{"observed_at":"2026-07-06T11:12:19.564081Z","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":"2026-07-06T11:12:19.561824Z","title":null,"venue":null,"work_id":"e5a68b69-a61e-4b52-83b3-65b6f29ee1fe","year":2018},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:047bbbeebbacc257e009d46f58b3fb948fe1c73425ba218cb342ffdc89944342","observation_id":"76a939ac-1171-4a04-8d70-46562fb4a4cc","resolution":{"observed_at":"2026-07-06T11:12:19.563787Z","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":"2026-07-06T11:12:19.572713Z","title":"automorphism-abelian-codes,","venue":null,"work_id":"ddca892d-e1d1-4b73-bb2b-cac895bd8aea","year":2026},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:3a5ce1e28b1ad87e22e19cc0a3575fdfa3dbe2c5fe1d7c155ffcd7b22207fd5c","observation_id":"2dccdf82-2f3a-420b-9d12-cc021e940d82","resolution":{"observed_at":"2026-07-06T11:12:19.574102Z","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":"2026-07-06T11:02:19.568254Z","title":"Solvability of groups of odd order,","venue":null,"work_id":"955c521b-5d4b-435f-9364-4179ce57b671","year":1963},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:88f98ee26a925f4600a8f5fa6710beac6466c9e98baff1e9ca89399611dba032","observation_id":"8f0e09df-484f-4a75-a7dd-92ca498cb6ad","resolution":{"observed_at":"2026-07-06T11:02:19.569520Z","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":"pii/0021869","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-01T16:15:49.077106Z","title":"Subgroups of prime power index in a sim ple group,","venue":null,"work_id":"b805e2e4-bc04-480e-82d3-fd2486f18aa7","year":1983},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:ab0fd95f3f16518f25be170d40ea0308ee202ab6fba963d830772c41ba5a4258","observation_id":"a6ca8735-d314-4ed3-a8f3-c1a1f3f452ea","resolution":{"observed_at":"2026-07-01T16:15:49.078452Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-06T11:12:19.570267Z","title":null,"venue":null,"work_id":"4bf7bc78-2ec1-4b0e-8a8d-bdc425dc21c3","year":2009},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:05eb4ab28723b0af420b7b79ffdd2d75444727208ed7a990659b1a77f1a9a174","observation_id":"efdaf46f-0175-4693-9a9c-a4d1fe918efe","resolution":{"observed_at":"2026-07-06T11:12:19.571952Z","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":"2026-07-06T11:12:19.569990Z","title":"Lam, Introduction to Quadratic F orms over Fields , ser","venue":null,"work_id":"9e817e7b-c296-48da-8c31-8c10f0424137","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:0ffb7b4c59162a79d7b2d5dec70c231e137b49a7dd6b4988cb8d405e6e20a4a8","observation_id":"32a17f12-8ac3-413a-accc-312bf10c4a31","resolution":{"observed_at":"2026-07-06T11:12:19.571715Z","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":"2026-07-06T11:02:19.562201Z","title":"A note on the graph isomorphism counting pro blem,","venue":null,"work_id":"a2e5c0fa-e94b-4d9d-ae36-a07efc792b82","year":1979},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:f906db984c6dc0e818a30526deefed4366d47525a63eca20a17c4d8ddb4ae50c","observation_id":"9b9d9266-bd8b-494a-bca0-a420db7f19b1","resolution":{"observed_at":"2026-07-06T11:02:19.563439Z","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":"7518.289754","doi":"10.1145/2897518.2897542","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Semidefinite Progr ams on Sparse Random Graphs and /T_heir Application to Community Detection","venue":null,"work_id":"01732f92-b764-429e-bfc2-ca72127d962c","year":2016},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:51c2bed0bcbcbc1758a9a73cc895c5bae3fcb18a4bdc1b0288dad5103b81d23d","observation_id":"f43d32c5-918e-4820-be21-4bdfb17decbb","resolution":{"observed_at":"2026-07-01T16:15:48.707870Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2026-07-06T11:02:20.469051Z","title":"Practical graph isomorphis m, ii,","venue":null,"work_id":"5faffbb0-7f7a-4978-82ed-99c4a54bd134","year":2014},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:a190d03a9d089eb95c118bf9d755d285e2e0e47c0453f49626b65e6439e27900","observation_id":"ca33ed89-5967-4054-8f82-d415b964c962","resolution":{"observed_at":"2026-07-06T11:02:20.471136Z","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":"2026-07-06T11:02:20.472486Z","title":"By definition, there exists some x ∈ ⋂ i∈ [ℓ] Xi such that f (x) = y","venue":null,"work_id":"878372f3-7447-461c-be50-ed0a3cf69475","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:617bcd17d82df3e4a020c56a5dac153d81f08b3a3b07be6b175e9f162b1c9e59","observation_id":"589f13d5-6db8-40f0-b598-74482302c5e9","resolution":{"observed_at":"2026-07-06T11:02:20.474084Z","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":"2026-07-06T11:02:19.555553Z","title":"This implies that for each i ∈ [ℓ], there exists an element xi ∈ Xi such that f (xi) = y","venue":null,"work_id":"47b79765-e508-4c9f-85a2-eee08d2246fc","year":null},"citing_paper":{"arxiv_id":"2605.27312","last_updated":"2026-05-26T17:23:25Z","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-01T16:11:11.144029Z"},"links":{"citing_paper":"/paper/2605.27312"},"observation_digest":"sha256:fc6c9373eb625f329f6eadd51bc0ff38723ff91748f87d5cb4c316d44dbc0c14","observation_id":"9316f5aa-15a0-4be4-a344-b98d2f469a94","resolution":{"observed_at":"2026-07-06T11:02:19.556900Z","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":"2605.27312","last_updated":"2026-05-26T17:23:25Z","latest_version":1,"primary_category":"cs.IT","snapshot_observed_at":"2026-08-13T13:17:02.890633Z","submitted_at":"2026-05-26T17:23:25Z","title":"On the Automorphism Groups of Berman Codes and associated Abelian Codes"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":1,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":4,"verified_exact":4,"verified_fuzzy":21},"total_outbound_references":32},"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 14 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2605.27312."}