{"as_of":"2026-08-18T02:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:20852e209723797f9fd36cab8d5728f072e8aa416dbba2deb947418d387ce521","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:28:03.576874Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-18T04:28:48.400311Z","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":"2026-05-18T04:30:52.947178Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"cited_work":{"arxiv_id":"2504.20847","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.20847","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal gates in nonadditive quantum codes","venue":null,"work_id":"b2b4cb50-6a68-41c6-abe8-655b668fbcaf","year":2025},"citing_paper":{"arxiv_id":"2510.20728","last_updated":"2026-04-06T14:46:30Z","snapshot_observed_at":"2026-08-13T17:01:58.945054Z","submitted_at":"2025-10-23T16:45:39Z","title":"Co-Designing Quantum Codes with Transversal Diagonal Gates via Multi-Agent Systems","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-18T04:28:48.400311Z"},"links":{"cited_paper":"/paper/2504.20847","citing_paper":"/paper/2510.20728"},"observation_digest":"sha256:15e0e308d85c4898469c56dd116433bd68947b2a8e7a9da0f6b0c40a9549458c","observation_id":"d63b5742-988b-48ac-b3a9-7420b1d14a4b","resolution":{"observed_at":"2026-05-18T04:30:52.950785Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"cited_work":{"arxiv_id":"2504.20847","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.20847","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal gates in nonadditive quantum codes","venue":null,"work_id":"b2b4cb50-6a68-41c6-abe8-655b668fbcaf","year":2025},"citing_paper":{"arxiv_id":"2604.21800","last_updated":"2026-04-23T15:59:05Z","snapshot_observed_at":"2026-08-15T00:37:02.064234Z","submitted_at":"2026-04-23T15:59:05Z","title":"Variance Geometry of Exact Pauli-Detecting Codes: Continuous Landscapes Beyond Stabilizers","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-09T22:30:38.979857Z"},"links":{"cited_paper":"/paper/2504.20847","citing_paper":"/paper/2604.21800"},"observation_digest":"sha256:0c9de377e58fc02781e9342151689530ac63eee2cf6a954813608b473c0915e2","observation_id":"7adb8a60-bd4c-405a-ad8d-3cc1ac7727da","resolution":{"observed_at":"2026-05-09T22:34:06.865744Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.20847/citation-record","integrity":"/paper/2504.20847/integrity","json":"/paper/2504.20847/citation-record.json","paper":"/paper/2504.20847"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:28:03.927891Z","title":"Boolean functi ons, projection operators, and quantum error correcting codes","venue":null,"work_id":"b4d3f468-f58a-4f43-8b52-c25d9dd239dc","year":2008},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.444306Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:273d8cea5150193ceca58d6a03a90d4057ea3d958a3b82748b116c83a94816d1","observation_id":"70989e39-ca72-46c0-8f91-ddf1d0b82935","resolution":{"observed_at":"2026-08-16T05:28:03.931017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.919360Z","title":"Classiﬁcat ion of transversal gates in qubit stabilizer codes","venue":null,"work_id":"0ef62898-3492-42f9-9600-120d2320f7e3","year":2016},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.449081Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:9dd167821988dd2541c4177309ed6576238cde36ac4036e3423d94282b728709","observation_id":"780f4a81-6138-4869-abfc-1be40f97a022","resolution":{"observed_at":"2026-08-16T05:28:03.922492Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0210097","last_updated":"2002-10-12T13:45:28Z","snapshot_observed_at":"2026-08-04T19:41:45.997765Z","submitted_at":"2002-10-12T13:45:28Z","title":"Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group","version":1},"cited_work":{"arxiv_id":"quant-ph/0210097","doi":null,"metadata_source":"pith","pith_arxiv_id":"quant-ph/0210097","snapshot_observed_at":"2026-08-16T05:28:03.655234Z","title":"Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group","venue":"quant-ph","work_id":"a32d4a68-08d3-4007-a528-33055ea418ed","year":2002},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.452670Z"},"links":{"cited_paper":"/paper/quant-ph/0210097","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:8776604ef92055587623cb483969ad2bdd487ab26d604d25044da112c981411c","observation_id":"91368fbe-1790-422c-9add-e200d033068f","resolution":{"observed_at":"2026-08-16T05:28:03.658891Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.910871Z","title":"Calderbank, E.M","venue":null,"work_id":"7674e2c6-0c8a-4bc5-a381-b176db8e4452","year":1998},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.457611Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:8d55683a4970aa8dccef4b34f8e73e3c15ffc08211e8a9bff3d3689b0026f11b","observation_id":"d87df23b-2f7e-4eca-867d-67768410cbe1","resolution":{"observed_at":"2026-08-16T05:28:03.913761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.902629Z","title":"Quantum variational learning for quantum error-correcting codes","venue":null,"work_id":"fbb43716-0947-4bc8-bb57-4f3808e5322f","year":2022},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.461543Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:cccdb7f5c08d09aa0cf129ef09ced822b517a563a7b9e715c4be7a25dcd27273","observation_id":"e2b7c05a-62ff-43cd-9a4f-a2a869181643","resolution":{"observed_at":"2026-08-16T05:28:03.905590Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.894496Z","title":"Codeword stabilized quantum codes: Algo- rithm and structure","venue":null,"work_id":"eff35fff-e9ad-4797-a42a-5937564e610e","year":2009},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.465323Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:84200b5206436421ec47f5c05e89c0ae7d746d6ff1a0e1342abad5fcf92c3626","observation_id":"696cf7c7-f230-4759-8cae-4b6db89426e4","resolution":{"observed_at":"2026-08-16T05:28:03.897512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.886459Z","title":"C odeword stabilized quantum codes","venue":null,"work_id":"24843462-8d32-4866-bbce-c407075c0c2b","year":2009},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.470113Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:b7b9dc21a1daf30ee01020a61306ddad7b565ec7a2e9b3609c293f2d4401ed1b","observation_id":"d9bf0b3e-0a3a-4715-938d-43ec6f458111","resolution":{"observed_at":"2026-08-16T05:28:03.889451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.17447","last_updated":"2025-01-29T07:11:15Z","snapshot_observed_at":"2026-08-16T12:58:26.799310Z","submitted_at":"2025-01-29T07:11:15Z","title":"Small Binary Stabilizer Subsystem Codes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.17447","snapshot_observed_at":"2026-08-16T05:28:03.473867Z","title":"Small binary stabilizer s ubsystem codes","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.473867Z"},"links":{"cited_paper":"/paper/2501.17447","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:e9957158dbcd9b7126bcb8601a673011920957105fb09c9c1e31826bde1e5245","observation_id":"ca880a6c-cd25-4cae-87f5-df4efb4eb5e3","resolution":{"observed_at":"2026-08-16T05:28:03.473867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:28:03.878425Z","title":null,"venue":null,"work_id":"6ee2447b-c66e-44a7-9d62-fd4d2e468017","year":1954},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.477938Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:bd46afca02315c2b3e44142f8e8c311eb8b25b9e6d806c25a23e522691ef97e7","observation_id":"f9c94c05-c8f8-4b75-a8c1-8fd775709bff","resolution":{"observed_at":"2026-08-16T05:28:03.881393Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.870392Z","title":"Computing irreducible representations o f groups","venue":null,"work_id":"d9d97949-a929-4e73-a2b9-51d1f12a61ef","year":1970},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.480930Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:fcc436c34047f4f016a0fe5c13e2e76a626ee2ad92efdf5688e9478233236a2b","observation_id":"3dc6df28-b227-445f-94f9-c50c64beb998","resolution":{"observed_at":"2026-08-16T05:28:03.873509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.07983","last_updated":"2024-10-10T14:38:15Z","snapshot_observed_at":"2026-08-16T13:10:40.812518Z","submitted_at":"2024-10-10T14:38:15Z","title":"Characterizing Quantum Codes via the Coefficients in Knill-Laflamme Conditions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.07983","snapshot_observed_at":"2026-08-16T05:28:03.484066Z","title":"Cha racterizing quantum codes via the coefﬁcients in knill- laﬂamme conditions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.484066Z"},"links":{"cited_paper":"/paper/2410.07983","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:5470dbb508f5f5027728a9e8299c4eaf3a4ebf9d25908f0b2bb470647c802dcc","observation_id":"931a9290-11a7-441c-949f-5465e185618b","resolution":{"observed_at":"2026-08-16T05:28:03.484066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:28:03.862157Z","title":"Restrictions on transv ersal encoded quantum gate sets","venue":null,"work_id":"b9d30f5a-4eaa-433a-ab6b-88f77e79ce09","year":2009},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.487780Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:8370daa3b66234175172f8e91ed97fea8df030859a5d5ee9a0e1c47ac4be2e8f","observation_id":"95da1d75-0d7e-42b1-89f9-249d890bc82c","resolution":{"observed_at":"2026-08-16T05:28:03.865213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.853747Z","title":"Stabilizer codes and quantum error c orrection","venue":null,"work_id":"bc05880c-24df-43a5-9aaf-a94a4584e111","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.491105Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:c68bcd4b0386d2f3a9f07862a21f3b7a4c31c36904a7659f8f20a1be5ba5681a","observation_id":"70239e5b-31eb-4f52-b775-b8a2dac96744","resolution":{"observed_at":"2026-08-16T05:28:03.857033Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9703016","last_updated":"1997-03-10T20:08:39Z","snapshot_observed_at":"2026-08-07T17:30:14.502799Z","submitted_at":"1997-03-10T20:08:39Z","title":"A Note on Non-Additive Quantum Codes","version":1},"cited_work":{"arxiv_id":"quant-ph/9703016","doi":null,"metadata_source":"pith","pith_arxiv_id":"quant-ph/9703016","snapshot_observed_at":"2026-08-16T05:28:03.629019Z","title":"A Note on Non-Additive Quantum Codes","venue":"quant-ph","work_id":"0c056815-f41e-405e-bce1-f850b2b3e2da","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.494486Z"},"links":{"cited_paper":"/paper/quant-ph/9703016","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:daa0010a21b5a87b959418bc9315e4fa1f098ad48db44282630de171000fd145","observation_id":"d157ac9c-93cf-47ad-8e75-3f3c89c52348","resolution":{"observed_at":"2026-08-16T05:28:03.632261Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.845580Z","title":"Non-additive quant um codes from goethals and preparata codes","venue":null,"work_id":"ab0bb3c6-38b1-4c5c-9b39-ba530a2c95e6","year":2008},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.498430Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:16ed1e0df9d3b7046142c59f572f5c20f4118e8269707485ccdcf6b4abe9ac37","observation_id":"db394066-be62-4f8f-9ce8-ec02e51ea8da","resolution":{"observed_at":"2026-08-16T05:28:03.848818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.837554Z","title":"Theory of quantum er ror-correcting codes","venue":null,"work_id":"548a75b4-a835-4f94-a657-4321e1b2219d","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.501594Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:99da0c773ac3beaf0f9bc87f2dc641e5f0228320c30ce5c5c4aff2bc06072400","observation_id":"8ef91c71-e6b4-4278-bff2-25b8dc267d9d","resolution":{"observed_at":"2026-08-16T05:28:03.840506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.829372Z","title":"Quantum Error Correction with T ransversal non-Clifford Ga tes","venue":null,"work_id":"ecbc565f-099f-4eab-8ff5-4d1aa7cf8b32","year":2024},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.505254Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:c392ee61ccb383a001eba5f2a613feb33f31cfc5ee395fa780709754e273a459","observation_id":"304cdfb4-7adb-4f40-8efd-333783bb4ed0","resolution":{"observed_at":"2026-08-16T05:28:03.832381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.820639Z","title":"Family of quantum code s with exotic transversal gates","venue":null,"work_id":"576580df-9f9f-4302-85d1-60abc3339ac7","year":2023},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.508681Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:64df1587b80fdf2cd53970bca216043f12effed75c80f37d12c2a889e08737ec","observation_id":"3e1729e0-53d3-49f3-9fbb-2917398e4b4c","resolution":{"observed_at":"2026-08-16T05:28:03.823550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.812084Z","title":"Permutation-invaria nt quantum codes with transversal generalized phase gates, 2024","venue":null,"work_id":"7d8aa341-5749-4a4c-8e2e-85453f133d6b","year":2024},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.511810Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:7f523960943559867abb7b1a190b4b49daef4bbbd36007f61f0bb277553dee44","observation_id":"ff8ea8cb-6cd7-43f2-bc5e-bb67c83fb019","resolution":{"observed_at":"2026-08-16T05:28:03.815351Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.804154Z","title":"Trivializations for gradient-b ased optimization on manifolds","venue":null,"work_id":"3ffc0aad-71d7-471e-b463-7018fa922fc9","year":2019},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.514997Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:e5ef4dc676c87a18da7d4d10f645ff8212fb80b6beacb9ad3df59c6660a26411","observation_id":"cfc36763-bbad-4d75-a415-1cb937b34839","resolution":{"observed_at":"2026-08-16T05:28:03.807201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.795191Z","title":null,"venue":null,"work_id":"4a65201c-43bb-467d-86c8-d3947cb0740b","year":1998},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.518359Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:7c092420ba5177cc804ebd6f24e28a963e8ee4921913ba615517498482edfe91","observation_id":"e78f4d8a-3f46-40ea-b588-93abe041b2f5","resolution":{"observed_at":"2026-08-16T05:28:03.799057Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.787273Z","title":"Lidar and K","venue":null,"work_id":"0d75d8c4-7761-447e-9374-a5db1c35b435","year":2003},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.521456Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:2f9342fa6e31683e0e739a2680854af67eaa576f0a0fb7817968d4397683eb0c","observation_id":"9fbfbec0-d41d-4e40-9b74-131693121b78","resolution":{"observed_at":"2026-08-16T05:28:03.790117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.16914","last_updated":"2026-06-02T22:09:15Z","snapshot_observed_at":"2026-08-16T13:22:47.560950Z","submitted_at":"2024-08-29T21:25:56Z","title":"Experimental measurement and a physical interpretation of quantum shadow enumerators","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.16914","snapshot_observed_at":"2026-08-16T05:28:03.524435Z","title":"Experimental measurem ent and a physical interpretation of quantum shadow enumerators","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.524435Z"},"links":{"cited_paper":"/paper/2408.16914","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:a4299b23b7976067ef7b8ca9de29d1c55c19424a31cca2b2f665dc0b7f84c1e5","observation_id":"c48a70ca-21a8-4542-95ca-86dff0d7629f","resolution":{"observed_at":"2026-08-16T05:28:03.524435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:28:03.778909Z","title":"A non-commuting stabilizer formalism","venue":null,"work_id":"ed212c09-cd20-45d1-9114-b1027c538c10","year":2015},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.527950Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:3506e045754f9c431285d70e13106fec354060ccaa821734a2d3226667ba116d","observation_id":"066efdf4-063d-48e5-b508-fadc0de9f01d","resolution":{"observed_at":"2026-08-16T05:28:03.782021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.770668Z","title":"Permutation-invariant quantum codes","venue":null,"work_id":"6ca53e60-f520-4ff4-8b06-37e1481cb1c2","year":2014},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.532094Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:097ab0331dd7b43481b22db028460a35dfa0c7b4420b801fcdb2b8acc3aec69b","observation_id":"d459ae49-e438-4e79-a601-561f0bafa1f2","resolution":{"observed_at":"2026-08-16T05:28:03.773663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.762302Z","title":"Permutation-invariant quantum codin g for quantum deletion channels","venue":null,"work_id":"443bc7ac-a9a5-4f68-95d5-b79d3cb3ddc0","year":2021},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.535032Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:8322b591c8c56a57d71e6b728f2a82380864cea0304b69f1d449320eaa6dcd5f","observation_id":"652d1cbe-888f-481b-8f24-1bece7b48eb7","resolution":{"observed_at":"2026-08-16T05:28:03.765396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.753910Z","title":"Permutational ly invariant codes for quantum error correction","venue":null,"work_id":"277b78cb-b8d5-4f68-83e8-9c74952afea3","year":2004},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.538064Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:0f6575a253701be042f0666af7707823541b6aa316ca197ef904a620c2652b4f","observation_id":"d979bf81-8900-423a-9d46-37dcd412b181","resolution":{"observed_at":"2026-08-16T05:28:03.756878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.745573Z","title":null,"venue":null,"work_id":"f4173a38-00c3-4217-ac81-625076d53aaa","year":1998},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.541144Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:59be4c5e250a4d6c0edb081918b73c618c792e9c14e08e85c596a1464fdb7fe9","observation_id":"9fcc3835-1e8a-493a-adfe-c1eb8aa74c8d","resolution":{"observed_at":"2026-08-16T05:28:03.748535Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.737105Z","title":null,"venue":null,"work_id":"57c44cef-1f8a-41ec-82f4-dc1d52f10c1f","year":1999},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.544258Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:83f52f5caa7b86b82e6b015b81005901cd7b3f323805bbfdeba443f9ce51a1eb","observation_id":"28f299b0-a208-4350-859d-bf8f6cb1afa0","resolution":{"observed_at":"2026-08-16T05:28:03.740024Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.728143Z","title":null,"venue":null,"work_id":"cb2d1ce1-128b-4b42-9808-3f57897ffeab","year":1999},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.547932Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:900e2a78ec4df1eef7309c80ca2728a81c8e22a8bd5b5c82e1ffb9c801bf0417","observation_id":"0a89571a-3223-41b8-9712-96c8dc761039","resolution":{"observed_at":"2026-08-16T05:28:03.731161Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.719525Z","title":"Rains, R","venue":null,"work_id":"4216b5a3-57c8-48d0-bc12-1c58fe24d3c6","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.551191Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:d174cecce61912046e1f42cdbf9249a0959362f6635b2123fd8e44e8256057e3","observation_id":"b9fcfc7a-80bc-4017-bd94-739bbb666a50","resolution":{"observed_at":"2026-08-16T05:28:03.722634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9710031","last_updated":"1997-10-09T21:46:39Z","snapshot_observed_at":"2026-07-07T07:27:14.662433Z","submitted_at":"1997-10-09T21:46:39Z","title":"On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes","version":1},"cited_work":{"arxiv_id":"quant-ph/9710031","doi":null,"metadata_source":"pith","pith_arxiv_id":"quant-ph/9710031","snapshot_observed_at":"2026-08-16T05:28:03.607223Z","title":"On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes","venue":"quant-ph","work_id":"1be0bbf2-0532-48cd-9ba1-7d2c99a77f03","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.554431Z"},"links":{"cited_paper":"/paper/quant-ph/9710031","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:5e41e25fd2c863c59a1bb3448969003bb2c44b534f5aac87ec732c052974b8a1","observation_id":"6f44d041-7a79-4bf0-bef3-14855e58b77a","resolution":{"observed_at":"2026-08-16T05:28:03.612335Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.710455Z","title":"Quantum analog of the ma cwilliams identities for classical coding theory","venue":null,"work_id":"0a55195e-fafc-49b0-ac3e-99618f00a5e5","year":1997},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.558144Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:9bcb66796d3d9eab0e3373b9052cb8c1f6ea0fdb16cc35d8e30a0c1ec3ef83c8","observation_id":"cc46616c-82df-436c-83ef-3d8f7ed7e19d","resolution":{"observed_at":"2026-08-16T05:28:03.713842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.701322Z","title":null,"venue":null,"work_id":"35501b53-c20f-4964-bb12-a8e5ae9b2997","year":1996},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.561075Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:9ad45dc198ff65d74b0b6a03a49a659bc41daca7970f99c242d1a648889317e7","observation_id":"ffa7a5e3-92d1-49b5-95ae-f242654d186e","resolution":{"observed_at":"2026-08-16T05:28:03.704402Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.692793Z","title":null,"venue":null,"work_id":"66726373-62e6-415f-a5e1-bcd79155b89b","year":1996},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.564087Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:c8741ecdbd4afa0cf532e6b05d99f89fdaf2ec5127ff7dea883fb594007008b6","observation_id":"95ec3660-9631-4c35-9f71-035d5aac79a1","resolution":{"observed_at":"2026-08-16T05:28:03.695691Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.683584Z","title":"The xp stabiliser formalism: a generalisation of the pauli stabiliser formalism with arbitrary phases","venue":null,"work_id":"d04ebff4-68f7-49ba-a457-3e86552cfd12","year":2022},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.567040Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:c2a5cf454e079fca8046eed61ab882ede909f8f3ba9b2d04ba260cf0311f902d","observation_id":"13d5140e-28f0-41af-9dc7-38e21af92cdd","resolution":{"observed_at":"2026-08-16T05:28:03.686710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-16T05:28:03.674335Z","title":"Nonadditive quant um error-correcting code","venue":null,"work_id":"91a43763-ac62-4989-b53f-56f0ba9f4d62","year":2008},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.570170Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:9b2ab874188575df88ab15c993ab8088c511f61c9f0aad40acfa8151a6d8ea46","observation_id":"afc798d2-e5d3-425f-9013-5faef715281c","resolution":{"observed_at":"2026-08-16T05:28:03.677724Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0709.1780","last_updated":"2007-09-12T09:33:16Z","snapshot_observed_at":"2026-08-15T10:32:29.728537Z","submitted_at":"2007-09-12T09:33:16Z","title":"Graphical Quantum Error-Correcting Codes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0709.1780","snapshot_observed_at":"2026-08-16T05:28:03.573642Z","title":"Graphical quantum error-correcting codes","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.573642Z"},"links":{"cited_paper":"/paper/0709.1780","citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:1fadec6a75a9017db816643b8195cbe6c16c5cc559d327eeeeda0c163b3c5dc8","observation_id":"e4bfb7ef-9afd-4552-a7d0-025d29afe1f4","resolution":{"observed_at":"2026-08-16T05:28:03.573642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:28:03.665279Z","title":"Transversal ity versus universality for additive quantum codes","venue":null,"work_id":"dcc6945f-3de6-4223-bb9c-da2f0813158e","year":2011},"citing_paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T05:28:03.576874Z"},"links":{"citing_paper":"/paper/2504.20847"},"observation_digest":"sha256:ee79423e54f923930505541487730043c9af67ebe0294e6c0afbd2980edb06c8","observation_id":"d9498d3b-4ef2-42fe-b88a-ee2f91125731","resolution":{"observed_at":"2026-08-16T05:28:03.668464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.20847","last_updated":"2025-04-29T15:18:33Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-17T20:43:35.059352Z","submitted_at":"2025-04-29T15:18:33Z","title":"Transversal Gates in Nonadditive Quantum Codes"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":3,"verified_fuzzy":25},"total_outbound_references":39},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 2 inbound Pith citation observations for arXiv:2504.20847."}