{"as_of":"2026-08-09T01:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:16c091863646a97c3fd1fc822728c267aea6a8b1949b73d7674e7cdf7472f54a","coverage":[{"denominator":51,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":51,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:54:37.319163Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T08:00:03.979334Z","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":"2026-05-21T19:15:31.096658Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":"2507.15056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal non-clifford gates on qldpc codes breaking the √ Ndistance barrier and quantum-inspired geometry with systolic freedom","venue":null,"work_id":"4cd61027-dbab-4996-8b97-d7613c4cfd2d","year":2025},"citing_paper":{"arxiv_id":"2508.10714","last_updated":"2025-11-06T19:03:24Z","snapshot_observed_at":"2026-07-06T22:13:00.029560Z","submitted_at":"2025-08-14T14:56:50Z","title":"Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes","version":2},"reference_index":101,"source":"pdf_text","source_observed_at":"2026-05-18T22:51:30.133403Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2508.10714"},"observation_digest":"sha256:b6065c14cc8c479f34c313edd7b8c240f0b6739eabb722ba32f87654483d90ba","observation_id":"7dbaf634-9ca4-4329-8f82-4f30a3918afa","resolution":{"observed_at":"2026-05-18T22:51:52.931375Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":"2507.15056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal non-clifford gates on qldpc codes breaking the √ Ndistance barrier and quantum-inspired geometry with systolic freedom","venue":null,"work_id":"4cd61027-dbab-4996-8b97-d7613c4cfd2d","year":2025},"citing_paper":{"arxiv_id":"2511.02900","last_updated":"2026-05-19T22:25:24Z","snapshot_observed_at":"2026-08-06T19:18:39.022814Z","submitted_at":"2025-11-04T19:00:00Z","title":"Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-21T19:14:49.965519Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2511.02900"},"observation_digest":"sha256:e1b4de92b3181ec8d91d5f1bb2e6e8a49f3c26fcdcb2b89f64c968e9e1d90c3a","observation_id":"a1c58749-90d6-4cd2-a79e-0827669f1303","resolution":{"observed_at":"2026-05-21T19:15:31.099017Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":"2507.15056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal non-clifford gates on qldpc codes breaking the √ Ndistance barrier and quantum-inspired geometry with systolic freedom","venue":null,"work_id":"4cd61027-dbab-4996-8b97-d7613c4cfd2d","year":2025},"citing_paper":{"arxiv_id":"2511.15783","last_updated":"2026-05-11T09:13:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-11-19T19:00:00Z","title":"Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-17T20:18:27.901205Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2511.15783"},"observation_digest":"sha256:c624f8db06fde52d7bc3f45b34a76db60eb8e1192b0eef8c74c7f3f4b5d55af3","observation_id":"df9a1729-9b78-46a6-abcb-0f525b079543","resolution":{"observed_at":"2026-05-17T20:20:11.704107Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-08-03T08:00:03.979334Z","title":"Zhu, Transversal non-clifford gates on qldpc codes breaking the √ Ndistance barrier and quantum- inspired geometry withZ 2 systolic freedom (2025), arXiv:2507.15056 [quant-ph]","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2601.18879","last_updated":"2026-05-24T01:40:16Z","snapshot_observed_at":"2026-08-03T11:12:49.778747Z","submitted_at":"2026-01-26T19:00:03Z","title":"Multivariate Multicycle Codes for Complete Single-Shot Decoding","version":2},"reference_index":124,"source":"pdf_text","source_observed_at":"2026-08-03T08:00:03.979334Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2601.18879"},"observation_digest":"sha256:e34e5aabe15fb33c3b589c9c222596645229ba76c980bbb20e5dc45d3715712b","observation_id":"c77d531f-889f-4853-82dd-e3c457a5a776","resolution":{"observed_at":"2026-08-03T08:00:03.979334Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":"2507.15056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transversal non-clifford gates on qldpc codes breaking the √ Ndistance barrier and quantum-inspired geometry with systolic freedom","venue":null,"work_id":"4cd61027-dbab-4996-8b97-d7613c4cfd2d","year":2025},"citing_paper":{"arxiv_id":"2603.04156","last_updated":"2026-04-04T00:57:58Z","snapshot_observed_at":"2026-08-05T20:11:28.155034Z","submitted_at":"2026-03-04T15:12:34Z","title":"Achieving Optimal-Distance Atom-Loss Correction via Pauli Envelope","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-15T17:03:21.262684Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2603.04156"},"observation_digest":"sha256:ec3398edb2cf988ff1c7ee1789edeae1ce5305605b1981d7b3f55720529242b8","observation_id":"5baca1e6-7945-4576-bf74-2dcfbd534be2","resolution":{"observed_at":"2026-05-15T17:06:19.174221Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.15056","snapshot_observed_at":"2026-07-13T14:10:32.422124Z","title":"Zhu,Transversal non-clifford gates on qldpc codes breaking the √ N distance barrier and quantum- inspired geometry with Z2 systolic freedom, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.01874","last_updated":"2026-07-02T17:00:07Z","snapshot_observed_at":"2026-08-07T05:23:44.285370Z","submitted_at":"2026-04-02T10:30:00Z","title":"Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-13T14:10:32.422124Z"},"links":{"cited_paper":"/paper/2507.15056","citing_paper":"/paper/2604.01874"},"observation_digest":"sha256:80161916ba9cc98c2e02319edfb5c80db8701696c9ab68dce971a60d1976b081","observation_id":"a859f022-84c6-4964-b79f-2cc15f5702e1","resolution":{"observed_at":"2026-07-13T14:10:32.422124Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.15056/citation-record","integrity":"/paper/2507.15056/integrity","json":"/paper/2507.15056/citation-record.json","paper":"/paper/2507.15056"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.491647Z","title":"[2, 10, 37, 38] applicable to more general stabilizer codes including non-Pauli stabilizer models","venue":null,"work_id":"6b71fe4a-0a0c-4c2c-bae9-5b7af6467f6a","year":1949},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.332527Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:d7aa32f9c9366cffda59a2e53153e1ea018267e02547c6065fda2b5c959d0ca9","observation_id":"033cfb44-d968-4370-8ca2-157b3ae6aa2b","resolution":{"observed_at":"2026-08-06T15:54:38.494814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:34.013792Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.013792Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:e644804163b9eded000e3bf64681e6031b430f24e8a64efaccdf6e7dd1ec195f","observation_id":"03d6a8e3-8f95-45a9-8f00-215eedda1b59","resolution":{"observed_at":"2026-08-06T15:54:34.013792Z","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":"2026-08-06T15:54:38.468750Z","title":"4.sys q( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 ), sysq( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 )","venue":null,"work_id":"5d65aac9-50e9-43f8-9669-a7b2b441bcaa","year":null},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.802871Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:bd2888c79aa78e1aa40231ce5a19a8815b9beb48902a714cadba850c95378e81","observation_id":"7ea5d9d6-b4b8-4bc2-8f99-1fd1fec7954d","resolution":{"observed_at":"2026-08-06T15:54:38.471482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.476445Z","title":"2.vol( fM) = Θ(N)","venue":null,"work_id":"995af48a-2871-4f8f-b09c-ed61095f2945","year":null},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.692152Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:27cfbe92f30d575b111435725e32518ff8f9b5054eef53d876afae18aa15fd89","observation_id":"deb2b39f-26ec-414d-9699-8012d68479cf","resolution":{"observed_at":"2026-08-06T15:54:38.479189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.461059Z","title":"bad dimensions","venue":null,"work_id":"f95ffba9-ec40-475f-bd2b-26c5210843d0","year":null},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.910327Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:db905f79fc47711fd3cc2465e1a226919b90167ac41950334c902c716ba1eadf","observation_id":"8e38e0a6-d440-4657-ac6c-bcbb55b22440","resolution":{"observed_at":"2026-08-06T15:54:38.463681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.09271","last_updated":"2021-07-28T10:58:06Z","snapshot_observed_at":"2026-08-02T14:41:28.656201Z","submitted_at":"2020-12-16T21:19:38Z","title":"Balanced Product Quantum Codes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.09271","snapshot_observed_at":"2026-08-06T15:54:34.296179Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.296179Z"},"links":{"cited_paper":"/paper/2012.09271","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:fabda0925f3a4e017074278026f863b1cf0356e548d6109ad41d7b7fbb84db3b","observation_id":"25f665f5-73e2-4a01-bc72-cf6f9d78d02d","resolution":{"observed_at":"2026-08-06T15:54:34.296179Z","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":"2026-08-06T15:54:38.483961Z","title":"Similarly,a ∗7 is the Poincar´ e dual cocycle of the cycle a4","venue":null,"work_id":"dc5bce03-555c-4466-b546-a7655ec3375d","year":null},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.540449Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:234de619aaf327a102c0c20bd97095420decc70deaa10a33a1103f07c9eee224","observation_id":"67912735-9d6e-46de-b71d-c286b4afb226","resolution":{"observed_at":"2026-08-06T15:54:38.486754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.453364Z","title":"Hastings, J","venue":null,"work_id":"dd86b78d-4260-41d4-80ca-32535cfa17eb","year":2021},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.956722Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:724808be3171bf7160f6d076ff157d3a7c12808617de806cc4329414e90867f2","observation_id":"644d9e0b-1b4b-42fc-be42-8fa5485125c3","resolution":{"observed_at":"2026-08-06T15:54:38.456070Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.444542Z","title":null,"venue":null,"work_id":"f49253b4-d574-4bae-8404-f0f2f55355ea","year":2002},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.055168Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:dadcedc84d94af4c11b616c3e2ea31d1f462fbda9df02ebd9de931b2728358de","observation_id":"e1c72e3e-b9ca-4f55-b1d0-5fcce0400bbc","resolution":{"observed_at":"2026-08-06T15:54:38.447449Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.435590Z","title":"Gromov, Systoles and intersystolic inequalities, Actes de la Table Ronde de G´ eom´ etrie Diff´ erentielle (Luminy, 1992), 291—362, S´ emin","venue":null,"work_id":"ca373ac2-a00a-4b2b-a466-1a2cdb2ebb57","year":1996},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.169782Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:4353fcedb3ec4edd95054d4b068d3d148c91324cf1b2ee5347a51bddd862f31c","observation_id":"8603aa27-7c9a-4ac5-a505-fc46a8ccfb9d","resolution":{"observed_at":"2026-08-06T15:54:38.438934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.426905Z","title":"Panteleev and G","venue":null,"work_id":"c47a5d8d-8770-40df-91bf-e057607249a1","year":2022},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.220534Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:bb40e442ac001654506bb56f1d19968a8d384fa204d259dbbcbbdc553c426a06","observation_id":"4056bca9-48ba-4f9b-8149-ad9cdb088104","resolution":{"observed_at":"2026-08-06T15:54:38.429826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:34.749023Z","title":"Cross, Z","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.749023Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:8fb4ff90a3c81e82077e74d0eb38e171b2d98f41258b5dd8a9f19d5b3d8f2a76","observation_id":"bc8bf259-9373-4a1d-b1aa-0a2b7f2d00a3","resolution":{"observed_at":"2026-08-06T15:54:34.749023Z","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":"2026-08-06T15:54:38.418195Z","title":"Panteleev and G","venue":null,"work_id":"8b6bb36b-7243-405b-89b3-6d9634059452","year":2022},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.344912Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:4e0858a83f72d21a13b6f8ba64d0973975697acc038cdccb01f2b6665ae30e41","observation_id":"dcb20a9d-dd62-492d-b443-a8143a41d17b","resolution":{"observed_at":"2026-08-06T15:54:38.421141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.409996Z","title":"Cohen, I","venue":null,"work_id":"99548115-733f-4454-954a-31bc52947678","year":2022},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.444931Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:c8c9f2e72f7bdc18e7a0fc5e39e0997c1d0b3e34bfbac04d8c34371e01fc1059","observation_id":"6b4e7567-ddba-436a-bdff-c2c961c3c4c9","resolution":{"observed_at":"2026-08-06T15:54:38.412926Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.401521Z","title":"Huang, T","venue":null,"work_id":"419a0c12-bc8d-4f54-8cf4-9269d9d9a316","year":2023},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.502795Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:63de7510f571783f3c4cf80851fb9fc8ae7aebd31cc25dc78d440fb30415e7a0","observation_id":"4d446ca3-47b0-4736-98cb-f24f42bbf439","resolution":{"observed_at":"2026-08-06T15:54:38.404632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:34.600317Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.600317Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:07f5724e58b7d498f2064f3da2cb048c2d0f9ead862df20cebb747258dc8b4e0","observation_id":"905a8790-9968-4236-a337-19d5027d519c","resolution":{"observed_at":"2026-08-06T15:54:34.600317Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18490","last_updated":"2024-07-26T03:49:59Z","snapshot_observed_at":"2026-08-08T07:57:33.971503Z","submitted_at":"2024-07-26T03:49:59Z","title":"Fast and Parallelizable Logical Computation with Homological Product Codes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.18490","snapshot_observed_at":"2026-08-06T15:54:34.664293Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.664293Z"},"links":{"cited_paper":"/paper/2407.18490","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:3b9e7739f4f4f6fecab5fdda1189a0f51503642a81acb3103032290f590230e1","observation_id":"1a0a771e-6c9e-4fa5-83d6-35fb4421057d","resolution":{"observed_at":"2026-08-06T15:54:34.664293Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:35.257076Z","title":"Kubica, B","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.257076Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:ba56ed55ad96f7f2023b40cc7d510c847e4bae89fc578f3665275f17fa0e65c2","observation_id":"480d4a13-7ca2-444d-a5a0-aa8eccbe4a85","resolution":{"observed_at":"2026-08-06T15:54:35.257076Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.02213","last_updated":"2026-07-07T06:51:25Z","snapshot_observed_at":"2026-07-10T23:17:13.211419Z","submitted_at":"2024-10-03T05:04:12Z","title":"Low-overhead fault-tolerant quantum computation by gauging logical operators","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.02213","snapshot_observed_at":"2026-08-06T15:54:34.825771Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.825771Z"},"links":{"cited_paper":"/paper/2410.02213","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:23944c11262dbe12089f410ee63c212e34c248b88ffcee8763df2e5d4cf9ef80","observation_id":"91e4c2ad-c69c-4032-be20-dabddff874dc","resolution":{"observed_at":"2026-08-06T15:54:34.825771Z","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":"2026-08-06T15:54:38.501799Z","title":"For instance, in a 3D torus (with zero curvature), the distance is determined by the minimal length of the logical string operator, which scales asO(N 1 3 )","venue":null,"work_id":"3f9fd385-4be9-4e8d-b25b-edc0f56ac4e2","year":null},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:33.114826Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:7718139dcd4dde3cc7b2ecc8d5da1d3914a61c633b2f21741b75a046b0dff9fa","observation_id":"1d89d1b9-1a54-402c-8237-1b1b7aa8aa2c","resolution":{"observed_at":"2026-08-06T15:54:38.505082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:34.928906Z","title":"Swaroop, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.928906Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:23d9b96a055cb248ae147d5c54d5eb982c043cda45713fb08818d1e076c01526","observation_id":"b6f65314-b892-462f-aa8f-c37e596bd187","resolution":{"observed_at":"2026-08-06T15:54:34.928906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.14662","last_updated":"2024-10-18T17:52:59Z","snapshot_observed_at":"2026-08-03T07:56:52.717785Z","submitted_at":"2024-10-18T17:52:59Z","title":"Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.14662","snapshot_observed_at":"2026-08-06T15:54:34.983401Z","title":"Golowich and T.-C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:34.983401Z"},"links":{"cited_paper":"/paper/2410.14662","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:c4e1d143aeaece9d86cc730733a4fe90bf55e4e02f943a866db285276a34b5cd","observation_id":"30b4106d-82f1-41c5-8f99-2613455c9ff3","resolution":{"observed_at":"2026-08-06T15:54:34.983401Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.14631","last_updated":"2024-10-18T17:31:19Z","snapshot_observed_at":"2026-07-06T19:36:05.879892Z","submitted_at":"2024-10-18T17:31:19Z","title":"Transversal non-Clifford gates for quantum LDPC codes on sheaves","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.14631","snapshot_observed_at":"2026-08-06T15:54:35.090547Z","title":"Lin, Transversal non-clifford gates for quantum ldpc codes on sheaves, arXiv preprint arXiv:2410.14631 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.090547Z"},"links":{"cited_paper":"/paper/2410.14631","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:e5f289ba98d55a6e083cd4150ba6845a48734672426127ed73ba5e649cadeb68","observation_id":"6f1df18d-5fd1-4696-95a2-c7e69afa62b6","resolution":{"observed_at":"2026-08-06T15:54:35.090547Z","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":"2026-08-06T15:54:38.393144Z","title":"Bombin, Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes, New Journal of Physics17, 083002 (2015)","venue":null,"work_id":"a3eeb87c-28e5-4013-806e-1097cfdb9c6b","year":2015},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.177629Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:a996e2e3bd69035c56653d3af8f4047f39f4d0b89fdc2a0995d0006b898219bf","observation_id":"e27a6d68-d0b6-4acd-9b04-cadd84d70b79","resolution":{"observed_at":"2026-08-06T15:54:38.396122Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:35.372776Z","title":"Vasmer and D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.372776Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:dd2adab2acc247142e61342f69e5856f88ba5875520b1093e1608048e85f23d7","observation_id":"2d06e8e1-cc08-49fd-9b29-fc667d127148","resolution":{"observed_at":"2026-08-06T15:54:35.372776Z","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":"2026-08-06T15:54:38.375710Z","title":"Bravyi and R","venue":null,"work_id":"28199095-25ed-47e8-a3b4-b574327c339e","year":2013},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.452114Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:6b35d16e6a2693832a981612f6cc8cee83ff08abdd6853a744f5ec69da5297d6","observation_id":"6e890265-1b0c-40cc-a56a-d6905da81195","resolution":{"observed_at":"2026-08-06T15:54:38.378408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.02249","last_updated":"2021-05-24T23:47:23Z","snapshot_observed_at":"2026-08-06T07:22:29.835405Z","submitted_at":"2020-12-03T20:36:50Z","title":"Building manifolds from quantum codes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.02249","snapshot_observed_at":"2026-08-06T15:54:35.544276Z","title":"Freedman and M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.544276Z"},"links":{"cited_paper":"/paper/2012.02249","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:3eaa293b1ca864be67b7dd6dcdf665ff25b7c77d1164d55ddf3605fb8259c2df","observation_id":"a2043088-5cef-4f9c-a5ee-5e55c507c56a","resolution":{"observed_at":"2026-08-06T15:54:35.544276Z","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":"2026-08-06T15:54:38.367519Z","title":"Barkeshli, Y.-A","venue":null,"work_id":"ccc222fb-f23e-44a6-94d6-25a17c6687f9","year":2023},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.600769Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:1152e2ee6eecfaebe80bb4509062aab0b9c6713ff2a0dbd6f19db4b54c1be22d","observation_id":"0a660acc-639f-4045-bdd2-ed8ebcfaa3c2","resolution":{"observed_at":"2026-08-06T15:54:38.370341Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.358905Z","title":"Barkeshli, Y.-A","venue":null,"work_id":"0a8e25a0-15e7-4255-a305-c4d42ba74fbb","year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.705330Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:0faf1d125ad3c3c15b30610722f4a8f19f61f7b4f2ff1649c770c1ee16557535","observation_id":"68aace2e-e2ef-46c2-b336-0692768d7c7c","resolution":{"observed_at":"2026-08-06T15:54:38.361764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.350516Z","title":"Yoshida, Topological color code and symmetry- 18 protected topological phases, Phys","venue":null,"work_id":"34c5b081-432a-4866-9752-52afa8ec0cc6","year":2015},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.774641Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:3ee2a6399f571158fa7df8b124d0465ace033af533b25ec2efea7e2c6e8bb9a4","observation_id":"e32f8c7e-87a2-4556-8751-149f8d78f1ae","resolution":{"observed_at":"2026-08-06T15:54:38.353508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:35.853000Z","title":"Yoshida, Topological phases with generalized global symmetries, Phys","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.853000Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:91d6f2a538c5a8b80dd34d576097ab8c6c448ce0239d588eaa028a65e04c6350","observation_id":"0e6d0141-393b-4e08-b138-d8a568929cf6","resolution":{"observed_at":"2026-08-06T15:54:35.853000Z","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":"2026-08-06T15:54:38.334033Z","title":"Yoshida, Gapped boundaries, group cohomology and fault-tolerant logical gates, Annals of Physics377, 387 (2017)","venue":null,"work_id":"76b3ff8e-c9c1-4a7e-8fe7-0f37b59980a4","year":2017},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.941294Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:2558c6636fd7baacf0a7bda3520583f8c5645cb5c7c86ad9ee6195913dc9564e","observation_id":"28b51524-b350-48d1-8c19-d52b679bbed8","resolution":{"observed_at":"2026-08-06T15:54:38.337427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.325066Z","title":null,"venue":null,"work_id":"6c191a60-9711-43c6-9b1f-35f8f0c86b81","year":2020},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.977088Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:b5d722af04a61a6ef19125a54a00e57b8458890d23782425b8281a9482955a16","observation_id":"de42d2a8-9b6f-456b-98ea-34e4573463da","resolution":{"observed_at":"2026-08-06T15:54:38.327839Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.316729Z","title":null,"venue":null,"work_id":"c4568018-32da-4557-934e-0a05f9d65971","year":2022},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:35.993108Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:aaf5b5a50c05203be845b45fbde3315b97f815e6a9c41bb4b4ced1a83ab03ce2","observation_id":"0a37fe9b-4151-423e-ab68-2fac9b49c88f","resolution":{"observed_at":"2026-08-06T15:54:38.319806Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:36.144494Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.144494Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:7550d1e139442a424da35116ced9740ecc3c06e6b8b99dd8ae2680938e1f9298","observation_id":"3e9a7fd1-c4a2-4ce2-938a-c82f5f938d4b","resolution":{"observed_at":"2026-08-06T15:54:36.144494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1803.05643","last_updated":"2018-03-15T08:56:33Z","snapshot_observed_at":"2026-08-01T12:47:33.721100Z","submitted_at":"2018-03-15T08:56:33Z","title":"Graph codes and local systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1803.05643","snapshot_observed_at":"2026-08-06T15:54:36.194019Z","title":"Meshulam, Graph codes and local systems, arXiv 10.48550/arxiv.1803.05643 (2018), 1803.05643","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.194019Z"},"links":{"cited_paper":"/paper/1803.05643","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:34adf34f2bd8afa147ad4d8b56369b1b79e12fbd4f66fe35801b06a222f2a1ee","observation_id":"f7ef84e7-1d7f-49e2-a35d-e6df6f1abd97","resolution":{"observed_at":"2026-08-06T15:54:36.194019Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.16250","last_updated":"2025-12-27T21:52:26Z","snapshot_observed_at":"2026-08-02T07:46:23.650899Z","submitted_at":"2024-10-21T17:53:17Z","title":"Cups and Gates I: Cohomology invariants and logical quantum operations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.16250","snapshot_observed_at":"2026-08-06T15:54:36.354896Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.354896Z"},"links":{"cited_paper":"/paper/2410.16250","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:a9835d3b3ed68fe2f1a5b3508e7079cfb9d6f4ebb2b9a0f351c8fa5789cf9e07","observation_id":"bf9b4440-fd88-428a-82b0-c2acd720485c","resolution":{"observed_at":"2026-08-06T15:54:36.354896Z","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":"2026-08-06T15:54:38.308585Z","title":"McCullough and H","venue":null,"work_id":"a498fe2a-0382-4e08-9605-63f4bb600d8d","year":2019},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.492775Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:e73ff41cbf0cc16d533cd5f799466dacf8e568cbd1431edac74b0d9a2aabc0e4","observation_id":"d0c2db4a-52e2-4db4-a4f7-b44d180ae91d","resolution":{"observed_at":"2026-08-06T15:54:38.311426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.300355Z","title":"Dotterrer, L","venue":null,"work_id":"d0adec76-ec35-4116-ab34-6ec9aa190882","year":2018},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.548262Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:22be3bde094cb10192cb4e2fd446d1b8565f77c75c6f441a6cc5440048bc2e2d","observation_id":"2a3db7cc-9f8e-4383-ae62-895a49faa7b9","resolution":{"observed_at":"2026-08-06T15:54:38.303292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1010.1400","last_updated":"2011-08-03T07:35:56Z","snapshot_observed_at":"2026-07-06T02:16:36.786552Z","submitted_at":"2010-10-07T11:21:03Z","title":"Collapsibility and vanishing of top homology in random simplicial complexes","version":2},"cited_work":{"arxiv_id":"1010.1400","doi":"10.48550/arxiv.1010.1400","metadata_source":"pith","pith_arxiv_id":"1010.1400","snapshot_observed_at":"2026-08-06T18:16:30.548575Z","title":"Collapsibility and vanishing of top homology in random simplicial complexes","venue":"math.CO","work_id":"ff099b00-95b6-442a-a2ce-92a227bbbbb8","year":2010},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.702007Z"},"links":{"cited_paper":"/paper/1010.1400","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:8b9be5da74844c2bdc650071bcdc5c83f39ad72928a5ea26fe22e806d67dd134","observation_id":"18119b30-61d1-4bba-99d3-603f66bd1dab","resolution":{"observed_at":"2026-08-06T15:54:37.589091Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.292358Z","title":"Linial* and R","venue":null,"work_id":"c379fbf5-34d6-4a48-8277-8c5aaa375425","year":2006},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.799650Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:9dd755d496e5804f3e47cdc3bfabbeef9bfc42c81dfe2d76e1263e36db143bb7","observation_id":"cb61c6f9-a950-4353-a332-4e8e46fd4d7c","resolution":{"observed_at":"2026-08-06T15:54:38.295106Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0609773","last_updated":"2006-09-27T21:05:16Z","snapshot_observed_at":"2026-07-07T06:00:44.851732Z","submitted_at":"2006-09-27T21:05:16Z","title":"Homological connectivity of random k-dimensional complexes","version":1},"cited_work":{"arxiv_id":"math/0609773","doi":"10.48550/arxiv.math/0609773","metadata_source":"pith","pith_arxiv_id":"math/0609773","snapshot_observed_at":"2026-08-06T18:16:30.548575Z","title":"Homological connectivity of random k-dimensional complexes","venue":"math.CO","work_id":"689ea7c5-54da-4e48-bbe4-9588f694ec6e","year":2006},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.835354Z"},"links":{"cited_paper":"/paper/math/0609773","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:04ae68691e4b990354385946a27001ebd08bbaa1054f1fbbfaeb128a8f619e83","observation_id":"c95ced72-033b-4bf2-8437-247a6485dc20","resolution":{"observed_at":"2026-08-06T15:54:37.465438Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15848","last_updated":"2025-06-27T13:01:13Z","snapshot_observed_at":"2026-07-06T19:56:08.504922Z","submitted_at":"2024-11-24T14:01:37Z","title":"Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15848","snapshot_observed_at":"2026-08-06T15:54:36.901487Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:36.901487Z"},"links":{"cited_paper":"/paper/2411.15848","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:06fa91b1e910abb60b8ef40dd8cbf4a147eafe060bf5a5f5eb7c9f643735e48f","observation_id":"dbe79c05-2800-433a-a048-672ab475e27f","resolution":{"observed_at":"2026-08-06T15:54:36.901487Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:37.000343Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.000343Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:83dbc14d878f81b85d0a6380975e6b3550fb1e5c174e1b7ee0f2fa8b478d5a35","observation_id":"056d673d-4bcf-42da-a9b0-eb27b7ef93cb","resolution":{"observed_at":"2026-08-06T15:54:37.000343Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:37.002852Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.002852Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:d3bf4f4aaff25be94e00697a40a37b9bfb192918ad6ddc26eb51f358641a8e04","observation_id":"deffe971-358b-400a-9134-58e7c2537cb1","resolution":{"observed_at":"2026-08-06T15:54:37.002852Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.06755","last_updated":"2023-06-20T15:31:04Z","snapshot_observed_at":"2026-08-07T05:08:13.956806Z","submitted_at":"2023-03-12T21:04:38Z","title":"Local Quantum Codes from Subdivided Manifolds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.06755","snapshot_observed_at":"2026-08-06T15:54:37.005387Z","title":"Portnoy, Local quantum codes from subdivided man- ifolds, arXiv preprint arXiv:2303.06755 (2023)","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.005387Z"},"links":{"cited_paper":"/paper/2303.06755","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:823ddf80645942afffabc45ef371873cd809ea7385396fe55af884702115736b","observation_id":"d2dd84b8-501e-4e74-874e-7bbd7d33f1f2","resolution":{"observed_at":"2026-08-06T15:54:37.005387Z","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":"2026-08-06T15:54:38.278371Z","title":"Bacon, Operator quantum error-correcting subsys- tems for self-correcting quantum memories, Physical Re- view A73, 012340 (2006)","venue":null,"work_id":"41e9d0e3-d44e-49ac-b4dc-35bfaf6804e5","year":2006},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.060958Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:ba4119e6c1b85211a09588b395061e2f10ae81fc3756e5630f76e58aa0d7b3c5","observation_id":"fbb85d87-cc17-4234-975c-c1a66180e209","resolution":{"observed_at":"2026-08-06T15:54:38.282209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:38.269991Z","title":"Hatcher, Algebraic Topology (CUP, Cambridge; New York, 2001)","venue":null,"work_id":"0ebfb778-a666-440e-a647-2f56d26431ec","year":2001},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.140273Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:cdcce3421c56c9432612197be0cd7310a45b04a2c6e4e6d4279dad8b7f4c5870","observation_id":"06cbd419-0aac-47f3-9dd2-28e5413b21a5","resolution":{"observed_at":"2026-08-06T15:54:38.272796Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/9810172","last_updated":"1998-11-19T19:50:38Z","snapshot_observed_at":"2026-07-07T06:09:35.946213Z","submitted_at":"1998-10-29T21:16:39Z","title":"Volume of Riemannian manifolds, geometric inequalities, and homotopy theory","version":2},"cited_work":{"arxiv_id":"math/9810172","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/9810172","snapshot_observed_at":"2026-08-06T15:54:37.770552Z","title":"Volume of Riemannian manifolds, geometric inequalities, and homotopy theory","venue":"math.DG","work_id":"e54dd0fc-8397-4aef-929b-07d0004294d9","year":1998},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.206144Z"},"links":{"cited_paper":"/paper/math/9810172","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:1844514477efa9be074571febff67d50fea98c1bc5aed4390bf87511d1274ea4","observation_id":"5f07ce7d-1714-46d8-ac14-4b12e59c31be","resolution":{"observed_at":"2026-08-06T15:54:37.773445Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.14327","last_updated":"2025-05-20T13:11:53Z","snapshot_observed_at":"2026-08-07T15:34:13.254004Z","submitted_at":"2025-05-20T13:11:53Z","title":"Lifting a CSS code via its handlebody realization","version":1},"cited_work":{"arxiv_id":"2505.14327","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.14327","snapshot_observed_at":"2026-08-06T15:54:37.759393Z","title":"Lifting a CSS code via its handlebody realization","venue":"quant-ph","work_id":"d7428cba-4fef-4f98-b12a-5c7addc71846","year":2025},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.260299Z"},"links":{"cited_paper":"/paper/2505.14327","citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:082321a7eddcef45bc83bb712f63bc03420e23c0d4d294b089154b641c45e4c3","observation_id":"5e18b50a-2d68-479a-9a5e-0255348eeaab","resolution":{"observed_at":"2026-08-06T15:54:37.762381Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:54:37.319163Z","title":"Bravyi, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T15:54:37.319163Z"},"links":{"citing_paper":"/paper/2507.15056"},"observation_digest":"sha256:c4a4689043b0ced63df3f15d1211bec9bd48e1af4401b78bad8d0b7b6c8e035e","observation_id":"d6c6f646-f5ac-4658-b07b-eb3bffed68de","resolution":{"observed_at":"2026-08-06T15:54:37.319163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.15056","last_updated":"2025-07-20T17:35:31Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-06T15:39:21.192737Z","submitted_at":"2025-07-20T17:35:31Z","title":"Transversal non-Clifford gates on qLDPC codes breaking the $\\sqrt{N}$ distance barrier and quantum-inspired geometry with $\\mathbb{Z}_2$ systolic freedom"},"reference_resolution":{"displayed":51,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":4,"verified_fuzzy":23},"total_outbound_references":51},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 6 inbound Pith citation observations for arXiv:2507.15056."}