{"as_of":"2026-08-09T13:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fd4e69101148af6ba27df45f3ee4a7a0eef0e34c43ea01cc979e3bfcc8217459","coverage":[{"denominator":62,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":62,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T19:23:26.930062Z","state":"measured"},{"denominator":62,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":62,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.04350/citation-record","integrity":"/paper/2608.04350/integrity","json":"/paper/2608.04350/citation-record.json","paper":"/paper/2608.04350"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:23:25.264399Z","title":"Gu and X.-G","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.264399Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:940854db0cfb50622c0979ade3fd6591564428b4c0bfb8dcb1a0ed9d6f83358b","observation_id":"468e6598-be33-4ddb-ab5a-7847543eaabb","resolution":{"observed_at":"2026-08-08T19:23:25.264399Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0910.1811","last_updated":"2010-04-22T17:39:46Z","snapshot_observed_at":"2026-07-06T01:58:44.105250Z","submitted_at":"2009-10-09T18:59:13Z","title":"Entanglement spectrum of a topological phase in one dimension","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0910.1811","snapshot_observed_at":"2026-08-08T19:23:25.357334Z","title":"Pollmann, A","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.357334Z"},"links":{"cited_paper":"/paper/0910.1811","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:e29eb15e415cdab221d3731555ed5630a92e186e1ca12c29cddc2ca4e9a4fd33","observation_id":"ea74250d-0992-4c48-b2c5-eac135010963","resolution":{"observed_at":"2026-08-08T19:23:25.357334Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0909.4059","last_updated":"2012-03-21T08:15:46Z","snapshot_observed_at":"2026-07-06T01:57:50.747234Z","submitted_at":"2009-09-22T19:27:18Z","title":"Symmetry protection of topological order in one-dimensional quantum spin systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0909.4059","snapshot_observed_at":"2026-08-08T19:23:25.367034Z","title":"Pollmann, E","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.367034Z"},"links":{"cited_paper":"/paper/0909.4059","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:c241984f396c5972a21d883778ca9d1e8a4c8c3590e0e8b6ea9c4eca6990f514","observation_id":"97b17413-32c2-4e00-b089-48a029351a7c","resolution":{"observed_at":"2026-08-08T19:23:25.367034Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1008.3745","last_updated":"2010-09-05T16:49:40Z","snapshot_observed_at":"2026-08-07T20:28:25.849303Z","submitted_at":"2010-08-23T04:08:40Z","title":"Classification of Gapped Symmetric Phases in 1D Spin Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1008.3745","snapshot_observed_at":"2026-08-08T19:23:25.379977Z","title":"Chen, Z.-C","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.379977Z"},"links":{"cited_paper":"/paper/1008.3745","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:f72f9a2701dc55bb2396c2aeea52e35134443a0e5d9813efa6a387ad4bdd8e67","observation_id":"a8b3ef31-4e9a-41f2-ad24-c21c161e7788","resolution":{"observed_at":"2026-08-08T19:23:25.379977Z","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":"2026-08-08T19:23:30.945806Z","title":"Chen, Z.-C","venue":null,"work_id":"2418ea41-1707-4c0f-89ed-75a8d3a6daa9","year":2011},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.398754Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:73e88bd7d35b5a9e37fc0001139687dfaca51ab6d5662be106be68f8439f822a","observation_id":"88fdd37c-48fa-4e8b-91d1-3989f145751c","resolution":{"observed_at":"2026-08-08T19:23:31.083862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1106.4772","last_updated":"2012-11-18T14:53:53Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2011-06-23T16:50:29Z","title":"Symmetry protected topological orders and the group cohomology of their symmetry group","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1106.4772","snapshot_observed_at":"2026-08-08T19:23:25.404869Z","title":"Chen, Z.-C","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.404869Z"},"links":{"cited_paper":"/paper/1106.4772","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:07eb54400d1c2b97a3a42f49daee4bba2526a161ebeb70a3d8e4e7e888581a37","observation_id":"ca6cf314-d659-4c5f-abac-e464d4989478","resolution":{"observed_at":"2026-08-08T19:23:25.404869Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1611.05450","last_updated":"2017-08-07T21:51:23Z","snapshot_observed_at":"2026-07-06T05:18:59.251691Z","submitted_at":"2016-11-16T21:00:03Z","title":"Symmetry protected topological order at nonzero temperature","version":2},"cited_work":{"arxiv_id":"1611.05450","doi":null,"metadata_source":"pith","pith_arxiv_id":"1611.05450","snapshot_observed_at":"2026-08-08T19:23:29.322284Z","title":"Symmetry protected topological order at nonzero temperature","venue":"quant-ph","work_id":"7c40a90b-c425-4240-98e3-d3e2984a128c","year":2016},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.410468Z"},"links":{"cited_paper":"/paper/1611.05450","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:7b4b4682184ca7471e9f7dfea3cfbbcc4db4f7afdf23d0ab37b2bb0554e8d340","observation_id":"12d8d68f-35bd-447a-9907-083a1fd736b5","resolution":{"observed_at":"2026-08-08T19:23:29.327858Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.02723","last_updated":"2023-08-24T03:20:57Z","snapshot_observed_at":"2026-08-05T13:54:07.191620Z","submitted_at":"2022-09-06T18:00:04Z","title":"Average Symmetry-Protected Topological Phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.02723","snapshot_observed_at":"2026-08-08T19:23:25.415696Z","title":"Ma and C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.415696Z"},"links":{"cited_paper":"/paper/2209.02723","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:8850241b8f647b866310ef4775a015a312d0c44b88c45d76bcd2fd85a738e4ec","observation_id":"1457ddfd-b2c8-4003-aaba-a8ddfcdcd6ef","resolution":{"observed_at":"2026-08-08T19:23:25.415696Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.04483","last_updated":"2022-11-09T12:21:24Z","snapshot_observed_at":"2026-08-09T01:41:40.775037Z","submitted_at":"2021-12-08T18:59:26Z","title":"Symmetry Protected Topological Order in Open Quantum Systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.04483","snapshot_observed_at":"2026-08-08T19:23:25.420396Z","title":"de Groot, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.420396Z"},"links":{"cited_paper":"/paper/2112.04483","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:4c4d80d08fa5913161ca20ca481b808b98a58d1e05d6ba4ea06830ca02ed2571","observation_id":"9e93a6c7-ffa0-4571-932a-7f6cec91f3e3","resolution":{"observed_at":"2026-08-08T19:23:25.420396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.03639","last_updated":"2024-11-18T02:28:47Z","snapshot_observed_at":"2026-08-08T10:11:26.129762Z","submitted_at":"2024-05-06T16:59:01Z","title":"Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.03639","snapshot_observed_at":"2026-08-08T19:23:25.426368Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.426368Z"},"links":{"cited_paper":"/paper/2405.03639","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:aaa7640c0afb2c31f637213e2eab4468ac15d4e35a5fd0cc668e0cb6c7ea9947","observation_id":"23b3c154-70e6-48d9-b3e0-23ba002fd92e","resolution":{"observed_at":"2026-08-08T19:23:25.426368Z","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":"2026-08-08T19:23:25.431148Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.431148Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:3f4a3fde223b206e1ed7259a28ddebb40016f9f740c746cc3a5c87aa2d3afdcd","observation_id":"23fedef4-590c-40c4-a345-cd68fb402816","resolution":{"observed_at":"2026-08-08T19:23:25.431148Z","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":"2026-08-08T19:23:25.485310Z","title":"Negari, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.485310Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:0f575a03fe0c8d1ccfc8dc5b9d626159cb521f35c27820c22fe8947b9278b5ab","observation_id":"2b5ed480-be1a-4b6e-b551-9dbe0b9e6c2d","resolution":{"observed_at":"2026-08-08T19:23:25.485310Z","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":"2026-08-08T19:23:30.876493Z","title":"Raussendorf, S","venue":null,"work_id":"9bf5d1b0-d02e-41da-85ae-b47f788c7c5c","year":2005},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.628627Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:02f2e193fba4a542ab7dbbd0098e3dedafddbdb9f626e4d9dec1c0b1fad7bc45","observation_id":"2439015c-edc4-4230-b635-3a72ba393627","resolution":{"observed_at":"2026-08-08T19:23:30.881743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:25.728799Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.728799Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:cc467cec0d53d1343b9fc5841b278f7d4d085c90e7b04cec14113f552f9c995d","observation_id":"d4418de8-8244-4b5c-a405-568d2dc5d2fc","resolution":{"observed_at":"2026-08-08T19:23:25.728799Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.03558","last_updated":"2018-06-09T23:43:09Z","snapshot_observed_at":"2026-07-06T06:43:56.885493Z","submitted_at":"2018-06-09T23:43:09Z","title":"Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.03558","snapshot_observed_at":"2026-08-08T19:23:25.734467Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.734467Z"},"links":{"cited_paper":"/paper/1806.03558","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:ddd023a49d85f2d6b77049d52ae92f5c45c9bfa189155602ffd0f1b7430b0b49","observation_id":"ea11dd38-cab8-42de-b44e-e38eae6068b8","resolution":{"observed_at":"2026-08-08T19:23:25.734467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1106.6026","last_updated":"2011-09-15T15:00:01Z","snapshot_observed_at":"2026-07-30T16:11:51.429034Z","submitted_at":"2011-06-29T19:00:20Z","title":"Topological Order at Non-zero Temperature","version":2},"cited_work":{"arxiv_id":"1106.6026","doi":null,"metadata_source":"pith","pith_arxiv_id":"1106.6026","snapshot_observed_at":"2026-08-08T19:23:28.823176Z","title":"Topological Order at Non-zero Temperature","venue":"quant-ph","work_id":"7435f914-61ab-407f-bd63-d9b7d3e3fa40","year":2011},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.740094Z"},"links":{"cited_paper":"/paper/1106.6026","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:22732f55d79d9c27770f22925ca952e5cfc5c953ac389670204a01d4366aa6e9","observation_id":"6c9b5a61-d702-4560-94aa-5dcd1286b595","resolution":{"observed_at":"2026-08-08T19:23:28.832066Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0804.3591","last_updated":"2008-10-21T23:32:41Z","snapshot_observed_at":"2026-07-06T01:37:47.320512Z","submitted_at":"2008-04-22T20:03:10Z","title":"Topological order in a 3D toric code at finite temperature","version":2},"cited_work":{"arxiv_id":"0804.3591","doi":null,"metadata_source":"pith","pith_arxiv_id":"0804.3591","snapshot_observed_at":"2026-08-08T19:23:28.687590Z","title":"Topological order in a 3D toric code at finite temperature","venue":"cond-mat.str-el","work_id":"04dc792b-9a49-4498-9d6f-05b0f3fb8729","year":2008},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.745139Z"},"links":{"cited_paper":"/paper/0804.3591","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:882c4fbcc8660043fd23fb2a8597a488afde1dd848f155528db9a96967f620c8","observation_id":"2d003806-bd03-4795-a3f9-d63e7545212f","resolution":{"observed_at":"2026-08-08T19:23:28.735955Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.24231","last_updated":"2026-08-06T02:38:44Z","snapshot_observed_at":"2026-08-09T13:09:36.499116Z","submitted_at":"2026-07-27T10:07:24Z","title":"Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals","version":2},"cited_work":{"arxiv_id":"2607.24231","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.24231","snapshot_observed_at":"2026-08-08T19:23:28.572616Z","title":"Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals","venue":"cond-mat.str-el","work_id":"1960f1a6-b13c-4929-86d5-f62dcb35d816","year":2026},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.751105Z"},"links":{"cited_paper":"/paper/2607.24231","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:965b7268d7cecaa5a0364c5424e5fb731e76ddcc057a92445392afbe5fcb6b07","observation_id":"d1dd9ceb-0292-4098-a86c-158da183932c","resolution":{"observed_at":"2026-08-08T19:23:28.634435Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.845437Z","title":null,"venue":null,"work_id":"1fc72081-827a-4089-9314-56c905ebfae0","year":2019},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.756689Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:4d4e2dab8bae540b77a3ad1475d698f41363c47c06d0ac84b0045f738ca3d2c8","observation_id":"b2ea74e3-1d52-4251-aff9-5ac2a8872579","resolution":{"observed_at":"2026-08-08T19:23:30.852583Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1603.04436","last_updated":"2016-03-14T20:00:00Z","snapshot_observed_at":"2026-07-06T04:49:28.300758Z","submitted_at":"2016-03-14T20:00:00Z","title":"Precision Islands in the Ising and $O(N)$ Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1603.04436","snapshot_observed_at":"2026-08-08T19:23:25.761691Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.761691Z"},"links":{"cited_paper":"/paper/1603.04436","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:6f294503879bbfa6f12b880f68353712d1b587f2beae301512f08ca960df3369","observation_id":"93bfba5f-4277-4530-898c-149a09709ae4","resolution":{"observed_at":"2026-08-08T19:23:25.761691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1204.0704","last_updated":"2012-04-03T15:01:17Z","snapshot_observed_at":"2026-07-06T02:45:41.432061Z","submitted_at":"2012-04-03T15:01:17Z","title":"Detection of Symmetry Protected Topological Phases in 1D","version":1},"cited_work":{"arxiv_id":"1204.0704","doi":null,"metadata_source":"pith","pith_arxiv_id":"1204.0704","snapshot_observed_at":"2026-08-08T19:23:28.530933Z","title":"Detection of Symmetry Protected Topological Phases in 1D","venue":"cond-mat.str-el","work_id":"94942114-ddaf-4596-be56-e08c2d44151d","year":2012},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.766554Z"},"links":{"cited_paper":"/paper/1204.0704","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:b8e4736632c01aeaf8ce1d33781010e11efa14ddc5ab04b2792011412479a102","observation_id":"55558974-2eab-49be-abec-9e3886fa83c7","resolution":{"observed_at":"2026-08-08T19:23:28.536588Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:25.800898Z","title":"Kennedy and H","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.800898Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:ec9682b7d94fcd23ef8ca1dc1da67077cce8f07f0759f8fc61654c14db88fb34","observation_id":"9f06760c-7dad-4299-9dfe-d287deed4af6","resolution":{"observed_at":"2026-08-08T19:23:25.800898Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.07899","last_updated":"2024-01-28T15:23:54Z","snapshot_observed_at":"2026-08-05T16:09:44.655859Z","submitted_at":"2023-01-19T05:57:55Z","title":"Non-Invertible Duality Transformation Between SPT and SSB Phases","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.07899","snapshot_observed_at":"2026-08-08T19:23:25.913888Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.913888Z"},"links":{"cited_paper":"/paper/2301.07899","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:da43a46e8e9deaacfeb71f9ff2318f2ef679923145681bcf4c6e82df0c8ea92b","observation_id":"79570631-2775-4b2a-a30e-d80d8a76ccec","resolution":{"observed_at":"2026-08-08T19:23:25.913888Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.05454","last_updated":"2025-01-01T13:25:34Z","snapshot_observed_at":"2026-07-06T18:27:33.030221Z","submitted_at":"2024-06-08T12:23:27Z","title":"Generating Lattice Non-invertible Symmetries","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.05454","snapshot_observed_at":"2026-08-08T19:23:25.982421Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:25.982421Z"},"links":{"cited_paper":"/paper/2406.05454","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:64a005eb578f6d6f312084bd56209c6e81e6d1a516a7f64e2b7020786d4c018d","observation_id":"e9e5aa15-bd48-46ac-9b94-12b9717f8d67","resolution":{"observed_at":"2026-08-08T19:23:25.982421Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.16017","last_updated":"2026-07-01T06:13:40Z","snapshot_observed_at":"2026-08-07T09:53:58.241898Z","submitted_at":"2024-03-24T05:35:59Z","title":"Generalized Kramers-Wannier Duality from Bilinear Phase Map","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.16017","snapshot_observed_at":"2026-08-08T19:23:26.007123Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.007123Z"},"links":{"cited_paper":"/paper/2403.16017","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:d1d73dfc100f77c545dbe5176cc2e34cbac6e3ccdb4aa9a54e8feb6d7396391b","observation_id":"035d21da-5eae-4dc0-aafb-de534f477d4b","resolution":{"observed_at":"2026-08-08T19:23:26.007123Z","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":"2507.02324","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:23:28.353506Z","title":null,"venue":null,"work_id":"4afc7900-0807-48f5-ace7-52311a23e0ba","year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.012853Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:5d2bf780b500736a22fa6af4697a1bbf54d8cefa1fe3abf3f8273c0df3bf85f4","observation_id":"ebde71a0-4f79-4ec4-91c1-9f2c642a43c9","resolution":{"observed_at":"2026-08-08T19:23:28.394385Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.24031","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:23:28.067692Z","title":"Li and Y","venue":null,"work_id":"04cdfcad-7a27-4e7f-91ae-5eb85935eca1","year":2026},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.018535Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:bec93e4ac885640c47aa9ba1cd1cbdfd65a877e9fd5f93c31d8b56a3e67b3fda","observation_id":"aa23d960-b7cc-48be-9e58-53f50ae8cf39","resolution":{"observed_at":"2026-08-08T19:23:28.099843Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.00134","last_updated":"2026-07-03T12:52:30Z","snapshot_observed_at":"2026-08-08T06:23:03.425044Z","submitted_at":"2026-06-30T20:12:45Z","title":"Phase distinction of Gibbs states without symmetry breaking: topological invariants of the 3D toric code","version":2},"cited_work":{"arxiv_id":"2607.00134","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.00134","snapshot_observed_at":"2026-08-08T19:23:27.868781Z","title":"Phase distinction of Gibbs states without symmetry breaking: topological invariants of the 3D toric code","venue":"cond-mat.str-el","work_id":"0849f128-83d1-45ae-b8e6-0fb9adc6d496","year":2026},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.023659Z"},"links":{"cited_paper":"/paper/2607.00134","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:d68e405b652745b5f2d50fdcfbcdc5b7760308b0e7fe3014caa4555d9204320c","observation_id":"e007d205-0667-43fa-b952-7376ef5fd455","resolution":{"observed_at":"2026-08-08T19:23:27.874194Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.13758","last_updated":"2025-01-22T06:34:41Z","snapshot_observed_at":"2026-07-06T15:58:27.523039Z","submitted_at":"2023-07-25T18:34:10Z","title":"Intrinsic Mixed-state Topological Order","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.13758","snapshot_observed_at":"2026-08-08T19:23:26.029432Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.029432Z"},"links":{"cited_paper":"/paper/2307.13758","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:ed07513f1d8ce546bce6c9185edd454d173d2db5a5292a205f3eafa42d6ee8f8","observation_id":"5faaca35-b92e-45ed-8b52-2d3e6d8c3ff2","resolution":{"observed_at":"2026-08-08T19:23:26.029432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.02390","last_updated":"2025-01-21T22:13:24Z","snapshot_observed_at":"2026-08-04T14:52:48.685234Z","submitted_at":"2024-05-03T18:00:00Z","title":"Towards a classification of mixed-state topological orders in two dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.02390","snapshot_observed_at":"2026-08-08T19:23:26.034335Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.034335Z"},"links":{"cited_paper":"/paper/2405.02390","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:e263d1b15292ba813cd8906e03bc790067ece887a49c5b88d93380e9b0f09a7a","observation_id":"0dc1fe2b-6531-45ef-aa9c-680213fd8c1d","resolution":{"observed_at":"2026-08-08T19:23:26.034335Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.16978","last_updated":"2025-04-24T14:32:17Z","snapshot_observed_at":"2026-07-06T17:50:18.017647Z","submitted_at":"2024-03-25T17:41:27Z","title":"Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.16978","snapshot_observed_at":"2026-08-08T19:23:26.039738Z","title":"Guo, J.-H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.039738Z"},"links":{"cited_paper":"/paper/2403.16978","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:90e1ccc730c1718e962e73f7fe4073721e91e17fab05874cc4a42662ad6f9438","observation_id":"b62da3e7-6b61-4443-8b1a-75efb3cf4948","resolution":{"observed_at":"2026-08-08T19:23:26.039738Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.13879","last_updated":"2024-09-25T23:29:55Z","snapshot_observed_at":"2026-08-03T06:25:09.316482Z","submitted_at":"2024-03-20T18:00:01Z","title":"A Noisy Approach to Intrinsically Mixed-State Topological Order","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.13879","snapshot_observed_at":"2026-08-08T19:23:26.045210Z","title":"Sohal and A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.045210Z"},"links":{"cited_paper":"/paper/2403.13879","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:3143c301be039c5a01e46276f49178457dbb817662cebe0cb5ee1edb504b20d8","observation_id":"aa6b2fb3-5828-4464-9023-3b80f586f4d4","resolution":{"observed_at":"2026-08-08T19:23:26.045210Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.08205","last_updated":"2025-02-14T00:31:28Z","snapshot_observed_at":"2026-07-06T19:31:23.072307Z","submitted_at":"2024-10-10T17:59:42Z","title":"Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.08205","snapshot_observed_at":"2026-08-08T19:23:26.049733Z","title":"Sun, J.-H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.049733Z"},"links":{"cited_paper":"/paper/2410.08205","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:96462168f52c6c79c9d5e445ffa28e317b9b900016398bfb9b1138ea5e72b30e","observation_id":"e193b22b-302a-4a14-9aa3-064a1db31282","resolution":{"observed_at":"2026-08-08T19:23:26.049733Z","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":"2026-08-08T19:23:26.055295Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.055295Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:9db896c7cfe1e7392eda25c8d7fdada2508a5cf40cd41ba7af734f8f426fcf53","observation_id":"dc8566fe-d4ef-4c16-b6f0-2dcead1400e4","resolution":{"observed_at":"2026-08-08T19:23:26.055295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06218","last_updated":"2025-07-08T17:51:00Z","snapshot_observed_at":"2026-08-08T16:53:37.750448Z","submitted_at":"2025-07-08T17:51:00Z","title":"Topological Holography for Mixed-State Phases and Phase Transitions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.06218","snapshot_observed_at":"2026-08-08T19:23:26.060869Z","title":"Luo, Y.-N","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.060869Z"},"links":{"cited_paper":"/paper/2507.06218","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:29c0c3a5ce1c85c1d24be7b87b0125010245084635323d8a11f05ffbfba45e79","observation_id":"0426b21d-6ad1-40da-9a76-3da1e7b6c255","resolution":{"observed_at":"2026-08-08T19:23:26.060869Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05350","last_updated":"2025-07-07T18:00:02Z","snapshot_observed_at":"2026-08-06T19:25:42.605470Z","submitted_at":"2025-07-07T18:00:02Z","title":"SymTFT Approach for Mixed States with Non-Invertible Symmetries","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.05350","snapshot_observed_at":"2026-08-08T19:23:26.101343Z","title":"Schafer-Nameki, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.101343Z"},"links":{"cited_paper":"/paper/2507.05350","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:fcb711b4c29d5d80e175b3dcb6a8690fae94e3ff7534497d9166bf5e552878ae","observation_id":"7286f5a8-5950-43bb-8c41-234d42ddef58","resolution":{"observed_at":"2026-08-08T19:23:26.101343Z","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":"2026-08-08T19:23:26.195267Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.195267Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:01f498d3fbfdb01f3f4d2f396841b7d08e6a40f687dc463c1b411f377a4950bf","observation_id":"341233c6-e10a-4596-9bfd-c10c2c343fcf","resolution":{"observed_at":"2026-08-08T19:23:26.195267Z","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":"2026-08-08T19:23:26.242444Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.242444Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:529e9dbecc756af4448531615b29961ebf563a9803874d313ae7acfb2d70c45b","observation_id":"d3ce4b8c-f1ab-437a-9f0a-0c431b5c98d9","resolution":{"observed_at":"2026-08-08T19:23:26.242444Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02292","last_updated":"2025-07-25T18:39:08Z","snapshot_observed_at":"2026-08-08T00:49:34.815340Z","submitted_at":"2025-07-03T03:59:07Z","title":"Mixed-state phases from local reversibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02292","snapshot_observed_at":"2026-08-08T19:23:26.275182Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.275182Z"},"links":{"cited_paper":"/paper/2507.02292","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:0589c407cae61db6d18c4093a57d0f7fa1630f180f92ac098e4bf31fe1dd9511","observation_id":"bcf49092-5114-4361-875b-4906fdf412de","resolution":{"observed_at":"2026-08-08T19:23:26.275182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.14781","last_updated":"2026-06-17T11:00:11Z","snapshot_observed_at":"2026-08-05T17:45:02.548755Z","submitted_at":"2025-10-16T15:16:13Z","title":"ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field","version":4},"cited_work":{"arxiv_id":"2510.14781","doi":null,"metadata_source":"pith","pith_arxiv_id":"2510.14781","snapshot_observed_at":"2026-08-08T19:23:27.035732Z","title":"ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field","venue":"quant-ph","work_id":"a9ae147e-e61d-46fd-a5be-c6875d638c34","year":2025},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.281647Z"},"links":{"cited_paper":"/paper/2510.14781","citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:850fef975290c3c001740e62b9e16b2613302eeaafd65c1cb1db90c893ef98ef","observation_id":"176b7523-9a0e-4a09-b040-e11a7e36b9b8","resolution":{"observed_at":"2026-08-08T19:23:27.052289Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.813500Z","title":"Aizenman, D","venue":null,"work_id":"9d97ff70-fe51-43f2-9c80-84678e7ef2b9","year":1987},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.288437Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:b51188a4d079d2e8015ecd8bd56ff0276bb4580b97fec2826d93531f24bf00aa","observation_id":"d2bfb8b7-4352-4608-906d-88cab6703f98","resolution":{"observed_at":"2026-08-08T19:23:30.818114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.796644Z","title":"strongly symmetric","venue":null,"work_id":"4db09fd9-f6d1-4e9d-8a18-8e746a00691d","year":1981},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.295990Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:9cd2a7a2d9ea7a6c8a061a3b4bc118845ef1d5757f4bed0acac680096b8e967d","observation_id":"b1fcf9ef-6674-4b01-bf44-3d278863814d","resolution":{"observed_at":"2026-08-08T19:23:30.802219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.752835Z","title":"contractible","venue":null,"work_id":"984e5d1a-4785-4bff-bf56-c47939402a4e","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.302676Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:e47f457592c3449a1ef52bd74814edab847a94bf21634bb68b8ef2d644390284","observation_id":"dcbe4b67-932b-48e0-bd58-244a6a732b23","resolution":{"observed_at":"2026-08-08T19:23:30.757971Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.726798Z","title":"Weighting configurations by (−1) wi(C) is, in the Ising dictionary, an antiperiodic twist of the spin model, as follows","venue":null,"work_id":"1d203d7f-5e84-468f-800b-b3e07dc2dfdb","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.348375Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:98d36290080b2dec40cdb85c3f070ba9abeef2459a12dfb2132008249f216d01","observation_id":"d581cc49-f443-4b14-9742-37257b92ebc6","resolution":{"observed_at":"2026-08-08T19:23:30.738654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.697078Z","title":"Along every scan B :=βµ= 4 is fixed, and the sampled exponent is −βH(s) +BG","venue":null,"work_id":"c33ade6c-64cb-43ab-8b87-36fce2b73801","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.435676Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:563ed942319529bb7cde27780deee90fda93e5cda4afba81a31832ace7f16d69","observation_id":"f767e593-5136-4e08-8981-7be42dbd2510","resolution":{"observed_at":"2026-08-08T19:23:30.708261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.563409Z","title":null,"venue":null,"work_id":"6e3efc89-877c-4f8d-a2ff-55ea37330a4e","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.461965Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:3b5663a352196fe634c1b8aef819b92e2f2280766c5b064db271a74da81caca5","observation_id":"39547733-2fe2-4c15-8a58-b602256f62ae","resolution":{"observed_at":"2026-08-08T19:23:30.628238Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.413185Z","title":null,"venue":null,"work_id":"faafa781-2e9f-4fe3-83c4-d582be0eca52","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.470626Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:1d59c36ed382f964b691f86a00d0b02e6c7b8b96d50ab680071b64f4bfde38e4","observation_id":"fc47afef-553e-4429-b0ad-25dbce2b1da0","resolution":{"observed_at":"2026-08-08T19:23:30.502411Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.247957Z","title":null,"venue":null,"work_id":"3ba2dd4e-107f-4004-ad6b-227653a0b5cf","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.479936Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:7928677c35ac3cd836cee450437ba393f6eccf920d6ff976f96de307ad1e6c61","observation_id":"5f7b0066-69e4-41ea-9c6f-55db9b17f287","resolution":{"observed_at":"2026-08-08T19:23:30.293096Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.183416Z","title":null,"venue":null,"work_id":"337be320-c89d-4753-9bf6-573a2fa01612","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.488828Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:c91e9152745d63b03c4b93c722380ca3222a0503aeb60ca1df35f92af883eca3","observation_id":"6ea38d71-661d-4666-b08c-fcbaffb63e2e","resolution":{"observed_at":"2026-08-08T19:23:30.188469Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.167144Z","title":null,"venue":null,"work_id":"1eeea46d-8637-403e-94de-1635f60c248d","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.496401Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:d8c586f99d199d13715c15af13a7866d91328674ab92528adc76010399d56d20","observation_id":"5f542930-fe31-41ad-97eb-265d1a8097bd","resolution":{"observed_at":"2026-08-08T19:23:30.172649Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.151223Z","title":"(S27) gives IL( 1 2 , T) =−IL( 1 2 , T) = 0.(S33) This holds at every temperature and finiteL, without a thermodynamic limit or Hypothesis (H)","venue":null,"work_id":"fdbae485-f4ed-454b-ab8a-978be4428d72","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.567381Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:fabee350980bdba8a5ac61c81e2bea53b3a7d328c60a79850172c587e8bcee2d","observation_id":"c8279d3d-fe9f-4c84-971a-d0a6ba6395e7","resolution":{"observed_at":"2026-08-08T19:23:30.156026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.133870Z","title":"We first considers ′ > 1 2 at finiteL","venue":null,"work_id":"ddd2fa63-7e33-4c3d-8a31-fc6b7f2cd146","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.633178Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:60d58ff8d3fee4d24fdc6328c47f771f94c71dfffc49dd5ab31b98371f754959","observation_id":"6879eff5-8f6c-46db-bffc-1ab67444023a","resolution":{"observed_at":"2026-08-08T19:23:30.139348Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:30.114856Z","title":"Conjugation byW, which preservesP loc, supplies the same (−1)Σ·γ prefactor as in Eq","venue":null,"work_id":"9fd95221-6da4-422b-a30e-a24b32e1651a","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.651399Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:852c500ea71cc61553966c14c7a4f91ff8ba4af64c023fe8f0695effb2aa4201","observation_id":"7eb7f375-2a9e-4213-aa0e-902bfe828883","resolution":{"observed_at":"2026-08-08T19:23:30.120683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.981476Z","title":null,"venue":null,"work_id":"cb4f6144-b709-4ace-847f-868f6ddf35ff","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.657369Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:64647563e899473df193d83754ce3365826ae8ec559fc853b34971813cf6a2c9","observation_id":"91daa530-1cc0-4cd5-8f37-38e3a93a1d64","resolution":{"observed_at":"2026-08-08T19:23:29.986523Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.963818Z","title":"The two winding sectorsm= + (even) andm=−(odd) are simulated independently, the latter seeded with a single winding line","venue":null,"work_id":"876e7af3-717a-4c44-b61d-ec004b670386","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.662839Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:9004b970783ca9846345085cf18eae83c01cf19651ef3b00680e6b28996f3cfe","observation_id":"34c655b2-3c1d-4508-9b5b-a078ffdf4ceb","resolution":{"observed_at":"2026-08-08T19:23:29.969619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.942161Z","title":"Fora̸= 0, define F A,m sp (a;L) :=−ln[Z (as=a) A,m /Z(as=0) A,m ], τA,m(a;L) :=L −2F A,m sp (a;L)","venue":null,"work_id":"ef704c3c-4e2c-494e-8379-0b79cafa5a77","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.669236Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:e4a3b93c32acb7f7396932e5a52f0c19bf440d2f8c506871f4743955f97cfd68","observation_id":"e1595a13-0570-4e1e-8a4b-8066812fa3fd","resolution":{"observed_at":"2026-08-08T19:23:29.952787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.914565Z","title":"S2 B–S4 A, where the same observable is com- puted independently by extended-ensemble Ising Monte Carlo","venue":null,"work_id":"ae200b5a-3f96-43f3-8a57-23016fa27722","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.675985Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:cda1bd26d3ae58861973384d2c0b06f3ab5f13c5bc8c4d1a9a76aebc78584a3f","observation_id":"c2b14ae9-d1d5-40b1-8a07-0fbd4e734a65","resolution":{"observed_at":"2026-08-08T19:23:29.925680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.883865Z","title":"S5, not replicas of the density matrix","venue":null,"work_id":"43608e28-6315-4471-9ef7-fa99e50d3823","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.683209Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:1422eb99877397456595066626311000cfa3a2c062181a5a7d27c34944121700","observation_id":"150fa089-f676-42c9-93c0-5681a574c3cd","resolution":{"observed_at":"2026-08-08T19:23:29.893421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.826154Z","title":"For eachC∈ {A, B}, letx C,l(τ) =±1 be its directed-link worldline variable and letn C,p(τ)∈ {0,1} record a plaquette-flip event between adjacent slices","venue":null,"work_id":"d50111c5-0eb8-42e2-8666-a7315ab52ec0","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.733590Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:9bcb0246a6b2071f73a8b7c81591552d2e83cf9b6495cfa19de76d05544fbf2c","observation_id":"f50469d4-3cf6-4092-a0ee-fd5d36294299","resolution":{"observed_at":"2026-08-08T19:23:29.869739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.649971Z","title":"ThusN τ and ∆τ eff are fixed before a chain is run","venue":null,"work_id":"b1a06e99-893c-4dd6-bc0a-4aa8bc10b6aa","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.819354Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:715a89b1e04205f517591fb338ecda5b7b1ce2e0528759c7abeb620790ed2f6b","observation_id":"b5e2e2bc-a559-4469-b073-0ce25910780d","resolution":{"observed_at":"2026-08-08T19:23:29.707411Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.505483Z","title":"In round 0 the offsetsb j learned dur- ing adaptation are frozen, and the round passes only if every bin is visited","venue":null,"work_id":"72ecd34c-d49d-40b6-a813-ab59c44399ac","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.875163Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:ac7b79c06ef67b723478f0bd86d8000671a384bd61eaf74109a9d1ac5f16aedf","observation_id":"8d849e2c-8675-4c79-a40e-0beb8dd23e99","resolution":{"observed_at":"2026-08-08T19:23:29.595674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T19:23:29.408453Z","title":"At (s, T) = (0.30,0.30), the three refinement factors give I (f=1) 4 =−0.9999995712, I (f=2) 4 =−0.9999994446, I (f=4) 4 =−0.9999994161","venue":null,"work_id":"241bb7b9-557e-4f6f-947e-415bd4390ac9","year":null},"citing_paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-08T19:23:26.930062Z"},"links":{"citing_paper":"/paper/2608.04350"},"observation_digest":"sha256:3eb570431022be1d35b4768d54f56bbd073b0719e9889ab906b03775b5fbdff1","observation_id":"93e0bb11-bde7-46ee-85ac-37aeb6dc262b","resolution":{"observed_at":"2026-08-08T19:23:29.452629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.04350","last_updated":"2026-08-05T01:49:48Z","latest_version":1,"primary_category":"cond-mat.str-el","snapshot_observed_at":"2026-08-08T23:11:30.316214Z","submitted_at":"2026-08-05T01:49:48Z","title":"Quantized topological invariant of symmetry-projected Gibbs states"},"reference_resolution":{"displayed":62,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":9,"verified_fuzzy":18},"total_outbound_references":62},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 0 inbound Pith citation observations for arXiv:2608.04350."}