{"as_of":"2026-08-19T14:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:75a86466d4d6e1d20da2e960ae3491f325788c3dfd8fa96abb7e2c33bb0ba8d6","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T00:46:16.535760Z","state":"measured"},{"denominator":16,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":16,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2606.26417/citation-record","integrity":"/paper/2606.26417/integrity","json":"/paper/2606.26417/citation-record.json","paper":"/paper/2606.26417"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2511.22339","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T16:19:57.800678Z","title":"Acuaviva,C(K)-spaces with few operators relative to posets, arXiv:2511.22339 (2025)","venue":null,"work_id":"a7db3d14-fc41-4b0b-8eeb-2bb7e20aaba3","year":2025},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:d5ce09ce1d3d712abd9f2e31a57673f9225a4d1ed84641a2f316583ba55ea679","observation_id":"c9a1afa7-91d9-4c69-9dc6-12b573d48f3e","resolution":{"observed_at":"2026-07-04T16:19:57.802122Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.29854","last_updated":"2026-05-28T12:36:00Z","snapshot_observed_at":"2026-07-06T23:39:15.620929Z","submitted_at":"2026-05-28T12:36:00Z","title":"Primariness of the spaces $\\ell_p(C(K))$ for $1 \\leq p \\leq \\infty$","version":1},"cited_work":{"arxiv_id":"2605.29854","doi":"10.48550/arxiv.2605.29854","metadata_source":"pith","pith_arxiv_id":"2605.29854","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Primariness of the spaces $\\ell_p(C(K))$ for $1 \\leq p \\leq \\infty$","venue":"math.FA","work_id":"3cde2dd1-52f2-41a2-a377-33191f5798ad","year":2026},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"cited_paper":"/paper/2605.29854","citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:074427e9b0cd4229f9f6fb8fe649a9d1a1902f0640a0e8f4342b2bd98e178a10","observation_id":"1378ac0e-3984-42b6-9d76-ff7c0b6bb9c3","resolution":{"observed_at":"2026-07-04T16:19:57.799537Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.21711","last_updated":"2026-05-20T20:14:33Z","snapshot_observed_at":"2026-08-18T11:26:50.060864Z","submitted_at":"2026-05-20T20:14:33Z","title":"Primariness and the Primary Factorisation Property","version":1},"cited_work":{"arxiv_id":"2605.21711","doi":"10.48550/arxiv.2605.21711","metadata_source":"pith","pith_arxiv_id":"2605.21711","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Primariness and the Primary Factorisation Property","venue":"math.FA","work_id":"9600d515-f046-4a32-a378-06e6430ae6b4","year":2026},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"cited_paper":"/paper/2605.21711","citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:e9e5c0c0e8e01f9dc0332624025d09fcce2045e04de527cf5f32b7a3cad783dc","observation_id":"97a3b070-f997-45e4-99c1-4cb8894864f2","resolution":{"observed_at":"2026-07-04T16:19:57.804707Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-06-26T00:46:16.535760Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:5db685737dc4dae6e6761e0614ec34b3a1253580746229e81127923518de3b8a","observation_id":"7b983f18-6393-4dca-bce8-5dea332668b6","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Alspach, P","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:c692d736982deb2723b961278bf26cda717886b4dc28505ca0811dea6d372efa","observation_id":"914f1219-38f5-4d02-8c71-38153ea3076c","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Capon,Primarité deℓp(L1), Math","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:076bcac0c5ba7f26f734ee54f1c09da8620434a08a4e74d2c3d502f412176dc6","observation_id":"a7b15f5f-1000-4646-8f31-9704e0e4b00a","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Dosev and W","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:b02f00757815af8a108a8973092c74741055ec849493b7e6ad3a63f67200810e","observation_id":"5e787cdb-534a-4295-8e3e-01e9555a0789","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Hajnal,Proof of a conjecture of S","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:5de38004f59945a000739737191f3c7705c3202d3a0abb24ce5a5ea5965bd218","observation_id":"063d73ab-3ed9-4eaf-852a-c0eef5401e07","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:9c78fd298b3ef9683d919e7ff1b520a77282cd7add9b33bec8a1dbae84d6dc0f","observation_id":"73ae16e3-7084-494e-8002-bcdd7ebaa75e","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:e829ccc55a86a7bdb0720d91ed429c118209fa0c3cd0d7029d1353e401214ac4","observation_id":"66597dc7-4a4e-4a8f-a6d8-ccf0b3bf099f","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Lechner and T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:3bb9843967383ea231794adc092d72a2b09c00e19f5be6e2b5f2b1ac67748324","observation_id":"17afceed-b951-4e89-ad81-7def58876f41","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Lindenstrauss and L","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:9e1612fb02ad6e35c0b92c8cb5678f99af74b91acc0071a88f4126352aafbb2f","observation_id":"b8ff274d-8248-4337-94ec-4b9068501354","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Maurey,Sous-espaces complémentés deLp, d’après P","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:d2f03e5c55b691ab9e5b035bdfbac2d7b1f034753088d57bb3266d656d228425","observation_id":"c849371c-a5d0-441c-a05d-8a8144e88929","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:a65e1e283e67399ea91f7fbeb5bc5908070bc511c937e56a900faabb075fce78","observation_id":"0054f4a0-f7a2-487b-8e82-1b980d528407","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":"Pełczyński,On strictly singular and strictly cosingular operators","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:a40dc1d5742f7a7fd67a6a020a745219f2829318f89e79850efc8af0d4564ced","observation_id":"21807880-05f5-4050-b15e-1148d91995e6","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","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":"2026-06-26T00:46:16.535760Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-26T00:46:16.535760Z"},"links":{"citing_paper":"/paper/2606.26417"},"observation_digest":"sha256:2447bb284c73ed39e295940dcd4d9a578882976eedeea3ab7a6db9d36bd5b63a","observation_id":"0d707fb2-e58b-4882-b2af-f8788eb8241b","resolution":{"observed_at":"2026-06-26T00:46:16.535760Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.26417","last_updated":"2026-06-24T22:14:44Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-07-07T00:00:46.505337Z","submitted_at":"2026-06-24T22:14:44Z","title":"Preservation of primariness under $\\ell_1$-, $c_0$-, and $\\ell_\\infty$-sums of Banach spaces"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":16},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2606.26417."}