{"as_of":"2026-08-08T17:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7b94b4404d8c0a1ace7821390b530cc27fa22cfe01172c491d972e14218887eb","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:51:54.083693Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2505.23681/citation-record","integrity":"/paper/2505.23681/integrity","json":"/paper/2505.23681/citation-record.json","paper":"/paper/2505.23681"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:57.730903Z","title":null,"venue":null,"work_id":"867b97ba-d1b8-48bc-8f41-2b32d3084146","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.109532Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:b14842069282a2bb67155d1fa295da33a7e63b883bb84f53f125720d53be4730","observation_id":"ddd0e29f-da12-48a8-9f94-309827f7f50d","resolution":{"observed_at":"2026-08-07T12:51:57.832234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:57.508347Z","title":null,"venue":null,"work_id":"65d26932-8162-436e-b09b-9c33d1e1b55d","year":2021},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.233713Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:817f3f11b9e7ed95413aefa8c62873f1f40e4502ffeadd0b7362e60a62670dc3","observation_id":"b4ad161d-d249-4a1b-9bf0-8c6be15c86d9","resolution":{"observed_at":"2026-08-07T12:51:57.611267Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:57.289685Z","title":"For any g ∈ GL(h) such that det(g) < 0, g · (W1, W2) and (W ′ 1, W′","venue":null,"work_id":"b40b595f-0346-4be3-a993-2145a7abfaf7","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.350485Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:6d6d5f038975fc90cf08c489c28e917f4b29b3c8219c092467910628afc9dd11","observation_id":"6b4e625c-02de-4858-b5c1-a137e834ceef","resolution":{"observed_at":"2026-08-07T12:51:57.376976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:57.093085Z","title":null,"venue":null,"work_id":"903cd166-9d7e-48ae-9db6-c53c3a0080c2","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.433197Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:e46dcd2d08ae2cd05fa8e43895141ba0a221c5472f4dcd52282858b071afdc08","observation_id":"571a76dd-6500-4c6c-ab24-70028680e546","resolution":{"observed_at":"2026-08-07T12:51:57.176093Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.895935Z","title":"Equivalently, det(gg ′) < 0","venue":null,"work_id":"639269c8-7ba9-4872-8ad8-af30b30791e2","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.516921Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:6d7a9c88ff0ac01589e55f2e9a95b7edcb5713f69795fa49538efe43877a7d4c","observation_id":"271d8241-fbdf-48e6-80be-3aa60b242d3c","resolution":{"observed_at":"2026-08-07T12:51:56.992325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.715031Z","title":null,"venue":null,"work_id":"13a0d696-14a3-40c9-94cf-89d09544ff30","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.636964Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:1e411367e961907424f0fa8517549d44f8b6588cc9e9860cfdb2b264894ee0fb","observation_id":"86f4cde0-1e88-4edd-a49c-c12637dd56e9","resolution":{"observed_at":"2026-08-07T12:51:56.780838Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.557318Z","title":"By Lemma 5.1, any g ∈ GL(h) with det(g) < 0 can bring (W1, W2) and (W ′ 1, W′","venue":null,"work_id":"3a4aa75b-ece6-4702-b112-1da05d799ceb","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.747456Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:2d34f01d2392dfad79fb5a63185fccb822b478251c45018dae3df391a7c3c6ff","observation_id":"b7bc7e22-193d-4ce9-9a56-f9b9499592c5","resolution":{"observed_at":"2026-08-07T12:51:56.600100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.378865Z","title":"Let g be the permutation matrix 0 1 1 0","venue":null,"work_id":"d0451b5a-76e4-4117-bd23-2e0cdc61752f","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.825837Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:b245b2accaf89d83831eb8f2203459d8af0af4412590aa8e73941917ea9f84bc","observation_id":"8ccbf496-c9f8-4e61-806b-90e98512179c","resolution":{"observed_at":"2026-08-07T12:51:56.450488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.211384Z","title":"Then W, W′ belong to the same connected component of L−1(0), connected by curve γ : R → Param, γ(t) = ((1− t)Wl + tWlm−k, (1 − t)Wl−1 + tmWl−1, Wl−2, ..., W1)","venue":null,"work_id":"5036385e-880b-4000-a127-0a0aefd10fcc","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.919249Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:d29a32b8afa4877fd7692008a08794398a44a5b38a7b32ee84a51dc93defdc66","observation_id":"672719e0-5f78-41ce-bce8-1ff1a294dc52","resolution":{"observed_at":"2026-08-07T12:51:56.274995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:56.057036Z","title":"Then L ((1 − α)W + αW ′) = 1 − 1 2 + 1 2 m−k 1 2 + 1 2 m k!2 ||Y ||2 2 = 1 − 2−(k+1)(1 +m−k)(1 +m)k 2 ||Y ||2 2 (15) Let m = 2k+1 √ b ||Y ||2 + 1 − 1 k","venue":null,"work_id":"a172778c-d523-4191-ba06-21ccab0891e1","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.028950Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:7b91e65270008f53552a3c29fbc2bc12568664d94ef8eb18ad35534a155cd8f7","observation_id":"efa16d2f-00af-4ef3-9659-dd16c885d4ad","resolution":{"observed_at":"2026-08-07T12:51:56.144745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:55.889661Z","title":"At large m, the two minima are farther apart, and the loss evaluated at the middle point of their linear interpolation grows unboundedly as predicted by Proposition 5.3","venue":null,"work_id":"e46e57e7-5d46-4537-bc4a-77d14188ae6c","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.143352Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:3e6b5a265f378b9d7273bfe09eb9c0691388e44afa0aea8d642a8dfb0b174864","observation_id":"74d28a4a-e160-435a-91ed-b699e11e4112","resolution":{"observed_at":"2026-08-07T12:51:55.958870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:55.676517Z","title":"Since W ∈ L−1(0), we have Wlσ [Wl−1f (Wl−2, ..., W1, X)] =Y","venue":null,"work_id":"200ad42d-b3b6-464a-894f-88d2b03de7a3","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.300382Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:04d033942dd46b0f21549871c74bb5f273bc4613297e6a26c8d56ec1aefe5f25","observation_id":"c5a2e286-9545-439e-9cce-17542dc965b1","resolution":{"observed_at":"2026-08-07T12:51:55.792841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:55.481057Z","title":"Then L ((1 − α)W + αW ′) =||Y − 1 4 Wl(I + m−kP )σ (I + mP −1)Wl−1f (Wl−2, ..., W1, X) ||2","venue":null,"work_id":"56499553-dcaa-4947-b4ea-83bdacccca00","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.412186Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:348ea2c7798cf35dc3f84a9db548f6bb9886332df31a398ab01017e96f765bdd","observation_id":"9cdf196e-4244-4fa4-9e0a-eda162c8a8b1","resolution":{"observed_at":"2026-08-07T12:51:55.572217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:55.296415Z","title":null,"venue":null,"work_id":"e79d4c76-c0f5-4a96-9cb8-d7c8c11781dc","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.493660Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:7ddcd3277e30eda6d30d1865013519d93c0f541e5ebeb92b48079fc897f5d2fe","observation_id":"3eef6d25-a3e3-46c5-bc5f-4b04aedeab76","resolution":{"observed_at":"2026-08-07T12:51:55.383579Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:55.074155Z","title":"Therefore, L ((1 − α)W + αW ′) is unbounded for any P","venue":null,"work_id":"789de669-f164-4561-b003-6f5b28c536f5","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.602246Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:8adf0afb05370196d6dfc12be30de8b0beef556deb5a095f5c905a358e54e800","observation_id":"1e1afdde-d229-4518-aa53-139b77a07bcc","resolution":{"observed_at":"2026-08-07T12:51:55.198525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:54.909220Z","title":null,"venue":null,"work_id":"cb9bfa66-3cf4-4b71-a864-9b510ff7a097","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.751908Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:ca0492b84919ff9e5ff180657f834a163d3109004af9b14013a1deed12d63a00","observation_id":"66c91ef4-c6a7-4df4-b05c-176515dacd0b","resolution":{"observed_at":"2026-08-07T12:51:54.995591Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:54.691876Z","title":"Let α = 1","venue":null,"work_id":"ea40895c-1984-4a7e-b31d-6233d7e52476","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.857566Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:ecc1f5d52f46337bfabd9c494c5baca37c9203b3c1f189de5243614f42841992","observation_id":"74de1ee3-7aff-4d80-8127-ba0509a6a1bd","resolution":{"observed_at":"2026-08-07T12:51:54.820965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:54.485256Z","title":"(23) As β → ∞, g and g−1 cannot approach β+β−1 2 I simultaneously","venue":null,"work_id":"e93c752f-98d4-4a16-9587-d531bba30210","year":null},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:53.966089Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:3fbde57c2995feb8959ee7ab9681f75b9287a7d901c5773b45bd502820e85d6a","observation_id":"0582a42b-45bf-4300-866b-274e26447dd9","resolution":{"observed_at":"2026-08-07T12:51:54.589548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:54.247069Z","title":"The connectedness results derived from symmetry raise several interesting questions about mode connectivity","venue":null,"work_id":"ca1e7d97-a18b-491a-8761-d2ea2a5f3201","year":2018},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:54.083693Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:6e431750789d1b2e1efb800a38f89e05a6d220f703ecdd9aba6556a62876377c","observation_id":"681d458a-a0f9-4f43-83c2-9ac5e34b260d","resolution":{"observed_at":"2026-08-07T12:51:54.334587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:51:57.929501Z","title":"Freeman, C","venue":null,"work_id":"e253a8df-d78d-4cd0-91ec-25ccb18abb32","year":2020},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":3269,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:51.894692Z"},"links":{"citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:7cbfcf60021cf0975d273269be3244447066d5c707efd2805e8f92324e338838","observation_id":"e1c06f88-fb73-434e-9d12-b1dbd40f7808","resolution":{"observed_at":"2026-08-07T12:51:58.011853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.08576","last_updated":"2021-01-21T12:43:26Z","snapshot_observed_at":"2026-08-04T06:11:21.991101Z","submitted_at":"2021-01-21T12:43:26Z","title":"A Note on Connectivity of Sublevel Sets in Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.08576","snapshot_observed_at":"2026-08-07T12:51:52.006681Z","title":"Nguyen, Q","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry","version":1},"reference_index":4799,"source":"pdf_text","source_observed_at":"2026-08-07T12:51:52.006681Z"},"links":{"cited_paper":"/paper/2101.08576","citing_paper":"/paper/2505.23681"},"observation_digest":"sha256:d4b2751405b9c4a427484db0012dc6d8f86b73798916fc7a48bfefdbd01fb30c","observation_id":"fa0d2c83-da96-4350-8ef7-d9971ddf499d","resolution":{"observed_at":"2026-08-07T12:51:52.006681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.23681","last_updated":"2025-05-29T17:20:54Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T12:37:40.215809Z","submitted_at":"2025-05-29T17:20:54Z","title":"Understanding Mode Connectivity via Parameter Space Symmetry"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":14},"total_outbound_references":21},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2505.23681."}