{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SOXS5ILVBVUUV2PMF5LCPYYXVV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b13b1885b5f4ef86f6a64bb2fbafc5f4c94926ae0f94a4783a5ef6f2cc69657","cross_cats_sorted":["math.MP","nlin.CD","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T05:20:44Z","title_canon_sha256":"bab47219b334b407058ef4314f9c7a64f804bf20490cfae79bcb3b6dbc69cab6"},"schema_version":"1.0","source":{"id":"1108.3650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3650","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3650v1","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3650","created_at":"2026-05-18T04:15:15Z"},{"alias_kind":"pith_short_12","alias_value":"SOXS5ILVBVUU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SOXS5ILVBVUUV2PM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SOXS5ILV","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:e9b534578b9961a1ad7b684ad2825b8744faefcacaa0227372171626c4a7e1ef","target":"graph","created_at":"2026-05-18T04:15:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in ${\\mathbb R}^2$ which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method (\"transplantability\") using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counte","authors_text":"Jeroen Schillewaert, Koen Thas","cross_cats":["math.MP","nlin.CD","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T05:20:44Z","title":"The 2-Transitive Transplantable Isospectral Drums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3650","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74647667c643b36665e626a8fd1b17a2e609dea2956d7c7bef3644368b89196e","target":"record","created_at":"2026-05-18T04:15:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b13b1885b5f4ef86f6a64bb2fbafc5f4c94926ae0f94a4783a5ef6f2cc69657","cross_cats_sorted":["math.MP","nlin.CD","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T05:20:44Z","title_canon_sha256":"bab47219b334b407058ef4314f9c7a64f804bf20490cfae79bcb3b6dbc69cab6"},"schema_version":"1.0","source":{"id":"1108.3650","kind":"arxiv","version":1}},"canonical_sha256":"93af2ea1750d694ae9ec2f5627e317ad4280bf07c3c5362e17981ca4a2e5a99e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93af2ea1750d694ae9ec2f5627e317ad4280bf07c3c5362e17981ca4a2e5a99e","first_computed_at":"2026-05-18T04:15:15.494783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:15.494783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5LOUOQY4i/RJtJMDyccDU6qHEZoaGmIf1gl1TMSJCJGQHAWbEHGtWc5WFeDcciC+G+ITAAF9v+iTuXO35Mw4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:15.495395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74647667c643b36665e626a8fd1b17a2e609dea2956d7c7bef3644368b89196e","sha256:e9b534578b9961a1ad7b684ad2825b8744faefcacaa0227372171626c4a7e1ef"],"state_sha256":"94c5894daac4e422f6c4609173bedf6f5d41d1bbb5092e1e6270fa53873c2bcf"}