{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KVLULX7BO66FE6O3CUXVBIHXT4","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":"be51e9543ec178235d794bded0e99e819d55a305dd4f974333d02650e1b7b590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-18T22:36:41Z","title_canon_sha256":"a8fb319d1d1b48e60dda41c50358e8e7d924270b821bb03050346fcb4f2a4f79"},"schema_version":"1.0","source":{"id":"1310.5178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5178","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5178v1","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5178","created_at":"2026-05-18T03:09:47Z"},{"alias_kind":"pith_short_12","alias_value":"KVLULX7BO66F","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KVLULX7BO66FE6O3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KVLULX7B","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:364299db1f8d042228256c29e41a8590fecf024f104d77418c6e63c3a88ae8e6","target":"graph","created_at":"2026-05-18T03:09:47Z","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":"In this work we are concerned with the multiplicity of the eigenvalues of the Neumann Laplacian in regions of Rn which are invariant under the natural action of a compact subgroup G of O(n). We give a partial positive answer (in the Neumann case) to a conjecture of V. Arnold [1] on the transversality of the transformation given by the Dirichlet integral to the stratification in the space of quadratic forms according to the multiplicities of the eigenvalues. We show, for some classes of subgroups of O(n) that, generically in the set of G-invariant, C2-regions, the action is irreducible in each ","authors_text":"Ant\\^onio L. Pereira, Marcus A. M. Marrocos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-18T22:36:41Z","title":"Eigenvalues of the Neumann Laplacian in symmetric regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5178","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":"sha256:4c925da917f2a104f8f8a51f2d0d5815f6e1179ed9d1977712d7232042b7bd8e","target":"record","created_at":"2026-05-18T03:09:47Z","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":"be51e9543ec178235d794bded0e99e819d55a305dd4f974333d02650e1b7b590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-18T22:36:41Z","title_canon_sha256":"a8fb319d1d1b48e60dda41c50358e8e7d924270b821bb03050346fcb4f2a4f79"},"schema_version":"1.0","source":{"id":"1310.5178","kind":"arxiv","version":1}},"canonical_sha256":"555745dfe177bc5279db152f50a0f79f19605e08b3f40251815ce2fc0379b8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"555745dfe177bc5279db152f50a0f79f19605e08b3f40251815ce2fc0379b8df","first_computed_at":"2026-05-18T03:09:47.060695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:47.060695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyqweIuT2lSiXwxMZ9EKvvy61oXavfGtAnBB1OYCpH5Jfwee/t6qatvUuCW5jWQaDqFfGZvfYbLlQckKcFjKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:47.061462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c925da917f2a104f8f8a51f2d0d5815f6e1179ed9d1977712d7232042b7bd8e","sha256:364299db1f8d042228256c29e41a8590fecf024f104d77418c6e63c3a88ae8e6"],"state_sha256":"65df137ebb12a62a81fef9fce7ca1293424ea7dc18110f5df9c1a38fbd369d88"}