{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LYMTK77PAT6JHMUOCO76X273AD","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":"8c72fc508f48811d82e6b35b1755d7c3c60f65000b4322588dc00b6f8ecb5a45","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T11:46:06Z","title_canon_sha256":"f589edb16f047df5433975edd589638b10f58119e4e8a7b5221a8d90ffc6e3e9"},"schema_version":"1.0","source":{"id":"1706.02138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02138","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02138v1","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02138","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"LYMTK77PAT6J","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LYMTK77PAT6JHMUO","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LYMTK77P","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:1a871741d28b262f28bdd65c856cc755cfe4a1161593e364c3b3b7271a97ebb9","target":"graph","created_at":"2026-05-18T00:42:49Z","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":"Let $\\Omega \\subset \\mathbb{R}^n$ be a bounded domain satisfying a Hayman-type asymmetry condition, and let $ D $ be an arbitrary bounded domain referred to as \"obstacle\". We are interested in the behaviour of the first Dirichlet eigenvalue $ \\lambda_1(\\Omega \\setminus (x+D)) $. First, we prove an upper bound on $ \\lambda_1(\\Omega \\setminus (x+D)) $ in terms of the distance of the set $ x+D $ to the set of maximum points $ x_0 $ of the first Dirichlet ground state $ \\phi_{\\lambda_1} > 0 $ of $ \\Omega $. In short, a direct corollary is that if \\begin{equation} \\mu_\\Omega := \\max_{x}\\lambda_1(\\O","authors_text":"Bogdan Georgiev, Mayukh Mukherjee","cross_cats":["math.OC","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T11:46:06Z","title":"On maximizing the fundamental frequency of the complement of an obstacle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02138","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:dd02f4950021b59080ae682b31fbe806290c64dee645d9c88ca8d2dd6f0150f9","target":"record","created_at":"2026-05-18T00:42:49Z","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":"8c72fc508f48811d82e6b35b1755d7c3c60f65000b4322588dc00b6f8ecb5a45","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-07T11:46:06Z","title_canon_sha256":"f589edb16f047df5433975edd589638b10f58119e4e8a7b5221a8d90ffc6e3e9"},"schema_version":"1.0","source":{"id":"1706.02138","kind":"arxiv","version":1}},"canonical_sha256":"5e19357fef04fc93b28e13bfebebfb00c04b29aeb354dbaec4832399d592f37c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e19357fef04fc93b28e13bfebebfb00c04b29aeb354dbaec4832399d592f37c","first_computed_at":"2026-05-18T00:42:49.882804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:49.882804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"garj5K7vKCv02JIv8+dz/foKf5LiAi7eL5Ftnj5fkHlAB9SbRHyIJwERpby/A6TzyCfgXzG9xrXMhaTZ4dy2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:49.883472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd02f4950021b59080ae682b31fbe806290c64dee645d9c88ca8d2dd6f0150f9","sha256:1a871741d28b262f28bdd65c856cc755cfe4a1161593e364c3b3b7271a97ebb9"],"state_sha256":"2a68bcb7fa786367c7bf5ce778d81960b72fa6e40c71c07ada789b3d4eb43396"}