{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RJUJJNZAA2XG66VW3YKMLYRE5Y","short_pith_number":"pith:RJUJJNZA","canonical_record":{"source":{"id":"1101.3988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-20T18:31:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d3ac9f9d2425a29f5256a4dd3d2fac939f58f34c2cbd31805e16feb78836c719","abstract_canon_sha256":"5e3bc0da6e94a098551dbca5fad5ff19e975c825bf8545354ef57460d95a1ad1"},"schema_version":"1.0"},"canonical_sha256":"8a6894b72006ae6f7ab6de14c5e224ee2743271781468a66096fec8f19423419","source":{"kind":"arxiv","id":"1101.3988","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3988","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3988v1","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3988","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"RJUJJNZAA2XG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RJUJJNZAA2XG66VW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RJUJJNZA","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RJUJJNZAA2XG66VW3YKMLYRE5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-20T18:31:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d3ac9f9d2425a29f5256a4dd3d2fac939f58f34c2cbd31805e16feb78836c719","abstract_canon_sha256":"5e3bc0da6e94a098551dbca5fad5ff19e975c825bf8545354ef57460d95a1ad1"},"schema_version":"1.0"},"canonical_sha256":"8a6894b72006ae6f7ab6de14c5e224ee2743271781468a66096fec8f19423419","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:20.698825Z","signature_b64":"mPg72tMeBA7H9g4jBEoTZWkW+Zr/q2HUsyeS2IiJmrqjKkr5wWh0BFNheY1H+GUqPEtYhR8rRR+bjX8L6z5FDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a6894b72006ae6f7ab6de14c5e224ee2743271781468a66096fec8f19423419","last_reissued_at":"2026-05-18T04:31:20.698256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:20.698256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3988","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkw1Pg3I8ZXHZ3Avma7EW0i1dUo0AHlSsJUwS5WwU6BUd9MfWF5yXIv15KhkdP9GPOEOg/QReHNGKA+wf1RnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:37:21.967610Z"},"content_sha256":"6af25c55455df9de7b17b90ddf81b653503f1345c6d20de72eeb612b2e214762","schema_version":"1.0","event_id":"sha256:6af25c55455df9de7b17b90ddf81b653503f1345c6d20de72eeb612b2e214762"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RJUJJNZAA2XG66VW3YKMLYRE5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcating extremal domains for the first eigenvalue of the Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Felix Schlenk, Pieralberto Sicbaldi","submitted_at":"2011-01-20T18:31:50Z","abstract_excerpt":"We prove the existence of a smooth family of non-compact domains $Omega_s \\subset R^{n+1}$ bifurcating from the straight cylinder $B^n \\times R$ for which the first eigenfunction of the Laplacian with 0 Dirichlet boundary condition also has constant Neumann data at the boundary. The domains $Omega_s$ are rotationally symmetric and periodic with respect to the R-axis of the cylinder; they are of the form $Omega_s = {(x,t) \\in R^n \\times R \\mid |x| < 1+s \\cos((2\\pi)/T_s t) + O(s^2)}$ where $T_s = T_0 + O(s)$ and T_0 is a positive real number depending on n. For $n \\ge 2$ these domains provide a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3988","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCzpLO6l3I7/hkRsM2DS5PwFq5xttY9Hczvpf2RRlh2MuAEWnf4ZcvEfnHNycX8/uLhM4TnE+fYKbY6+9yXPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:37:21.967953Z"},"content_sha256":"1c04aeaea9776614ed2f5417bc735d5dd5a003e1218c6ffb440f58197c1ded62","schema_version":"1.0","event_id":"sha256:1c04aeaea9776614ed2f5417bc735d5dd5a003e1218c6ffb440f58197c1ded62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/bundle.json","state_url":"https://pith.science/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T04:37:21Z","links":{"resolver":"https://pith.science/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y","bundle":"https://pith.science/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/bundle.json","state":"https://pith.science/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJUJJNZAA2XG66VW3YKMLYRE5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RJUJJNZAA2XG66VW3YKMLYRE5Y","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":"5e3bc0da6e94a098551dbca5fad5ff19e975c825bf8545354ef57460d95a1ad1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-20T18:31:50Z","title_canon_sha256":"d3ac9f9d2425a29f5256a4dd3d2fac939f58f34c2cbd31805e16feb78836c719"},"schema_version":"1.0","source":{"id":"1101.3988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3988","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3988v1","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3988","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"RJUJJNZAA2XG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RJUJJNZAA2XG66VW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RJUJJNZA","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:1c04aeaea9776614ed2f5417bc735d5dd5a003e1218c6ffb440f58197c1ded62","target":"graph","created_at":"2026-05-18T04:31:20Z","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":"We prove the existence of a smooth family of non-compact domains $Omega_s \\subset R^{n+1}$ bifurcating from the straight cylinder $B^n \\times R$ for which the first eigenfunction of the Laplacian with 0 Dirichlet boundary condition also has constant Neumann data at the boundary. The domains $Omega_s$ are rotationally symmetric and periodic with respect to the R-axis of the cylinder; they are of the form $Omega_s = {(x,t) \\in R^n \\times R \\mid |x| < 1+s \\cos((2\\pi)/T_s t) + O(s^2)}$ where $T_s = T_0 + O(s)$ and T_0 is a positive real number depending on n. For $n \\ge 2$ these domains provide a ","authors_text":"Felix Schlenk, Pieralberto Sicbaldi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-20T18:31:50Z","title":"Bifurcating extremal domains for the first eigenvalue of the Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3988","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":"sha256:6af25c55455df9de7b17b90ddf81b653503f1345c6d20de72eeb612b2e214762","target":"record","created_at":"2026-05-18T04:31:20Z","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":"5e3bc0da6e94a098551dbca5fad5ff19e975c825bf8545354ef57460d95a1ad1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-20T18:31:50Z","title_canon_sha256":"d3ac9f9d2425a29f5256a4dd3d2fac939f58f34c2cbd31805e16feb78836c719"},"schema_version":"1.0","source":{"id":"1101.3988","kind":"arxiv","version":1}},"canonical_sha256":"8a6894b72006ae6f7ab6de14c5e224ee2743271781468a66096fec8f19423419","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a6894b72006ae6f7ab6de14c5e224ee2743271781468a66096fec8f19423419","first_computed_at":"2026-05-18T04:31:20.698256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:20.698256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPg72tMeBA7H9g4jBEoTZWkW+Zr/q2HUsyeS2IiJmrqjKkr5wWh0BFNheY1H+GUqPEtYhR8rRR+bjX8L6z5FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:20.698825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6af25c55455df9de7b17b90ddf81b653503f1345c6d20de72eeb612b2e214762","sha256:1c04aeaea9776614ed2f5417bc735d5dd5a003e1218c6ffb440f58197c1ded62"],"state_sha256":"7c264cc988442dbd6b9c01e7861077bb53318749aa8b4c1607f29bce6b0d4990"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJIgiXC0Mg0ar+oYNuoWNWuNlrj79jk4XmDKTx9bPSJrUR0KZ7x6Yo8aD/KklEb0wLTqLAAUKw7Cmb81iA2oCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:37:21.969938Z","bundle_sha256":"e135ea230ed86dcccb2c77689b4186bb91df5016c81c62fc940dd164b6589ab7"}}