{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:X2CGALXZPCENA5VRBWISJBZ2WV","short_pith_number":"pith:X2CGALXZ","canonical_record":{"source":{"id":"1208.3396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-16T15:18:04Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"800750f2d2497088e2e23c8b4fcf687a8b045cb696e65ee4d488ac49ac813f40","abstract_canon_sha256":"718b202884b60e47b66eb7320b5726183cc7dbd6fd995e2dbc47e624583b9e12"},"schema_version":"1.0"},"canonical_sha256":"be84602ef97888d076b10d9124873ab5631725b1839113620c9c9c93035611a2","source":{"kind":"arxiv","id":"1208.3396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3396","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3396v1","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3396","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"X2CGALXZPCEN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X2CGALXZPCENA5VR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X2CGALXZ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:X2CGALXZPCENA5VRBWISJBZ2WV","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-16T15:18:04Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"800750f2d2497088e2e23c8b4fcf687a8b045cb696e65ee4d488ac49ac813f40","abstract_canon_sha256":"718b202884b60e47b66eb7320b5726183cc7dbd6fd995e2dbc47e624583b9e12"},"schema_version":"1.0"},"canonical_sha256":"be84602ef97888d076b10d9124873ab5631725b1839113620c9c9c93035611a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.282597Z","signature_b64":"MTHYL3MPsYd9P8PGuJnAgh6whq+fG+7I0q4aL2bTjoM4y3MTC/YHDCFICfZd6kADOKJ6k4uHJVOteAaEqcbRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be84602ef97888d076b10d9124873ab5631725b1839113620c9c9c93035611a2","last_reissued_at":"2026-05-18T03:38:23.282084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.282084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3396","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQYoiDNSSf8itj5Xy9mSrQeeu+ZrM07Exwr/jmcVZLhgVQyjQM1X/aQCYxYuJaAkJ4RKvHu9Xks5lCEXQp+TBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:25:38.745713Z"},"content_sha256":"932801ea803c8cf88bca87fcfdcf57c1aed83f7ae7b7c27774d1a0ae2aa8d5c4","schema_version":"1.0","event_id":"sha256:932801ea803c8cf88bca87fcfdcf57c1aed83f7ae7b7c27774d1a0ae2aa8d5c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:X2CGALXZPCENA5VRBWISJBZ2WV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the lowest eigenvalue of Laplace operators with mixed boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Hynek Kovarik","submitted_at":"2012-08-16T15:18:04Z","abstract_excerpt":"In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3396","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M2cpcl8Jze4g2AG1hhH+cYutTL7NUIjm9z9nD8dVTsfuNdyg1yLCjJW8bbLXyiCpVjv9AwxP0ctUzGsLEih/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:25:38.746063Z"},"content_sha256":"71f366a4be36c9f743add9bebae725c97f3357746bc31b2a19207d8a811b2b80","schema_version":"1.0","event_id":"sha256:71f366a4be36c9f743add9bebae725c97f3357746bc31b2a19207d8a811b2b80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2CGALXZPCENA5VRBWISJBZ2WV/bundle.json","state_url":"https://pith.science/pith/X2CGALXZPCENA5VRBWISJBZ2WV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2CGALXZPCENA5VRBWISJBZ2WV/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":"2026-06-02T19:25:38Z","links":{"resolver":"https://pith.science/pith/X2CGALXZPCENA5VRBWISJBZ2WV","bundle":"https://pith.science/pith/X2CGALXZPCENA5VRBWISJBZ2WV/bundle.json","state":"https://pith.science/pith/X2CGALXZPCENA5VRBWISJBZ2WV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2CGALXZPCENA5VRBWISJBZ2WV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X2CGALXZPCENA5VRBWISJBZ2WV","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":"718b202884b60e47b66eb7320b5726183cc7dbd6fd995e2dbc47e624583b9e12","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-16T15:18:04Z","title_canon_sha256":"800750f2d2497088e2e23c8b4fcf687a8b045cb696e65ee4d488ac49ac813f40"},"schema_version":"1.0","source":{"id":"1208.3396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3396","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3396v1","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3396","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"X2CGALXZPCEN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X2CGALXZPCENA5VR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X2CGALXZ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:71f366a4be36c9f743add9bebae725c97f3357746bc31b2a19207d8a811b2b80","target":"graph","created_at":"2026-05-18T03:38:23Z","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 paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions.","authors_text":"Hynek Kovarik","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-16T15:18:04Z","title":"On the lowest eigenvalue of Laplace operators with mixed boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3396","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":"sha256:932801ea803c8cf88bca87fcfdcf57c1aed83f7ae7b7c27774d1a0ae2aa8d5c4","target":"record","created_at":"2026-05-18T03:38:23Z","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":"718b202884b60e47b66eb7320b5726183cc7dbd6fd995e2dbc47e624583b9e12","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-16T15:18:04Z","title_canon_sha256":"800750f2d2497088e2e23c8b4fcf687a8b045cb696e65ee4d488ac49ac813f40"},"schema_version":"1.0","source":{"id":"1208.3396","kind":"arxiv","version":1}},"canonical_sha256":"be84602ef97888d076b10d9124873ab5631725b1839113620c9c9c93035611a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be84602ef97888d076b10d9124873ab5631725b1839113620c9c9c93035611a2","first_computed_at":"2026-05-18T03:38:23.282084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.282084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MTHYL3MPsYd9P8PGuJnAgh6whq+fG+7I0q4aL2bTjoM4y3MTC/YHDCFICfZd6kADOKJ6k4uHJVOteAaEqcbRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.282597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932801ea803c8cf88bca87fcfdcf57c1aed83f7ae7b7c27774d1a0ae2aa8d5c4","sha256:71f366a4be36c9f743add9bebae725c97f3357746bc31b2a19207d8a811b2b80"],"state_sha256":"df04ca1f0e812fc3cbed7c71215f04ce95e4a52c3dba65707c949f823e67cc01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GECEhQwcNoBw15rMOPL6tdYwDT6lN+pPSHWd5YKIK4Ogpi7/DG6bXe04dMjCjMCDUVDNXq4pJHPWO3sam1c4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:25:38.748017Z","bundle_sha256":"a56d4c18570e86a57d983f8270c7f4a000a3b2500cdca97bf6bd4d68d9b0849d"}}