{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TD2GKBKL7CVD3HMCRIAMZ3WWC7","short_pith_number":"pith:TD2GKBKL","canonical_record":{"source":{"id":"2304.11297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-22T02:45:34Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"7d1a5d259bb61ba60aed54b8c211770c5bffdfe7a0c2a68e3d39e69221e8ef42","abstract_canon_sha256":"9a445d10bb4b1ac8cc8e2272479ae693a37d0851e063e5033005d11d8be94941"},"schema_version":"1.0"},"canonical_sha256":"98f465054bf8aa3d9d828a00cceed617d1225aa48a48f005185bfae948105534","source":{"kind":"arxiv","id":"2304.11297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.11297","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"2304.11297v1","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.11297","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"TD2GKBKL7CVD","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_16","alias_value":"TD2GKBKL7CVD3HMC","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_8","alias_value":"TD2GKBKL","created_at":"2026-07-05T06:03:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TD2GKBKL7CVD3HMCRIAMZ3WWC7","target":"record","payload":{"canonical_record":{"source":{"id":"2304.11297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-22T02:45:34Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"7d1a5d259bb61ba60aed54b8c211770c5bffdfe7a0c2a68e3d39e69221e8ef42","abstract_canon_sha256":"9a445d10bb4b1ac8cc8e2272479ae693a37d0851e063e5033005d11d8be94941"},"schema_version":"1.0"},"canonical_sha256":"98f465054bf8aa3d9d828a00cceed617d1225aa48a48f005185bfae948105534","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:30.929233Z","signature_b64":"0gUbRKgLKon/cWgvabR5Wf66IIvNxDcqfW9PXEFlIrrK/geGit+hqa+iFmtcYb1DJdwrMaRILu4EO7GN3A+pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98f465054bf8aa3d9d828a00cceed617d1225aa48a48f005185bfae948105534","last_reissued_at":"2026-07-05T06:03:30.928775Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:30.928775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.11297","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":"2026-07-05T06:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zp+tibsv2UlwBUFzHsQniHwzTs9YWTbiZfCicSM4lk+8zYPYoJJA9l66fHlj2Ry5ehrdBsxHA7HZ2GA6r2inAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:31:43.072536Z"},"content_sha256":"10608fda00cbe9fa8153c210a6d417eb015b6c1cbe136a2957de63ab10ed4adf","schema_version":"1.0","event_id":"sha256:10608fda00cbe9fa8153c210a6d417eb015b6c1cbe136a2957de63ab10ed4adf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TD2GKBKL7CVD3HMCRIAMZ3WWC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp bounds for the first two eigenvalues of an exterior Steklov eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Changwei Xiong","submitted_at":"2023-04-22T02:45:34Z","abstract_excerpt":"Let $U\\subset \\mathbb{R}^n$ ($n\\geq 3$) be an exterior Euclidean domain with smooth boundary $\\partial U$. We consider the Steklov eigenvalue problem on $U$. First we derive a sharp lower bound for the first eigenvalue in terms of the support function and the distance function to the origin of $\\partial U$. Second under various geometric conditions on $\\partial U$ we obtain sharp upper bounds for the first eigenvalue. Along the proof, we get a sharp upper bound for the capacity of $\\partial U$ when $n=3$ and $\\partial U$ is connected. Last we also discuss an upper bound for the second eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.11297","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.11297/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VD3TF2NDZUwdzYBwRALozvqVfNuaKSzjRHQ8W0GQbN76dsVcUkIusFjK0vwYogj4ubxxWEM5a7m07eaAo/IaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:31:43.073078Z"},"content_sha256":"7bd5455795ff24ce7dd07fc1850b3137240a5a520dfbf267d44a33b2aed7b501","schema_version":"1.0","event_id":"sha256:7bd5455795ff24ce7dd07fc1850b3137240a5a520dfbf267d44a33b2aed7b501"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/bundle.json","state_url":"https://pith.science/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/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":"2026-08-15T04:31:43Z","links":{"resolver":"https://pith.science/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7","bundle":"https://pith.science/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/bundle.json","state":"https://pith.science/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TD2GKBKL7CVD3HMCRIAMZ3WWC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TD2GKBKL7CVD3HMCRIAMZ3WWC7","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":"9a445d10bb4b1ac8cc8e2272479ae693a37d0851e063e5033005d11d8be94941","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-22T02:45:34Z","title_canon_sha256":"7d1a5d259bb61ba60aed54b8c211770c5bffdfe7a0c2a68e3d39e69221e8ef42"},"schema_version":"1.0","source":{"id":"2304.11297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.11297","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"2304.11297v1","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.11297","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"TD2GKBKL7CVD","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_16","alias_value":"TD2GKBKL7CVD3HMC","created_at":"2026-07-05T06:03:30Z"},{"alias_kind":"pith_short_8","alias_value":"TD2GKBKL","created_at":"2026-07-05T06:03:30Z"}],"graph_snapshots":[{"event_id":"sha256:7bd5455795ff24ce7dd07fc1850b3137240a5a520dfbf267d44a33b2aed7b501","target":"graph","created_at":"2026-07-05T06:03:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.11297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $U\\subset \\mathbb{R}^n$ ($n\\geq 3$) be an exterior Euclidean domain with smooth boundary $\\partial U$. We consider the Steklov eigenvalue problem on $U$. First we derive a sharp lower bound for the first eigenvalue in terms of the support function and the distance function to the origin of $\\partial U$. Second under various geometric conditions on $\\partial U$ we obtain sharp upper bounds for the first eigenvalue. Along the proof, we get a sharp upper bound for the capacity of $\\partial U$ when $n=3$ and $\\partial U$ is connected. Last we also discuss an upper bound for the second eigenval","authors_text":"Changwei Xiong","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-22T02:45:34Z","title":"Sharp bounds for the first two eigenvalues of an exterior Steklov eigenvalue problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.11297","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":"sha256:10608fda00cbe9fa8153c210a6d417eb015b6c1cbe136a2957de63ab10ed4adf","target":"record","created_at":"2026-07-05T06:03:30Z","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":"9a445d10bb4b1ac8cc8e2272479ae693a37d0851e063e5033005d11d8be94941","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-22T02:45:34Z","title_canon_sha256":"7d1a5d259bb61ba60aed54b8c211770c5bffdfe7a0c2a68e3d39e69221e8ef42"},"schema_version":"1.0","source":{"id":"2304.11297","kind":"arxiv","version":1}},"canonical_sha256":"98f465054bf8aa3d9d828a00cceed617d1225aa48a48f005185bfae948105534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98f465054bf8aa3d9d828a00cceed617d1225aa48a48f005185bfae948105534","first_computed_at":"2026-07-05T06:03:30.928775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:30.928775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0gUbRKgLKon/cWgvabR5Wf66IIvNxDcqfW9PXEFlIrrK/geGit+hqa+iFmtcYb1DJdwrMaRILu4EO7GN3A+pCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:30.929233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.11297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10608fda00cbe9fa8153c210a6d417eb015b6c1cbe136a2957de63ab10ed4adf","sha256:7bd5455795ff24ce7dd07fc1850b3137240a5a520dfbf267d44a33b2aed7b501"],"state_sha256":"39d8ade9ae386f416d88a2d7b6253de35f5977509a9e6596a65354ee4c9d62cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vmk8Boh2PXIEBpp9IxE2lTMa/qC5VYlnESUyGPjA712FcNxzl+ZqLTpB5wKYg2NbhbQbiSlySW1F7Nj4uDWpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T04:31:43.077460Z","bundle_sha256":"69745043d974f769f25c8eadd0b1b8f7948ef3edfd69499661b386a705c4e438"}}