{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OODOFAECBHIJ7HGZRZKF53ASMJ","short_pith_number":"pith:OODOFAEC","canonical_record":{"source":{"id":"1705.08643","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T07:47:45Z","cross_cats_sorted":["math.DG","math.PR"],"title_canon_sha256":"3c68ec3c966cc98ac66c19db43d8131ce95ec5985e8350b06f8a1723ada1a194","abstract_canon_sha256":"353e9593f83f252c67b5c0dfe5b488bbdcaa6a7f16b52ad94a413ef3e2809c76"},"schema_version":"1.0"},"canonical_sha256":"7386e2808209d09f9cd98e545eec126277464cb0d66d225ced69c77390d71ba1","source":{"kind":"arxiv","id":"1705.08643","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08643","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08643v3","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08643","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"OODOFAECBHIJ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OODOFAECBHIJ7HGZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OODOFAEC","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OODOFAECBHIJ7HGZRZKF53ASMJ","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08643","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T07:47:45Z","cross_cats_sorted":["math.DG","math.PR"],"title_canon_sha256":"3c68ec3c966cc98ac66c19db43d8131ce95ec5985e8350b06f8a1723ada1a194","abstract_canon_sha256":"353e9593f83f252c67b5c0dfe5b488bbdcaa6a7f16b52ad94a413ef3e2809c76"},"schema_version":"1.0"},"canonical_sha256":"7386e2808209d09f9cd98e545eec126277464cb0d66d225ced69c77390d71ba1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:32.108006Z","signature_b64":"Y1RJZKg0hJDkvlxUpQelJy4NnKVGRoIasNdbIxMuE1sQKqFaZtQQMBQOb7HPZODYCvnhO2PrTFZ4nAgPTj56BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7386e2808209d09f9cd98e545eec126277464cb0d66d225ced69c77390d71ba1","last_reissued_at":"2026-05-18T00:28:32.107155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:32.107155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08643","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5FIm9ibfqQ7yvM3PLtqFXHXk06c+YAxYTa9qDz10Ot4fWR8wKOoQdZCIH0XUCJY3Awv70Rkn/AJ8m78jS0KCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:20:23.104866Z"},"content_sha256":"3d7b6e519eac5989e473e8b9987c88a8814537b2d7e42d281ed91ed8fdb12050","schema_version":"1.0","event_id":"sha256:3d7b6e519eac5989e473e8b9987c88a8814537b2d7e42d281ed91ed8fdb12050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OODOFAECBHIJ7HGZRZKF53ASMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order Cheeger inequalities for Steklov eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.PR"],"primary_cat":"math.SP","authors_text":"Asma Hassannezhad, Laurent Miclo","submitted_at":"2017-05-24T07:47:45Z","abstract_excerpt":"We prove a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Steklov eigenvalues. In particular it extends the Cheeger type inequality for the first nonzero Steklov eigenvalue previously studied by Escobar in 1997 and by Jammes in 2015 to higher order Steklov eigenvalues. The technique we develop to get this lower bound is based on considerin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08643","kind":"arxiv","version":3},"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":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqxdGs1m4SYNtkoDEWE3Q7fjZVmns/3hkwJHG+u6tHDmTigqSEPXG8CxWfTsbKp3Ns2mr4qQOo/j+T/wb82JBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:20:23.105216Z"},"content_sha256":"188a32cd877aa6751dac668529ff3a3f9a97c80d6f9cd297e47c4f145ac67269","schema_version":"1.0","event_id":"sha256:188a32cd877aa6751dac668529ff3a3f9a97c80d6f9cd297e47c4f145ac67269"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/bundle.json","state_url":"https://pith.science/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/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":"2026-06-25T09:20:23Z","links":{"resolver":"https://pith.science/pith/OODOFAECBHIJ7HGZRZKF53ASMJ","bundle":"https://pith.science/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/bundle.json","state":"https://pith.science/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OODOFAECBHIJ7HGZRZKF53ASMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OODOFAECBHIJ7HGZRZKF53ASMJ","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":"353e9593f83f252c67b5c0dfe5b488bbdcaa6a7f16b52ad94a413ef3e2809c76","cross_cats_sorted":["math.DG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T07:47:45Z","title_canon_sha256":"3c68ec3c966cc98ac66c19db43d8131ce95ec5985e8350b06f8a1723ada1a194"},"schema_version":"1.0","source":{"id":"1705.08643","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08643","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08643v3","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08643","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"OODOFAECBHIJ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OODOFAECBHIJ7HGZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OODOFAEC","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:188a32cd877aa6751dac668529ff3a3f9a97c80d6f9cd297e47c4f145ac67269","target":"graph","created_at":"2026-05-18T00:28:32Z","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 a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Steklov eigenvalues. In particular it extends the Cheeger type inequality for the first nonzero Steklov eigenvalue previously studied by Escobar in 1997 and by Jammes in 2015 to higher order Steklov eigenvalues. The technique we develop to get this lower bound is based on considerin","authors_text":"Asma Hassannezhad, Laurent Miclo","cross_cats":["math.DG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T07:47:45Z","title":"Higher order Cheeger inequalities for Steklov eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08643","kind":"arxiv","version":3},"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":"sha256:3d7b6e519eac5989e473e8b9987c88a8814537b2d7e42d281ed91ed8fdb12050","target":"record","created_at":"2026-05-18T00:28:32Z","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":"353e9593f83f252c67b5c0dfe5b488bbdcaa6a7f16b52ad94a413ef3e2809c76","cross_cats_sorted":["math.DG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T07:47:45Z","title_canon_sha256":"3c68ec3c966cc98ac66c19db43d8131ce95ec5985e8350b06f8a1723ada1a194"},"schema_version":"1.0","source":{"id":"1705.08643","kind":"arxiv","version":3}},"canonical_sha256":"7386e2808209d09f9cd98e545eec126277464cb0d66d225ced69c77390d71ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7386e2808209d09f9cd98e545eec126277464cb0d66d225ced69c77390d71ba1","first_computed_at":"2026-05-18T00:28:32.107155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:32.107155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y1RJZKg0hJDkvlxUpQelJy4NnKVGRoIasNdbIxMuE1sQKqFaZtQQMBQOb7HPZODYCvnhO2PrTFZ4nAgPTj56BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:32.108006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08643","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d7b6e519eac5989e473e8b9987c88a8814537b2d7e42d281ed91ed8fdb12050","sha256:188a32cd877aa6751dac668529ff3a3f9a97c80d6f9cd297e47c4f145ac67269"],"state_sha256":"bc30dfa4a389069a06c5e8404ce3187d88b8b51b61159fa3252773b56b00f2b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7LSvkgVu9XOj0PLyGqfsL+MawkcopGqlbKkAbg6d3QH8JFDf2lmPTSdT7vaX0N+B3RzCsSu0vGmkqC9iO+uAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:20:23.107197Z","bundle_sha256":"efe404b463114630d85ae6e0f13b6931bc3a1b559cbd27e69cc67c88e9205a35"}}