{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MMNZQELRNJGLQWMNJT52VN66TG","short_pith_number":"pith:MMNZQELR","schema_version":"1.0","canonical_sha256":"631b9811716a4cb8598d4cfbaab7de99ba5f9a8b2caf9b56732873c1dc6f289d","source":{"kind":"arxiv","id":"1703.02587","version":1},"attestation_state":"computed","paper":{"title":"On the boundary of almost isoperimetric domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MG","math.SP"],"primary_cat":"math.DG","authors_text":"Erwann Aubry, Jean-Fran\\c{c}ois Grosjean","submitted_at":"2017-03-07T20:42:23Z","abstract_excerpt":"We prove that finite perimeter subsets of $\\mathbb{R}^{n+1}$ with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also refine this closeness under some additional a priori integral curvature bounds. As an application, we answer a question raised by B. Colbois concerning the almost extremal hypersurfaces for Chavel's inequality."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.02587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-07T20:42:23Z","cross_cats_sorted":["math.AP","math.MG","math.SP"],"title_canon_sha256":"eb9dc783e079b4b31c8e3339365b291674fb916f4ad8dda26c2f295f4774aea1","abstract_canon_sha256":"ca2268c624358780cfd3863f1c57ab231321613fa01e05736b5b7b2e81f7ae17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:06.085006Z","signature_b64":"1xoKnv91ZtCiKnxN0KS7z7K9TqfrXtQU6S90VVsrCRnXk7L47JvXWdzDeW8PHRkZ3xCOMvjv2nEV7BUiBkDQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"631b9811716a4cb8598d4cfbaab7de99ba5f9a8b2caf9b56732873c1dc6f289d","last_reissued_at":"2026-05-18T00:49:06.084623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:06.084623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the boundary of almost isoperimetric domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MG","math.SP"],"primary_cat":"math.DG","authors_text":"Erwann Aubry, Jean-Fran\\c{c}ois Grosjean","submitted_at":"2017-03-07T20:42:23Z","abstract_excerpt":"We prove that finite perimeter subsets of $\\mathbb{R}^{n+1}$ with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also refine this closeness under some additional a priori integral curvature bounds. As an application, we answer a question raised by B. Colbois concerning the almost extremal hypersurfaces for Chavel's inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02587","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.02587","created_at":"2026-05-18T00:49:06.084681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02587v1","created_at":"2026-05-18T00:49:06.084681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02587","created_at":"2026-05-18T00:49:06.084681+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMNZQELRNJGL","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMNZQELRNJGLQWMN","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMNZQELR","created_at":"2026-05-18T12:31:31.346846+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG","json":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG.json","graph_json":"https://pith.science/api/pith-number/MMNZQELRNJGLQWMNJT52VN66TG/graph.json","events_json":"https://pith.science/api/pith-number/MMNZQELRNJGLQWMNJT52VN66TG/events.json","paper":"https://pith.science/paper/MMNZQELR"},"agent_actions":{"view_html":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG","download_json":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG.json","view_paper":"https://pith.science/paper/MMNZQELR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02587&json=true","fetch_graph":"https://pith.science/api/pith-number/MMNZQELRNJGLQWMNJT52VN66TG/graph.json","fetch_events":"https://pith.science/api/pith-number/MMNZQELRNJGLQWMNJT52VN66TG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG/action/storage_attestation","attest_author":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG/action/author_attestation","sign_citation":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG/action/citation_signature","submit_replication":"https://pith.science/pith/MMNZQELRNJGLQWMNJT52VN66TG/action/replication_record"}},"created_at":"2026-05-18T00:49:06.084681+00:00","updated_at":"2026-05-18T00:49:06.084681+00:00"}