{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ATWQWKSG3IIXEJ7QAN6RVVP25Q","short_pith_number":"pith:ATWQWKSG","schema_version":"1.0","canonical_sha256":"04ed0b2a46da117227f0037d1ad5faec0fbd10c2f31d57a7b2034ab116873e67","source":{"kind":"arxiv","id":"2607.21539","version":1},"attestation_state":"computed","paper":{"title":"The Faber-Krahn position of convex bodies and Gaussian measure inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.SP","authors_text":"Dmitry Faifman, Iosif Polterovich","submitted_at":"2026-07-23T17:24:31Z","abstract_excerpt":"We say that a convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. We prove that this position is unique up to orthogonal transformations, answering a question of Schmuckenschlaeger from 2011. This is a corollary of a new log-convexity property of the first eigenvalue under positive definite linear deformations. While the centrally symmetric case follows from the Gaussian B-theorem, the extension to arbitrary convex bodies requires a quantitative analysis of conditioned Brownian motion. As consequences, we obtain a new"},"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":"2607.21539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-07-23T17:24:31Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"aa697111889de1b7e8e7e0e1c445dbc54e777fdcc8c3cebe940e3a1ed2667f1e","abstract_canon_sha256":"e52fe5abc5b6209baf6b2feec0f5f371c54272597b9a508b345b23517102d6bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:38.442182Z","signature_b64":"G8Uxk6XjNVDZx8AgtXH1UF1wFbX6+NHHk2ySVACp3Ij/TIqYNq8itsUxTqFyP7vTU5/buap9Qj42KGmW5KlhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04ed0b2a46da117227f0037d1ad5faec0fbd10c2f31d57a7b2034ab116873e67","last_reissued_at":"2026-07-24T01:24:38.441278Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:38.441278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Faber-Krahn position of convex bodies and Gaussian measure inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.SP","authors_text":"Dmitry Faifman, Iosif Polterovich","submitted_at":"2026-07-23T17:24:31Z","abstract_excerpt":"We say that a convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. We prove that this position is unique up to orthogonal transformations, answering a question of Schmuckenschlaeger from 2011. This is a corollary of a new log-convexity property of the first eigenvalue under positive definite linear deformations. While the centrally symmetric case follows from the Gaussian B-theorem, the extension to arbitrary convex bodies requires a quantitative analysis of conditioned Brownian motion. As consequences, we obtain a new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21539","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/2607.21539/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.21539","created_at":"2026-07-24T01:24:38.441770+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.21539v1","created_at":"2026-07-24T01:24:38.441770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21539","created_at":"2026-07-24T01:24:38.441770+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATWQWKSG3IIX","created_at":"2026-07-24T01:24:38.441770+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATWQWKSG3IIXEJ7Q","created_at":"2026-07-24T01:24:38.441770+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATWQWKSG","created_at":"2026-07-24T01:24:38.441770+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/ATWQWKSG3IIXEJ7QAN6RVVP25Q","json":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q.json","graph_json":"https://pith.science/api/pith-number/ATWQWKSG3IIXEJ7QAN6RVVP25Q/graph.json","events_json":"https://pith.science/api/pith-number/ATWQWKSG3IIXEJ7QAN6RVVP25Q/events.json","paper":"https://pith.science/paper/ATWQWKSG"},"agent_actions":{"view_html":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q","download_json":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q.json","view_paper":"https://pith.science/paper/ATWQWKSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.21539&json=true","fetch_graph":"https://pith.science/api/pith-number/ATWQWKSG3IIXEJ7QAN6RVVP25Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ATWQWKSG3IIXEJ7QAN6RVVP25Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q/action/storage_attestation","attest_author":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q/action/author_attestation","sign_citation":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q/action/citation_signature","submit_replication":"https://pith.science/pith/ATWQWKSG3IIXEJ7QAN6RVVP25Q/action/replication_record"}},"created_at":"2026-07-24T01:24:38.441770+00:00","updated_at":"2026-07-24T01:24:38.441770+00:00"}