{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QZBYIB2LFZIOMRZEYB2Z7SRD5O","short_pith_number":"pith:QZBYIB2L","schema_version":"1.0","canonical_sha256":"864384074b2e50e64724c0759fca23eb9c230bca49222908b682a6b9e423184b","source":{"kind":"arxiv","id":"1504.04961","version":1},"attestation_state":"computed","paper":{"title":"An isoperimetric inequality for Gauss--like product measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Mercaldo, Francesco Chiacchio, Friedemann Brock","submitted_at":"2015-04-20T08:09:14Z","abstract_excerpt":"This paper deals with various questions related to the isoperimetic problem for smooth positive measure $d\\mu = \\varphi(x)dx$, with $x \\in \\Omega \\subset \\mathbb{R}^N$. Firstly we find some necessary conditions on the density of the measure $ \\varphi(x)$ that render the intersection of half spaces with $\\Omega$ a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a wide class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value prob"},"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":"1504.04961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-20T08:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"6fd0efd24fe36ede9a65e157af108697eedb0329608efbfd679b065c6d364c8e","abstract_canon_sha256":"3182298eabb59cefd1b78f04cf425ba0af6b976ac3a46c0626a37adb224a8168"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:23.101961Z","signature_b64":"/tjS5CeLZ6iHhwaiZxoLbGPlNYoIwXcwwGcLPt269cJ05WtyiON/wobGKrSWk+AtvpqfH5jK/IE/iRjyepQhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"864384074b2e50e64724c0759fca23eb9c230bca49222908b682a6b9e423184b","last_reissued_at":"2026-05-18T02:18:23.101058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:23.101058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An isoperimetric inequality for Gauss--like product measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Mercaldo, Francesco Chiacchio, Friedemann Brock","submitted_at":"2015-04-20T08:09:14Z","abstract_excerpt":"This paper deals with various questions related to the isoperimetic problem for smooth positive measure $d\\mu = \\varphi(x)dx$, with $x \\in \\Omega \\subset \\mathbb{R}^N$. Firstly we find some necessary conditions on the density of the measure $ \\varphi(x)$ that render the intersection of half spaces with $\\Omega$ a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a wide class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04961","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":"1504.04961","created_at":"2026-05-18T02:18:23.101249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04961v1","created_at":"2026-05-18T02:18:23.101249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04961","created_at":"2026-05-18T02:18:23.101249+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZBYIB2LFZIO","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZBYIB2LFZIOMRZE","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZBYIB2L","created_at":"2026-05-18T12:29:39.896362+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/QZBYIB2LFZIOMRZEYB2Z7SRD5O","json":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O.json","graph_json":"https://pith.science/api/pith-number/QZBYIB2LFZIOMRZEYB2Z7SRD5O/graph.json","events_json":"https://pith.science/api/pith-number/QZBYIB2LFZIOMRZEYB2Z7SRD5O/events.json","paper":"https://pith.science/paper/QZBYIB2L"},"agent_actions":{"view_html":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O","download_json":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O.json","view_paper":"https://pith.science/paper/QZBYIB2L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04961&json=true","fetch_graph":"https://pith.science/api/pith-number/QZBYIB2LFZIOMRZEYB2Z7SRD5O/graph.json","fetch_events":"https://pith.science/api/pith-number/QZBYIB2LFZIOMRZEYB2Z7SRD5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O/action/storage_attestation","attest_author":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O/action/author_attestation","sign_citation":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O/action/citation_signature","submit_replication":"https://pith.science/pith/QZBYIB2LFZIOMRZEYB2Z7SRD5O/action/replication_record"}},"created_at":"2026-05-18T02:18:23.101249+00:00","updated_at":"2026-05-18T02:18:23.101249+00:00"}