{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:K6F5ZBRHPCEQ3JMROYJKXWN23A","short_pith_number":"pith:K6F5ZBRH","schema_version":"1.0","canonical_sha256":"578bdc862778890da5917612abd9bad804baaa7c1cb2d836ce590f3a5135d769","source":{"kind":"arxiv","id":"1604.01524","version":1},"attestation_state":"computed","paper":{"title":"Poincar\\'e trace inequalities in $BV(\\mathbb B^n)$ with nonstandard normalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrea Cianchi, Carlo Nitsch, Cristina Trombetti, Vincenzo Ferone","submitted_at":"2016-04-06T08:00:30Z","abstract_excerpt":"Extremal functions are exhibited in Poincar\\'e trace inequalities for functions of bounded variation in the unit ball ${\\mathbb B}^n$ of the $n$-dimensional Euclidean space ${\\mathbb R}^n$. Trial functions are subject to either a vanishing mean value condition, or a vanishing median condition in the whole of ${\\mathbb B}^n$, instead of just on $\\partial {\\mathbb B}^n$, as customary. The extremals in question take a different form, depending on the constraint imposed. In particular, under the latter constraint, unusually shaped extremal functions appear. A key step in our approach is a characte"},"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":"1604.01524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-06T08:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"5c2e8f5d50380f10872a537bdb71e1f77ee316b0906b115978ebce23115c4148","abstract_canon_sha256":"1bf00fd09bbba905753882ed7fe0fdace479e45035d77f4898d9c09b73829a85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:36.223522Z","signature_b64":"ZayQAiqxYFENABqwb9691NXkov/vxnC63YmtyP7hBWpoKLpMGZ3xZ0BKNFdws7A0eBC8oRA7i19jTLvqrjoyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578bdc862778890da5917612abd9bad804baaa7c1cb2d836ce590f3a5135d769","last_reissued_at":"2026-05-18T01:17:36.222935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:36.222935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e trace inequalities in $BV(\\mathbb B^n)$ with nonstandard normalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrea Cianchi, Carlo Nitsch, Cristina Trombetti, Vincenzo Ferone","submitted_at":"2016-04-06T08:00:30Z","abstract_excerpt":"Extremal functions are exhibited in Poincar\\'e trace inequalities for functions of bounded variation in the unit ball ${\\mathbb B}^n$ of the $n$-dimensional Euclidean space ${\\mathbb R}^n$. Trial functions are subject to either a vanishing mean value condition, or a vanishing median condition in the whole of ${\\mathbb B}^n$, instead of just on $\\partial {\\mathbb B}^n$, as customary. The extremals in question take a different form, depending on the constraint imposed. In particular, under the latter constraint, unusually shaped extremal functions appear. A key step in our approach is a characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01524","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":"1604.01524","created_at":"2026-05-18T01:17:36.223039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.01524v1","created_at":"2026-05-18T01:17:36.223039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01524","created_at":"2026-05-18T01:17:36.223039+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6F5ZBRHPCEQ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6F5ZBRHPCEQ3JMR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6F5ZBRH","created_at":"2026-05-18T12:30:25.849896+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/K6F5ZBRHPCEQ3JMROYJKXWN23A","json":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A.json","graph_json":"https://pith.science/api/pith-number/K6F5ZBRHPCEQ3JMROYJKXWN23A/graph.json","events_json":"https://pith.science/api/pith-number/K6F5ZBRHPCEQ3JMROYJKXWN23A/events.json","paper":"https://pith.science/paper/K6F5ZBRH"},"agent_actions":{"view_html":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A","download_json":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A.json","view_paper":"https://pith.science/paper/K6F5ZBRH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.01524&json=true","fetch_graph":"https://pith.science/api/pith-number/K6F5ZBRHPCEQ3JMROYJKXWN23A/graph.json","fetch_events":"https://pith.science/api/pith-number/K6F5ZBRHPCEQ3JMROYJKXWN23A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A/action/storage_attestation","attest_author":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A/action/author_attestation","sign_citation":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A/action/citation_signature","submit_replication":"https://pith.science/pith/K6F5ZBRHPCEQ3JMROYJKXWN23A/action/replication_record"}},"created_at":"2026-05-18T01:17:36.223039+00:00","updated_at":"2026-05-18T01:17:36.223039+00:00"}