{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7R3RWVFVHMFC6V27GX3EHGQSXZ","short_pith_number":"pith:7R3RWVFV","schema_version":"1.0","canonical_sha256":"fc771b54b53b0a2f575f35f6439a12be7e148d0509c4f72842330c11fc2ca0f6","source":{"kind":"arxiv","id":"2605.15849","version":1},"attestation_state":"computed","paper":{"title":"Anisotropic gradient rearrangement of BV functions and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gloria Paoli, Yabo Yang","submitted_at":"2026-05-15T11:01:39Z","abstract_excerpt":"In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in [Amato-Gentile-Nitsch-Trombetti, 2024] by separating the absolutely continuous part of the anisotropic gradient from its singular part. Our main result is an $L^1$ comparison between the function and its anisotropic symmetrization. Moreover, as an application, we\n  derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity."},"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":"2605.15849","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T11:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"96486b4c141efe8bb91bef961b68495fc4d12a60dc44e8875d6f618627de3301","abstract_canon_sha256":"f61f4a9a2b94a4dc63dc79b74184fc1847c403bde74911de2473174f677a70ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:21.772961Z","signature_b64":"jc9UCgvaOHSGUioK4Wzf9uKu7aUGJPcy5UyYDJWVybjakGTh3Ku0CLoNkVphGfZ+uuzcWcdx5RwqTeDDeSSjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc771b54b53b0a2f575f35f6439a12be7e148d0509c4f72842330c11fc2ca0f6","last_reissued_at":"2026-05-20T00:01:21.772136Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:21.772136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anisotropic gradient rearrangement of BV functions and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gloria Paoli, Yabo Yang","submitted_at":"2026-05-15T11:01:39Z","abstract_excerpt":"In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in [Amato-Gentile-Nitsch-Trombetti, 2024] by separating the absolutely continuous part of the anisotropic gradient from its singular part. Our main result is an $L^1$ comparison between the function and its anisotropic symmetrization. Moreover, as an application, we\n  derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15849","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/2605.15849/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.708746Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.825039Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"42728cf14a41703be5a60578e6b8907c8fce5703e1fc2dbcac3796b493165050"},"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":"2605.15849","created_at":"2026-05-20T00:01:21.772267+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.15849v1","created_at":"2026-05-20T00:01:21.772267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15849","created_at":"2026-05-20T00:01:21.772267+00:00"},{"alias_kind":"pith_short_12","alias_value":"7R3RWVFVHMFC","created_at":"2026-05-20T00:01:21.772267+00:00"},{"alias_kind":"pith_short_16","alias_value":"7R3RWVFVHMFC6V27","created_at":"2026-05-20T00:01:21.772267+00:00"},{"alias_kind":"pith_short_8","alias_value":"7R3RWVFV","created_at":"2026-05-20T00:01:21.772267+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/7R3RWVFVHMFC6V27GX3EHGQSXZ","json":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ.json","graph_json":"https://pith.science/api/pith-number/7R3RWVFVHMFC6V27GX3EHGQSXZ/graph.json","events_json":"https://pith.science/api/pith-number/7R3RWVFVHMFC6V27GX3EHGQSXZ/events.json","paper":"https://pith.science/paper/7R3RWVFV"},"agent_actions":{"view_html":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ","download_json":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ.json","view_paper":"https://pith.science/paper/7R3RWVFV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.15849&json=true","fetch_graph":"https://pith.science/api/pith-number/7R3RWVFVHMFC6V27GX3EHGQSXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/7R3RWVFVHMFC6V27GX3EHGQSXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ/action/storage_attestation","attest_author":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ/action/author_attestation","sign_citation":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ/action/citation_signature","submit_replication":"https://pith.science/pith/7R3RWVFVHMFC6V27GX3EHGQSXZ/action/replication_record"}},"created_at":"2026-05-20T00:01:21.772267+00:00","updated_at":"2026-05-20T00:01:21.772267+00:00"}