{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GALOXJBCLOIP4S7S255KZECFIX","short_pith_number":"pith:GALOXJBC","schema_version":"1.0","canonical_sha256":"3016eba4225b90fe4bf2d77aac904545ccc8efa8f46f8489579020a632e934aa","source":{"kind":"arxiv","id":"2507.12725","version":2},"attestation_state":"computed","paper":{"title":"Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bohan Wang, Guozhen Lu, Hanli Tang, Lu Chen","submitted_at":"2025-07-17T02:03:05Z","abstract_excerpt":"In this paper, we are concerned with the optimal asymptotic lower bound for the stability of Sobolev inequality on the Heisenberg group. We first establish the optimal local stability of Sobolev inequality on the CR sphere through bispherical harmonics and complicated orthogonality technique ( see Lemma 3.1). The loss of rearrangement inequality in the CR setting makes it impossible to use any rearrangement flow technique (either differential rearrangement flow or integral rearrangement flow) to derive the optimal stability of Sobolev inequality on the CR sphere from corresponding optimal loca"},"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":"2507.12725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-17T02:03:05Z","cross_cats_sorted":[],"title_canon_sha256":"fae8444229e10284faf4bba8f090c59da589c487563850aa78bc1fed01c20b13","abstract_canon_sha256":"332091e18b695fea28b6b977828faf966f084254ee6e35e85c35090ddfe1ad32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:01.734374Z","signature_b64":"TfuTWYkDmGewZU3xKTWcuW26UmfvFYY78HhDKRl3252D13zEMxY/1s67qg5Oc6oW9HDpPZGONnqnD0vHBlW9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3016eba4225b90fe4bf2d77aac904545ccc8efa8f46f8489579020a632e934aa","last_reissued_at":"2026-07-05T11:40:01.733816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:01.733816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bohan Wang, Guozhen Lu, Hanli Tang, Lu Chen","submitted_at":"2025-07-17T02:03:05Z","abstract_excerpt":"In this paper, we are concerned with the optimal asymptotic lower bound for the stability of Sobolev inequality on the Heisenberg group. We first establish the optimal local stability of Sobolev inequality on the CR sphere through bispherical harmonics and complicated orthogonality technique ( see Lemma 3.1). The loss of rearrangement inequality in the CR setting makes it impossible to use any rearrangement flow technique (either differential rearrangement flow or integral rearrangement flow) to derive the optimal stability of Sobolev inequality on the CR sphere from corresponding optimal loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12725","kind":"arxiv","version":2},"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/2507.12725/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":"2507.12725","created_at":"2026-07-05T11:40:01.733886+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12725v2","created_at":"2026-07-05T11:40:01.733886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12725","created_at":"2026-07-05T11:40:01.733886+00:00"},{"alias_kind":"pith_short_12","alias_value":"GALOXJBCLOIP","created_at":"2026-07-05T11:40:01.733886+00:00"},{"alias_kind":"pith_short_16","alias_value":"GALOXJBCLOIP4S7S","created_at":"2026-07-05T11:40:01.733886+00:00"},{"alias_kind":"pith_short_8","alias_value":"GALOXJBC","created_at":"2026-07-05T11:40:01.733886+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/GALOXJBCLOIP4S7S255KZECFIX","json":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX.json","graph_json":"https://pith.science/api/pith-number/GALOXJBCLOIP4S7S255KZECFIX/graph.json","events_json":"https://pith.science/api/pith-number/GALOXJBCLOIP4S7S255KZECFIX/events.json","paper":"https://pith.science/paper/GALOXJBC"},"agent_actions":{"view_html":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX","download_json":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX.json","view_paper":"https://pith.science/paper/GALOXJBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12725&json=true","fetch_graph":"https://pith.science/api/pith-number/GALOXJBCLOIP4S7S255KZECFIX/graph.json","fetch_events":"https://pith.science/api/pith-number/GALOXJBCLOIP4S7S255KZECFIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX/action/storage_attestation","attest_author":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX/action/author_attestation","sign_citation":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX/action/citation_signature","submit_replication":"https://pith.science/pith/GALOXJBCLOIP4S7S255KZECFIX/action/replication_record"}},"created_at":"2026-07-05T11:40:01.733886+00:00","updated_at":"2026-07-05T11:40:01.733886+00:00"}