{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LICKXZZGCWMSB3B3YIZH2C2ACA","short_pith_number":"pith:LICKXZZG","schema_version":"1.0","canonical_sha256":"5a04abe726159920ec3bc2327d0b401016d771575317ea2ae0975288511ba4f1","source":{"kind":"arxiv","id":"2606.24683","version":1},"attestation_state":"computed","paper":{"title":"Lagrangian Submanifolds with Legendrian Boundary in the Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dong Gao, Hui Ma, Zeke Yao","submitted_at":"2026-06-23T15:12:22Z","abstract_excerpt":"We study compact Lagrangian submanifolds in the unit ball $\\mathbb B^{2n}\\subset\\mathbb C^n$ with Legendrian boundary. We prove that any compact exact Lagrangian self-similar submanifold with connected Legendrian boundary must be an equatorial $n$-disk. The same rigidity holds, without exactness, for Legendrian boundary under a fixed sign assumption on the cosine of the contact angle; in particular, it holds for Legendrian free boundary. These results extend the two dimensional minimal rigidity theorems of Li-Wang-Weng and Luo-Sun to higher dimensions and to the Lagrangian self-similar setting"},"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":"2606.24683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-23T15:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"296d36c9157a11e84dfe82edf215d04265ae64732ecffcd153aa9f1217235bcc","abstract_canon_sha256":"7cb6b162fa59d66ae3a26f0e77284c4721c38864f38432b4fc050994c8247d9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:39.138844Z","signature_b64":"tMMH/De2ETR9+7+BhlGTUJUzV2RzKrqyHmbnGu3uacNoKbm5WYOfEna/dwLlQZm7Umuyw1V/9NSfeQ/rQTALAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a04abe726159920ec3bc2327d0b401016d771575317ea2ae0975288511ba4f1","last_reissued_at":"2026-06-24T01:15:39.138502Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:39.138502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangian Submanifolds with Legendrian Boundary in the Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dong Gao, Hui Ma, Zeke Yao","submitted_at":"2026-06-23T15:12:22Z","abstract_excerpt":"We study compact Lagrangian submanifolds in the unit ball $\\mathbb B^{2n}\\subset\\mathbb C^n$ with Legendrian boundary. We prove that any compact exact Lagrangian self-similar submanifold with connected Legendrian boundary must be an equatorial $n$-disk. The same rigidity holds, without exactness, for Legendrian boundary under a fixed sign assumption on the cosine of the contact angle; in particular, it holds for Legendrian free boundary. These results extend the two dimensional minimal rigidity theorems of Li-Wang-Weng and Luo-Sun to higher dimensions and to the Lagrangian self-similar setting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24683","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/2606.24683/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":"2606.24683","created_at":"2026-06-24T01:15:39.138563+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.24683v1","created_at":"2026-06-24T01:15:39.138563+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24683","created_at":"2026-06-24T01:15:39.138563+00:00"},{"alias_kind":"pith_short_12","alias_value":"LICKXZZGCWMS","created_at":"2026-06-24T01:15:39.138563+00:00"},{"alias_kind":"pith_short_16","alias_value":"LICKXZZGCWMSB3B3","created_at":"2026-06-24T01:15:39.138563+00:00"},{"alias_kind":"pith_short_8","alias_value":"LICKXZZG","created_at":"2026-06-24T01:15:39.138563+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/LICKXZZGCWMSB3B3YIZH2C2ACA","json":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA.json","graph_json":"https://pith.science/api/pith-number/LICKXZZGCWMSB3B3YIZH2C2ACA/graph.json","events_json":"https://pith.science/api/pith-number/LICKXZZGCWMSB3B3YIZH2C2ACA/events.json","paper":"https://pith.science/paper/LICKXZZG"},"agent_actions":{"view_html":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA","download_json":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA.json","view_paper":"https://pith.science/paper/LICKXZZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.24683&json=true","fetch_graph":"https://pith.science/api/pith-number/LICKXZZGCWMSB3B3YIZH2C2ACA/graph.json","fetch_events":"https://pith.science/api/pith-number/LICKXZZGCWMSB3B3YIZH2C2ACA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA/action/storage_attestation","attest_author":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA/action/author_attestation","sign_citation":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA/action/citation_signature","submit_replication":"https://pith.science/pith/LICKXZZGCWMSB3B3YIZH2C2ACA/action/replication_record"}},"created_at":"2026-06-24T01:15:39.138563+00:00","updated_at":"2026-06-24T01:15:39.138563+00:00"}