{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:I2ZDP6QC5Z6IMIVXB3DYNPIWLQ","short_pith_number":"pith:I2ZDP6QC","schema_version":"1.0","canonical_sha256":"46b237fa02ee7c8622b70ec786bd165c3c6837eb74cbea4b4ae707512056fc44","source":{"kind":"arxiv","id":"2306.01636","version":1},"attestation_state":"computed","paper":{"title":"Generalized Monge-Amp\\`ere functionals and related variational problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Freid Tong, Shing-Tung Yau","submitted_at":"2023-06-02T15:54:11Z","abstract_excerpt":"In this paper, we introduce a family of real Monge-Amp\\`ere functionals and study their variational properties. We prove a Sobolev type inequality for these functionals and use this to study the existence and uniqueness of some associated Dirichlet problems. In particular, we prove the existence of solutions for a nonlinear eigenvalue problem associated to this family of functionals."},"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":"2306.01636","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-02T15:54:11Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"98cbcc69a0aee67999453121452b57d4212e49e64ea81d0ab98eacded31b6837","abstract_canon_sha256":"e732168c2d20771048a2eb93d449cd111681498fef299831bf228dc3c0a26519"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:16:56.335731Z","signature_b64":"i/kZues4PmqzT15g3pNMNBel7De+5FPMFi1fdWs3tB9VNzqJsCkpvgCx0W2YinA+xRZk7ncyIv7VDogXNluaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b237fa02ee7c8622b70ec786bd165c3c6837eb74cbea4b4ae707512056fc44","last_reissued_at":"2026-07-05T06:16:56.335374Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:16:56.335374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Monge-Amp\\`ere functionals and related variational problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Freid Tong, Shing-Tung Yau","submitted_at":"2023-06-02T15:54:11Z","abstract_excerpt":"In this paper, we introduce a family of real Monge-Amp\\`ere functionals and study their variational properties. We prove a Sobolev type inequality for these functionals and use this to study the existence and uniqueness of some associated Dirichlet problems. In particular, we prove the existence of solutions for a nonlinear eigenvalue problem associated to this family of functionals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.01636","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/2306.01636/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":"2306.01636","created_at":"2026-07-05T06:16:56.335439+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.01636v1","created_at":"2026-07-05T06:16:56.335439+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.01636","created_at":"2026-07-05T06:16:56.335439+00:00"},{"alias_kind":"pith_short_12","alias_value":"I2ZDP6QC5Z6I","created_at":"2026-07-05T06:16:56.335439+00:00"},{"alias_kind":"pith_short_16","alias_value":"I2ZDP6QC5Z6IMIVX","created_at":"2026-07-05T06:16:56.335439+00:00"},{"alias_kind":"pith_short_8","alias_value":"I2ZDP6QC","created_at":"2026-07-05T06:16:56.335439+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.05551","citing_title":"On a general class of free boundary Monge-Amp\\`ere equations","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ","json":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ.json","graph_json":"https://pith.science/api/pith-number/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/graph.json","events_json":"https://pith.science/api/pith-number/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/events.json","paper":"https://pith.science/paper/I2ZDP6QC"},"agent_actions":{"view_html":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ","download_json":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ.json","view_paper":"https://pith.science/paper/I2ZDP6QC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.01636&json=true","fetch_graph":"https://pith.science/api/pith-number/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/graph.json","fetch_events":"https://pith.science/api/pith-number/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/action/storage_attestation","attest_author":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/action/author_attestation","sign_citation":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/action/citation_signature","submit_replication":"https://pith.science/pith/I2ZDP6QC5Z6IMIVXB3DYNPIWLQ/action/replication_record"}},"created_at":"2026-07-05T06:16:56.335439+00:00","updated_at":"2026-07-05T06:16:56.335439+00:00"}