{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IGT2B5XCXXI4QDNYVHEVWPJF4L","short_pith_number":"pith:IGT2B5XC","schema_version":"1.0","canonical_sha256":"41a7a0f6e2bdd1c80db8a9c95b3d25e2f6bd38f9f2a58a60eac3368d6ab4ce7a","source":{"kind":"arxiv","id":"1305.3004","version":1},"attestation_state":"computed","paper":{"title":"Some higher order isoperimetric inequalities via the method of optimal transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Sun-Yung A. Chang, Yi Wang","submitted_at":"2013-05-14T02:40:48Z","abstract_excerpt":"In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation."},"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":"1305.3004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-14T02:40:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cd0a34976406cf57110cc69221506e405d2c615677799f90182064ee839f9285","abstract_canon_sha256":"862e2b6f04b2dcb01efc1bd5143800c7d8e4bd36e78e8522e1faa049c0abd1b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:45.178493Z","signature_b64":"T1FqhnwlYrWjFB5aXbc9SdI1LM5qbbqQgBwfDhz+67A1w5V7XH0gzl7z3RIPB+co8sunEmrq6SdYImgvWo/8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41a7a0f6e2bdd1c80db8a9c95b3d25e2f6bd38f9f2a58a60eac3368d6ab4ce7a","last_reissued_at":"2026-05-18T03:25:45.177596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:45.177596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some higher order isoperimetric inequalities via the method of optimal transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Sun-Yung A. Chang, Yi Wang","submitted_at":"2013-05-14T02:40:48Z","abstract_excerpt":"In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3004","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":"1305.3004","created_at":"2026-05-18T03:25:45.177757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3004v1","created_at":"2026-05-18T03:25:45.177757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3004","created_at":"2026-05-18T03:25:45.177757+00:00"},{"alias_kind":"pith_short_12","alias_value":"IGT2B5XCXXI4","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IGT2B5XCXXI4QDNY","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IGT2B5XC","created_at":"2026-05-18T12:27:46.883200+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/IGT2B5XCXXI4QDNYVHEVWPJF4L","json":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L.json","graph_json":"https://pith.science/api/pith-number/IGT2B5XCXXI4QDNYVHEVWPJF4L/graph.json","events_json":"https://pith.science/api/pith-number/IGT2B5XCXXI4QDNYVHEVWPJF4L/events.json","paper":"https://pith.science/paper/IGT2B5XC"},"agent_actions":{"view_html":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L","download_json":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L.json","view_paper":"https://pith.science/paper/IGT2B5XC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3004&json=true","fetch_graph":"https://pith.science/api/pith-number/IGT2B5XCXXI4QDNYVHEVWPJF4L/graph.json","fetch_events":"https://pith.science/api/pith-number/IGT2B5XCXXI4QDNYVHEVWPJF4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L/action/storage_attestation","attest_author":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L/action/author_attestation","sign_citation":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L/action/citation_signature","submit_replication":"https://pith.science/pith/IGT2B5XCXXI4QDNYVHEVWPJF4L/action/replication_record"}},"created_at":"2026-05-18T03:25:45.177757+00:00","updated_at":"2026-05-18T03:25:45.177757+00:00"}