{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XYHMO34E3YAIVJLE2XG6WSRSH2","short_pith_number":"pith:XYHMO34E","schema_version":"1.0","canonical_sha256":"be0ec76f84de008aa564d5cdeb4a323e8dd323d1bc1adb935ffd40ef18888944","source":{"kind":"arxiv","id":"2301.07603","version":2},"attestation_state":"computed","paper":{"title":"The $L_p$ Chord Minkowski problem in a critical interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Dongmeng Xi, Lujun Guo, Yiming Zhao","submitted_at":"2023-01-18T15:34:59Z","abstract_excerpt":"Chord measures and $L_p$ chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the $L_p$ chord measure is known as the $L_p$ chord Minkowski problem, which includes the $L_p$ Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the $L_p$ chord Minkowski problem when $0\\leq p<1$, without symmetry assumptions."},"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":"2301.07603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-01-18T15:34:59Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f0b7f4d881e29f30b97e38547d3ea439b28b236d76e5f6299a3d3570c1faf277","abstract_canon_sha256":"ffbf44140456236fbc8588435f2fb68d21b7eb75c5dbd72cc155d790272278f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:12.304084Z","signature_b64":"wOb/ho4TuAZPswp/5eeBTl1Zf6WfE+/hXajTxTOj05RYIPtQ4JnQVo0NgO9lasOGtZkQxvlfcdrcBRA6rS3AAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be0ec76f84de008aa564d5cdeb4a323e8dd323d1bc1adb935ffd40ef18888944","last_reissued_at":"2026-07-05T06:50:12.303615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:12.303615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $L_p$ Chord Minkowski problem in a critical interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Dongmeng Xi, Lujun Guo, Yiming Zhao","submitted_at":"2023-01-18T15:34:59Z","abstract_excerpt":"Chord measures and $L_p$ chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the $L_p$ chord measure is known as the $L_p$ chord Minkowski problem, which includes the $L_p$ Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the $L_p$ chord Minkowski problem when $0\\leq p<1$, without symmetry assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07603","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/2301.07603/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":"2301.07603","created_at":"2026-07-05T06:50:12.303666+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.07603v2","created_at":"2026-07-05T06:50:12.303666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.07603","created_at":"2026-07-05T06:50:12.303666+00:00"},{"alias_kind":"pith_short_12","alias_value":"XYHMO34E3YAI","created_at":"2026-07-05T06:50:12.303666+00:00"},{"alias_kind":"pith_short_16","alias_value":"XYHMO34E3YAIVJLE","created_at":"2026-07-05T06:50:12.303666+00:00"},{"alias_kind":"pith_short_8","alias_value":"XYHMO34E","created_at":"2026-07-05T06:50:12.303666+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/XYHMO34E3YAIVJLE2XG6WSRSH2","json":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2.json","graph_json":"https://pith.science/api/pith-number/XYHMO34E3YAIVJLE2XG6WSRSH2/graph.json","events_json":"https://pith.science/api/pith-number/XYHMO34E3YAIVJLE2XG6WSRSH2/events.json","paper":"https://pith.science/paper/XYHMO34E"},"agent_actions":{"view_html":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2","download_json":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2.json","view_paper":"https://pith.science/paper/XYHMO34E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.07603&json=true","fetch_graph":"https://pith.science/api/pith-number/XYHMO34E3YAIVJLE2XG6WSRSH2/graph.json","fetch_events":"https://pith.science/api/pith-number/XYHMO34E3YAIVJLE2XG6WSRSH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2/action/storage_attestation","attest_author":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2/action/author_attestation","sign_citation":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2/action/citation_signature","submit_replication":"https://pith.science/pith/XYHMO34E3YAIVJLE2XG6WSRSH2/action/replication_record"}},"created_at":"2026-07-05T06:50:12.303666+00:00","updated_at":"2026-07-05T06:50:12.303666+00:00"}