{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:LPCY6LHRFSKBJ6WXALQFKLBYKX","short_pith_number":"pith:LPCY6LHR","schema_version":"1.0","canonical_sha256":"5bc58f2cf12c9414fad702e0552c3855e391a0858321d2bd1c74f86edce3fe78","source":{"kind":"arxiv","id":"2111.07321","version":1},"attestation_state":"computed","paper":{"title":"The discrete logarithmic Minkowski problem for the electrostatic $\\mathfrak{p}$-capacity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Minhyun Kim, Taehun Lee","submitted_at":"2021-11-14T12:02:13Z","abstract_excerpt":"The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem for $\\mathfrak{p}$-capacity. In particular, the logarithmic case $p=0$ relates to cone-volumes and therefore has a geometric significance. In this paper we solve the discrete logarithmic Minkowski problem for $1<\\mathfrak{p}<n$ in the case where the support of the given measure is in general position."},"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":"2111.07321","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2021-11-14T12:02:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8e45eebe77403da663affb487976865fabf203de40b50d9f1d1694a08970567b","abstract_canon_sha256":"2b1b152c177af87e281f62cf31459771610c6729878cbd49e34f9a572de5f8fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:38.851120Z","signature_b64":"CiYEVpstHFK5fPY/2hYhEmqRkf1gT2CGR/QLkh2uHdVHYmJDpNhe3J72dRX7Vt3g1cag91gf5OV3j/Gw9PWvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bc58f2cf12c9414fad702e0552c3855e391a0858321d2bd1c74f86edce3fe78","last_reissued_at":"2026-07-05T03:31:38.850604Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:38.850604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The discrete logarithmic Minkowski problem for the electrostatic $\\mathfrak{p}$-capacity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Minhyun Kim, Taehun Lee","submitted_at":"2021-11-14T12:02:13Z","abstract_excerpt":"The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem for $\\mathfrak{p}$-capacity. In particular, the logarithmic case $p=0$ relates to cone-volumes and therefore has a geometric significance. In this paper we solve the discrete logarithmic Minkowski problem for $1<\\mathfrak{p}<n$ in the case where the support of the given measure is in general position."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07321","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/2111.07321/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":"2111.07321","created_at":"2026-07-05T03:31:38.850658+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.07321v1","created_at":"2026-07-05T03:31:38.850658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07321","created_at":"2026-07-05T03:31:38.850658+00:00"},{"alias_kind":"pith_short_12","alias_value":"LPCY6LHRFSKB","created_at":"2026-07-05T03:31:38.850658+00:00"},{"alias_kind":"pith_short_16","alias_value":"LPCY6LHRFSKBJ6WX","created_at":"2026-07-05T03:31:38.850658+00:00"},{"alias_kind":"pith_short_8","alias_value":"LPCY6LHR","created_at":"2026-07-05T03:31:38.850658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00687","citing_title":"Minkowski problem of anisotropic p-torsional rigidity","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX","json":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX.json","graph_json":"https://pith.science/api/pith-number/LPCY6LHRFSKBJ6WXALQFKLBYKX/graph.json","events_json":"https://pith.science/api/pith-number/LPCY6LHRFSKBJ6WXALQFKLBYKX/events.json","paper":"https://pith.science/paper/LPCY6LHR"},"agent_actions":{"view_html":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX","download_json":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX.json","view_paper":"https://pith.science/paper/LPCY6LHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.07321&json=true","fetch_graph":"https://pith.science/api/pith-number/LPCY6LHRFSKBJ6WXALQFKLBYKX/graph.json","fetch_events":"https://pith.science/api/pith-number/LPCY6LHRFSKBJ6WXALQFKLBYKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX/action/storage_attestation","attest_author":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX/action/author_attestation","sign_citation":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX/action/citation_signature","submit_replication":"https://pith.science/pith/LPCY6LHRFSKBJ6WXALQFKLBYKX/action/replication_record"}},"created_at":"2026-07-05T03:31:38.850658+00:00","updated_at":"2026-07-05T03:31:38.850658+00:00"}