{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HHUZPQGBX37ZV5R75II7NYNEPG","short_pith_number":"pith:HHUZPQGB","schema_version":"1.0","canonical_sha256":"39e997c0c1beff9af63fea11f6e1a4799180a2668f86c506feebe5f6ccef2827","source":{"kind":"arxiv","id":"2412.15505","version":3},"attestation_state":"computed","paper":{"title":"The monopolist's free boundary problem in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Cale Rankin, Kelvin Shuangjian Zhang, Robert J. McCann","submitted_at":"2024-12-20T02:36:56Z","abstract_excerpt":"We study the Monopolist's problem with a focus on the free boundary separating bunched from unbunched consumers, especially in the plane, and give a full description of its solution for the family of square domains $\\{(a,a+1)^2\\}_{a \\ge 0}$. The Monopolist's problem is fundamental in economics, yet widely considered analytically intractable when both consumers and products have more than one degree of heterogeneity. Mathematically, the problem is to minimize a smooth, uniformly convex Lagrangian over the space of nonnegative convex functions. What results is a free boundary problem between the"},"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":"2412.15505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-20T02:36:56Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"2b7d81c4a532d9da8ef0bf4ea5399022e4dc566b8aa764c6963b23f45f75d194","abstract_canon_sha256":"4dc8e213384db72fe7fe84db77143011119daa8e9639cb7aff0bee4a803f4254"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:19.446484Z","signature_b64":"Tv+H9WLZ1qG/1ojg1TmvzJ46aOpSDDQawuAFPAmFfA27S8PZrSEEEmn/bXd01sfFtot0xCN2s9k3lasn4RqAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39e997c0c1beff9af63fea11f6e1a4799180a2668f86c506feebe5f6ccef2827","last_reissued_at":"2026-06-24T01:14:19.446051Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:19.446051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The monopolist's free boundary problem in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Cale Rankin, Kelvin Shuangjian Zhang, Robert J. McCann","submitted_at":"2024-12-20T02:36:56Z","abstract_excerpt":"We study the Monopolist's problem with a focus on the free boundary separating bunched from unbunched consumers, especially in the plane, and give a full description of its solution for the family of square domains $\\{(a,a+1)^2\\}_{a \\ge 0}$. The Monopolist's problem is fundamental in economics, yet widely considered analytically intractable when both consumers and products have more than one degree of heterogeneity. Mathematically, the problem is to minimize a smooth, uniformly convex Lagrangian over the space of nonnegative convex functions. What results is a free boundary problem between the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15505","kind":"arxiv","version":3},"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/2412.15505/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":"2412.15505","created_at":"2026-06-24T01:14:19.446107+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.15505v3","created_at":"2026-06-24T01:14:19.446107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15505","created_at":"2026-06-24T01:14:19.446107+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHUZPQGBX37Z","created_at":"2026-06-24T01:14:19.446107+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHUZPQGBX37ZV5R7","created_at":"2026-06-24T01:14:19.446107+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHUZPQGB","created_at":"2026-06-24T01:14:19.446107+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/HHUZPQGBX37ZV5R75II7NYNEPG","json":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG.json","graph_json":"https://pith.science/api/pith-number/HHUZPQGBX37ZV5R75II7NYNEPG/graph.json","events_json":"https://pith.science/api/pith-number/HHUZPQGBX37ZV5R75II7NYNEPG/events.json","paper":"https://pith.science/paper/HHUZPQGB"},"agent_actions":{"view_html":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG","download_json":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG.json","view_paper":"https://pith.science/paper/HHUZPQGB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.15505&json=true","fetch_graph":"https://pith.science/api/pith-number/HHUZPQGBX37ZV5R75II7NYNEPG/graph.json","fetch_events":"https://pith.science/api/pith-number/HHUZPQGBX37ZV5R75II7NYNEPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG/action/storage_attestation","attest_author":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG/action/author_attestation","sign_citation":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG/action/citation_signature","submit_replication":"https://pith.science/pith/HHUZPQGBX37ZV5R75II7NYNEPG/action/replication_record"}},"created_at":"2026-06-24T01:14:19.446107+00:00","updated_at":"2026-06-24T01:14:19.446107+00:00"}