{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:YN267RIHVKUI3ABQLMHYDN35EV","short_pith_number":"pith:YN267RIH","schema_version":"1.0","canonical_sha256":"c375efc507aaa88d80305b0f81b77d25678586e32fc600ae617623c0c785137b","source":{"kind":"arxiv","id":"2311.12937","version":1},"attestation_state":"computed","paper":{"title":"On the convolution of convex 2-gons","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Adri\\'an Llinares, Alejandro Mas, Martin Chuaqui, Rodrigo Hern\\'andez","submitted_at":"2023-11-21T19:02:20Z","abstract_excerpt":"We study the convolution of functions of the form \\[ f_\\alpha (z) := \\dfrac{\\left( \\frac{1 + z}{1 - z} \\right)^\\alpha - 1}{2 \\alpha}, \\] which map the open unit disk of the complex plane onto polygons of 2 edges when $\\alpha\\in(0,1)$. We extend results by Cima by studying limits of convolutions of finitely many $f_\\alpha$ and by considering the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of angle at infinity, which provides an estimate for the growth at infinity and determines whether the convolution is bounded or not. A generalization"},"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":"2311.12937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2023-11-21T19:02:20Z","cross_cats_sorted":[],"title_canon_sha256":"83225e2fd26b53a77dfebcaf1187e572b0505ffee21325a59749f26d9adc33fd","abstract_canon_sha256":"664d25d92562c95044ba0ca9c7815e82e7d4dc39b85327f343430e0251372bbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:26:22.869826Z","signature_b64":"K+LtDV/RXyeEdVj6c9YAJZubqqCELeGNg7ESy7nxGEdbIKC/50ri4+4bi9c3homgp+sQtmAeCp2AqP4b/4w9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c375efc507aaa88d80305b0f81b77d25678586e32fc600ae617623c0c785137b","last_reissued_at":"2026-07-05T09:26:22.869290Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:26:22.869290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the convolution of convex 2-gons","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Adri\\'an Llinares, Alejandro Mas, Martin Chuaqui, Rodrigo Hern\\'andez","submitted_at":"2023-11-21T19:02:20Z","abstract_excerpt":"We study the convolution of functions of the form \\[ f_\\alpha (z) := \\dfrac{\\left( \\frac{1 + z}{1 - z} \\right)^\\alpha - 1}{2 \\alpha}, \\] which map the open unit disk of the complex plane onto polygons of 2 edges when $\\alpha\\in(0,1)$. We extend results by Cima by studying limits of convolutions of finitely many $f_\\alpha$ and by considering the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of angle at infinity, which provides an estimate for the growth at infinity and determines whether the convolution is bounded or not. A generalization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.12937","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/2311.12937/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":"2311.12937","created_at":"2026-07-05T09:26:22.869362+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.12937v1","created_at":"2026-07-05T09:26:22.869362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.12937","created_at":"2026-07-05T09:26:22.869362+00:00"},{"alias_kind":"pith_short_12","alias_value":"YN267RIHVKUI","created_at":"2026-07-05T09:26:22.869362+00:00"},{"alias_kind":"pith_short_16","alias_value":"YN267RIHVKUI3ABQ","created_at":"2026-07-05T09:26:22.869362+00:00"},{"alias_kind":"pith_short_8","alias_value":"YN267RIH","created_at":"2026-07-05T09:26:22.869362+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/YN267RIHVKUI3ABQLMHYDN35EV","json":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV.json","graph_json":"https://pith.science/api/pith-number/YN267RIHVKUI3ABQLMHYDN35EV/graph.json","events_json":"https://pith.science/api/pith-number/YN267RIHVKUI3ABQLMHYDN35EV/events.json","paper":"https://pith.science/paper/YN267RIH"},"agent_actions":{"view_html":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV","download_json":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV.json","view_paper":"https://pith.science/paper/YN267RIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.12937&json=true","fetch_graph":"https://pith.science/api/pith-number/YN267RIHVKUI3ABQLMHYDN35EV/graph.json","fetch_events":"https://pith.science/api/pith-number/YN267RIHVKUI3ABQLMHYDN35EV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV/action/storage_attestation","attest_author":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV/action/author_attestation","sign_citation":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV/action/citation_signature","submit_replication":"https://pith.science/pith/YN267RIHVKUI3ABQLMHYDN35EV/action/replication_record"}},"created_at":"2026-07-05T09:26:22.869362+00:00","updated_at":"2026-07-05T09:26:22.869362+00:00"}