{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HW6TIVON4W4XARPYGEZXOWDG37","short_pith_number":"pith:HW6TIVON","canonical_record":{"source":{"id":"2606.20872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-18T19:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"409fe16b9d0ee66237fc1f082de406df9bcad1d3d5637b99c41f5edf03708cd9","abstract_canon_sha256":"5460b4af0ba343ab520e12b45a6ef29106c0d194f7971995f6bca4027c8c2a60"},"schema_version":"1.0"},"canonical_sha256":"3dbd3455cde5b97045f83133775866dfd84cf55173204bd5754c7572f72e2138","source":{"kind":"arxiv","id":"2606.20872","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20872","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20872v1","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20872","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"HW6TIVON4W4X","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"HW6TIVON4W4XARPY","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"HW6TIVON","created_at":"2026-06-23T00:12:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HW6TIVON4W4XARPYGEZXOWDG37","target":"record","payload":{"canonical_record":{"source":{"id":"2606.20872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-18T19:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"409fe16b9d0ee66237fc1f082de406df9bcad1d3d5637b99c41f5edf03708cd9","abstract_canon_sha256":"5460b4af0ba343ab520e12b45a6ef29106c0d194f7971995f6bca4027c8c2a60"},"schema_version":"1.0"},"canonical_sha256":"3dbd3455cde5b97045f83133775866dfd84cf55173204bd5754c7572f72e2138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T00:12:01.406081Z","signature_b64":"UiGfY4xIhpjRbmkO3Hm83u6StAd/vjTmBh8/EYgpE04Pl9f+bQfvRq/Iw8WOHRgoeBWKQtavqKI5Xr1+WhL5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dbd3455cde5b97045f83133775866dfd84cf55173204bd5754c7572f72e2138","last_reissued_at":"2026-06-23T00:12:01.405693Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T00:12:01.405693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.20872","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFkpTgrd9+BfTW0TZ9ZDDi33Kdwm+FYKCDkahquAzABhpcSUlKo8GqFZtXrtMF7AQ7N9O99bqPPhFcjgWWI2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:36:34.657287Z"},"content_sha256":"61d02f288f9c74ee7e1d7fd202db4df482f5791ae5917aae6ffce6951e4df392","schema_version":"1.0","event_id":"sha256:61d02f288f9c74ee7e1d7fd202db4df482f5791ae5917aae6ffce6951e4df392"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HW6TIVON4W4XARPYGEZXOWDG37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radius of convexity of certain classes of functions defined by convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Souvik Biswas","submitted_at":"2026-06-18T19:02:10Z","abstract_excerpt":"Let $\\mathcal{S}$ be the class of analytic univalent functions defined in the open unit disc $\\mathbb{D}$ of the complex plane with the normalizations $f(0)=0$ and $f'(0)=1$. For $A\\in (1,2]$, let $Co(A)$ denote the class of concave univalent functions defined in $\\mathbb{D}$ with the opening angle $\\pi A$ at infinity. In this article, by applying certain convolution techniques, we investigate the radius of convexity for the class $Co(A)\\ast\\mathcal{S}t(1/2)$, where $\\mathcal{S}t(1/2)\\subsetneq \\mathcal{S}$ denotes the class of starlike functions of order $1/2$. Furthermore, we establish that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20872","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/2606.20872/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1YWU5mxpAV+3nmJucolZ1eSQUkp4buo6DUCbJ4mDMNfLbJi1dZaGAu0jUjRnFwCtnMtEP3vC+/+EzuJEv6TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:36:34.657670Z"},"content_sha256":"e7ca6953d396ae909d1ebfae72fb2f0487dcd036ced1a4e3c8d069f469d97d51","schema_version":"1.0","event_id":"sha256:e7ca6953d396ae909d1ebfae72fb2f0487dcd036ced1a4e3c8d069f469d97d51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HW6TIVON4W4XARPYGEZXOWDG37/bundle.json","state_url":"https://pith.science/pith/HW6TIVON4W4XARPYGEZXOWDG37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HW6TIVON4W4XARPYGEZXOWDG37/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T16:36:34Z","links":{"resolver":"https://pith.science/pith/HW6TIVON4W4XARPYGEZXOWDG37","bundle":"https://pith.science/pith/HW6TIVON4W4XARPYGEZXOWDG37/bundle.json","state":"https://pith.science/pith/HW6TIVON4W4XARPYGEZXOWDG37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HW6TIVON4W4XARPYGEZXOWDG37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HW6TIVON4W4XARPYGEZXOWDG37","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5460b4af0ba343ab520e12b45a6ef29106c0d194f7971995f6bca4027c8c2a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-18T19:02:10Z","title_canon_sha256":"409fe16b9d0ee66237fc1f082de406df9bcad1d3d5637b99c41f5edf03708cd9"},"schema_version":"1.0","source":{"id":"2606.20872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20872","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20872v1","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20872","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"HW6TIVON4W4X","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"HW6TIVON4W4XARPY","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"HW6TIVON","created_at":"2026-06-23T00:12:01Z"}],"graph_snapshots":[{"event_id":"sha256:e7ca6953d396ae909d1ebfae72fb2f0487dcd036ced1a4e3c8d069f469d97d51","target":"graph","created_at":"2026-06-23T00:12:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.20872/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{S}$ be the class of analytic univalent functions defined in the open unit disc $\\mathbb{D}$ of the complex plane with the normalizations $f(0)=0$ and $f'(0)=1$. For $A\\in (1,2]$, let $Co(A)$ denote the class of concave univalent functions defined in $\\mathbb{D}$ with the opening angle $\\pi A$ at infinity. In this article, by applying certain convolution techniques, we investigate the radius of convexity for the class $Co(A)\\ast\\mathcal{S}t(1/2)$, where $\\mathcal{S}t(1/2)\\subsetneq \\mathcal{S}$ denotes the class of starlike functions of order $1/2$. Furthermore, we establish that ","authors_text":"Bappaditya Bhowmik, Souvik Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-18T19:02:10Z","title":"Radius of convexity of certain classes of functions defined by convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20872","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:61d02f288f9c74ee7e1d7fd202db4df482f5791ae5917aae6ffce6951e4df392","target":"record","created_at":"2026-06-23T00:12:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5460b4af0ba343ab520e12b45a6ef29106c0d194f7971995f6bca4027c8c2a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-18T19:02:10Z","title_canon_sha256":"409fe16b9d0ee66237fc1f082de406df9bcad1d3d5637b99c41f5edf03708cd9"},"schema_version":"1.0","source":{"id":"2606.20872","kind":"arxiv","version":1}},"canonical_sha256":"3dbd3455cde5b97045f83133775866dfd84cf55173204bd5754c7572f72e2138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dbd3455cde5b97045f83133775866dfd84cf55173204bd5754c7572f72e2138","first_computed_at":"2026-06-23T00:12:01.405693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T00:12:01.405693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiGfY4xIhpjRbmkO3Hm83u6StAd/vjTmBh8/EYgpE04Pl9f+bQfvRq/Iw8WOHRgoeBWKQtavqKI5Xr1+WhL5DQ==","signature_status":"signed_v1","signed_at":"2026-06-23T00:12:01.406081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61d02f288f9c74ee7e1d7fd202db4df482f5791ae5917aae6ffce6951e4df392","sha256:e7ca6953d396ae909d1ebfae72fb2f0487dcd036ced1a4e3c8d069f469d97d51"],"state_sha256":"86df40764e5e82bd2c195858a147c4775eb42f19f8d59b9ac776b56fd26e1c29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UYPu+R3v6DrbtFYxDdoWn7E4gAIQ59uEAhL2FvcefJfhAhvntIuQQOx5YBOaNepiEgV/2fIs5mb3HVA9pDKrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:36:34.659692Z","bundle_sha256":"80965a2faa90bafd9075a618b260592bd064627d7e56f4ae58bcf1cbb129a936"}}