{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UA3SU533WVALLK3RJ2NSX3FJIR","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":"06d1e9d571ecec056203da5b57aae7f78f8673326ae58d2cf95697d355e04b8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-21T14:57:41Z","title_canon_sha256":"1b89a35e1fa848bf681075ce498f55b9b0f79899655968457ccb7f6a07ef569a"},"schema_version":"1.0","source":{"id":"1411.5898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5898","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5898v1","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5898","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"UA3SU533WVAL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UA3SU533WVALLK3R","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UA3SU533","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:bd6b2e78198d165b5e8b7333f45687e712cdfaf7e262163ea2307993c6d50c61","target":"graph","created_at":"2026-05-18T02:33:01Z","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"},"paper":{"abstract_excerpt":"Let $\\mathcal{W}_{\\beta}^\\delta(\\alpha,\\gamma)$ be the class of normalized analytic functions $f$ defined in the domain $|z|<1$ satisfying \\begin{align*} {\\rm Re\\,} e^{i\\phi}\\left(\\dfrac{}{}(1\\!-\\!\\alpha\\!+\\!2\\gamma)\\!\\left({f}/{z}\\right)^\\delta +\\left(\\alpha\\!-\\!3\\gamma+\\gamma\\left[\\dfrac{}{}\\left(1-{1}/{\\delta}\\right)\\left({zf'}/{f}\\right)+ {1}/{\\delta}\\left(1+{zf''}/{f'}\\right)\\right]\\right)\\right.\\\\ \\left.\\dfrac{}{}\\left({f}/{z}\\right)^\\delta \\!\\left({zf'}/{f}\\right)-\\beta\\right)>0, \\end{align*} with the conditions $\\alpha\\geq 0$, $\\beta<1$, $\\gamma\\geq 0$, $\\delta>0$ and $\\phi\\in\\mathbb{R","authors_text":"A. Swaminathan, Satwanti Devi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-21T14:57:41Z","title":"Convexity of the Generalized Integral Transform and Duality Techniques"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5898","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":"sha256:524a538e9c5a66095aadf63c0be60b73848d363868fd64add20da2582680ea45","target":"record","created_at":"2026-05-18T02:33:01Z","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":"06d1e9d571ecec056203da5b57aae7f78f8673326ae58d2cf95697d355e04b8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-21T14:57:41Z","title_canon_sha256":"1b89a35e1fa848bf681075ce498f55b9b0f79899655968457ccb7f6a07ef569a"},"schema_version":"1.0","source":{"id":"1411.5898","kind":"arxiv","version":1}},"canonical_sha256":"a0372a777bb540b5ab714e9b2beca9446f6cd1c2f6fd9818878c71b7c7fb8155","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0372a777bb540b5ab714e9b2beca9446f6cd1c2f6fd9818878c71b7c7fb8155","first_computed_at":"2026-05-18T02:33:01.953259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:01.953259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S1IxvKGq9ip9cI+rGtZEEj7xRY6VVjribLCEe2OCprkaZa5ymWUcnzK/rbzC8dYeSMxr5MzUjNg74XEwIdycBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:01.953680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:524a538e9c5a66095aadf63c0be60b73848d363868fd64add20da2582680ea45","sha256:bd6b2e78198d165b5e8b7333f45687e712cdfaf7e262163ea2307993c6d50c61"],"state_sha256":"5e76956560d6b11055a41ea31c9e00412b439c9387add87fd85f440e7f91aaaa"}