{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EPRTRGOCQDNF7WLTJOTJC267VP","short_pith_number":"pith:EPRTRGOC","canonical_record":{"source":{"id":"1705.03663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-10T08:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"c92edb039c17bf3253ec44d22d146f14d49b0bda60858316d85978153b57b9c0","abstract_canon_sha256":"3606665a72d3d00d937dbf4389bbb0dd386fc21b353f9b8c8b896a7d33ac61c7"},"schema_version":"1.0"},"canonical_sha256":"23e33899c280da5fd9734ba6916bdfabcd379ea419c35e19f8478a5e0042b3a0","source":{"kind":"arxiv","id":"1705.03663","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03663","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03663v1","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03663","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"EPRTRGOCQDNF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPRTRGOCQDNF7WLT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPRTRGOC","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EPRTRGOCQDNF7WLTJOTJC267VP","target":"record","payload":{"canonical_record":{"source":{"id":"1705.03663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-10T08:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"c92edb039c17bf3253ec44d22d146f14d49b0bda60858316d85978153b57b9c0","abstract_canon_sha256":"3606665a72d3d00d937dbf4389bbb0dd386fc21b353f9b8c8b896a7d33ac61c7"},"schema_version":"1.0"},"canonical_sha256":"23e33899c280da5fd9734ba6916bdfabcd379ea419c35e19f8478a5e0042b3a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:43.272433Z","signature_b64":"iOg7RSWam6vpMthfTs0Zfd8eGGFHLWx6KQi9P5agCPWL/6REoOqudBs3aAJuCvk88jICzuapp1yOL/GASIkODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e33899c280da5fd9734ba6916bdfabcd379ea419c35e19f8478a5e0042b3a0","last_reissued_at":"2026-05-18T00:44:43.272017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:43.272017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.03663","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":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LcsZDfGo9mcZWXeLXyX0/hrYRfe6aHg32s12HvPIgmPMBO+gK6obi5O215AAPzWtvhJnKjE6zVu3oMr98kxcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:28:05.177496Z"},"content_sha256":"848fd19cc7df106de6d83329b76d72f2ff4013dbb6bc6576e5465029ad9cd519","schema_version":"1.0","event_id":"sha256:848fd19cc7df106de6d83329b76d72f2ff4013dbb6bc6576e5465029ad9cd519"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EPRTRGOCQDNF7WLTJOTJC267VP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Criteria for univalence, Integral means and Dirichlet integral for Meromorphic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Firdoshi Parveen","submitted_at":"2017-05-10T08:47:50Z","abstract_excerpt":"Let $\\mathcal{A}(p)$ be the class consisting of functions $f$ that are holomorphic in $\\ID\\setminus \\{p\\}$, $p\\in (0,1)$ possessing a simple pole at the point $z=p$ with nonzero residue and normalized by the condition $f(0)=0=f'(0)-1$. In this article, we first prove a sufficient condition for univalency for functions in $\\mathcal{A}(p)$. Thereafter, we consider the class denoted by $\\Sigma(p)$ that consists of functions $f \\in \\mathcal{A}(p)$ that are univalent in $\\ID$. We obtain the exact value for $\\ds\\max_ {f\\in \\Sigma(p)}\\Delta(r,z/f)$, where the Dirichlet integral $\\Delta(r,z/f)$ is giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03663","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":""},"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":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wzN2I1QoghlWXAS1sfksYhxZJbkfUKlgUJ0av0hW88TpqBci6DfbyjeQfP48lx8FN0pSBYXJMv7mbIIjIIXCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:28:05.178151Z"},"content_sha256":"bf6211fed9278681caf025d958398a2511b8b0b9bd2fb21cc4702467ade82b3b","schema_version":"1.0","event_id":"sha256:bf6211fed9278681caf025d958398a2511b8b0b9bd2fb21cc4702467ade82b3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPRTRGOCQDNF7WLTJOTJC267VP/bundle.json","state_url":"https://pith.science/pith/EPRTRGOCQDNF7WLTJOTJC267VP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPRTRGOCQDNF7WLTJOTJC267VP/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":"2026-06-10T22:28:05Z","links":{"resolver":"https://pith.science/pith/EPRTRGOCQDNF7WLTJOTJC267VP","bundle":"https://pith.science/pith/EPRTRGOCQDNF7WLTJOTJC267VP/bundle.json","state":"https://pith.science/pith/EPRTRGOCQDNF7WLTJOTJC267VP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPRTRGOCQDNF7WLTJOTJC267VP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EPRTRGOCQDNF7WLTJOTJC267VP","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":"3606665a72d3d00d937dbf4389bbb0dd386fc21b353f9b8c8b896a7d33ac61c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-10T08:47:50Z","title_canon_sha256":"c92edb039c17bf3253ec44d22d146f14d49b0bda60858316d85978153b57b9c0"},"schema_version":"1.0","source":{"id":"1705.03663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03663","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03663v1","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03663","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"EPRTRGOCQDNF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPRTRGOCQDNF7WLT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPRTRGOC","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:bf6211fed9278681caf025d958398a2511b8b0b9bd2fb21cc4702467ade82b3b","target":"graph","created_at":"2026-05-18T00:44:43Z","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 $\\mathcal{A}(p)$ be the class consisting of functions $f$ that are holomorphic in $\\ID\\setminus \\{p\\}$, $p\\in (0,1)$ possessing a simple pole at the point $z=p$ with nonzero residue and normalized by the condition $f(0)=0=f'(0)-1$. In this article, we first prove a sufficient condition for univalency for functions in $\\mathcal{A}(p)$. Thereafter, we consider the class denoted by $\\Sigma(p)$ that consists of functions $f \\in \\mathcal{A}(p)$ that are univalent in $\\ID$. We obtain the exact value for $\\ds\\max_ {f\\in \\Sigma(p)}\\Delta(r,z/f)$, where the Dirichlet integral $\\Delta(r,z/f)$ is giv","authors_text":"Bappaditya Bhowmik, Firdoshi Parveen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-10T08:47:50Z","title":"Criteria for univalence, Integral means and Dirichlet integral for Meromorphic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03663","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":"sha256:848fd19cc7df106de6d83329b76d72f2ff4013dbb6bc6576e5465029ad9cd519","target":"record","created_at":"2026-05-18T00:44:43Z","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":"3606665a72d3d00d937dbf4389bbb0dd386fc21b353f9b8c8b896a7d33ac61c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-10T08:47:50Z","title_canon_sha256":"c92edb039c17bf3253ec44d22d146f14d49b0bda60858316d85978153b57b9c0"},"schema_version":"1.0","source":{"id":"1705.03663","kind":"arxiv","version":1}},"canonical_sha256":"23e33899c280da5fd9734ba6916bdfabcd379ea419c35e19f8478a5e0042b3a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23e33899c280da5fd9734ba6916bdfabcd379ea419c35e19f8478a5e0042b3a0","first_computed_at":"2026-05-18T00:44:43.272017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:43.272017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iOg7RSWam6vpMthfTs0Zfd8eGGFHLWx6KQi9P5agCPWL/6REoOqudBs3aAJuCvk88jICzuapp1yOL/GASIkODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:43.272433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:848fd19cc7df106de6d83329b76d72f2ff4013dbb6bc6576e5465029ad9cd519","sha256:bf6211fed9278681caf025d958398a2511b8b0b9bd2fb21cc4702467ade82b3b"],"state_sha256":"386e478aba8af5f882d5da4f97b8e83da1e08d33bb3d45038e693dcbecfd93df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKB4fQpi1vV5zbd8LomEfDYyTLe9TAP/Bm3YneTc6zc3co+1z7irHgNhtZOsfU4uzMaHaIbgc5bmQJKWgXJ7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:28:05.181843Z","bundle_sha256":"8901aef5cfe5e0aa31f4902710a59622ae9639fa10f5364cbff11de98f230612"}}