{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NHKQ5MGNG5R3MVHAVP7HNYCWBS","short_pith_number":"pith:NHKQ5MGN","canonical_record":{"source":{"id":"1903.10232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-25T10:50:36Z","cross_cats_sorted":[],"title_canon_sha256":"f6e3e6f22d169c8af92d10db3c6651d4bfc5abde502dd734bbfb69569734773e","abstract_canon_sha256":"53067211ea6274b7d4b815f8028891adb23242d9a37beb08795a4dc09630b2f8"},"schema_version":"1.0"},"canonical_sha256":"69d50eb0cd3763b654e0abfe76e0560cac41ac599824e144eed807bc30fe6700","source":{"kind":"arxiv","id":"1903.10232","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10232","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10232v1","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10232","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"NHKQ5MGNG5R3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NHKQ5MGNG5R3MVHA","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NHKQ5MGN","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NHKQ5MGNG5R3MVHAVP7HNYCWBS","target":"record","payload":{"canonical_record":{"source":{"id":"1903.10232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-25T10:50:36Z","cross_cats_sorted":[],"title_canon_sha256":"f6e3e6f22d169c8af92d10db3c6651d4bfc5abde502dd734bbfb69569734773e","abstract_canon_sha256":"53067211ea6274b7d4b815f8028891adb23242d9a37beb08795a4dc09630b2f8"},"schema_version":"1.0"},"canonical_sha256":"69d50eb0cd3763b654e0abfe76e0560cac41ac599824e144eed807bc30fe6700","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:30.232820Z","signature_b64":"NEUiy9hNhH9UpkpTXK5AlCEJdM5bcSEq0Bz2x7GIyTAAN499Vcpp5gOjbpfgYbrD2EOkOg7dyV9shrhc6t9TAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69d50eb0cd3763b654e0abfe76e0560cac41ac599824e144eed807bc30fe6700","last_reissued_at":"2026-05-17T23:50:30.232070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:30.232070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.10232","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":"2026-05-17T23:50:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzq3FUMcS/Jh1h6Dvz9Hz8Vj9WktJsFvebzggz0PAMMPhUyB37dOFcN5kLCDcvO9NBsKCQgITelX1LeB/IzIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:17:48.177653Z"},"content_sha256":"e32c833e36fb32e7db257728e880d585bcc8241f174a29c387e6cd548960dd8a","schema_version":"1.0","event_id":"sha256:e32c833e36fb32e7db257728e880d585bcc8241f174a29c387e6cd548960dd8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NHKQ5MGNG5R3MVHAVP7HNYCWBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Successive coefficients for spirallike and related functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saminathan Ponnusamy, Swadesh Kumar Sahoo, Vibhuti Arora","submitted_at":"2019-03-25T10:50:36Z","abstract_excerpt":"We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\\big | |a_{n+1}|-|a_n|\\big |$, for $f$ belonging to the family of $\\gamma$-spirallike functions of order $\\alpha$. Our particular results include the case of starlike and convex functions of order $\\alpha$\n  and other related class of functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10232","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":"2026-05-17T23:50:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KeLfYHE8GayyiBER8V+wb0mBgSYaFOs/tm9p8FVEKfeRSldL34tNalf0KyEOAfeWGwxqMkCWvpFeds3t7RfOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:17:48.178292Z"},"content_sha256":"41e9e0881f3b38ada3164b0c7be89c8305593bb79ca55a9c723e8c0bc2938e29","schema_version":"1.0","event_id":"sha256:41e9e0881f3b38ada3164b0c7be89c8305593bb79ca55a9c723e8c0bc2938e29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/bundle.json","state_url":"https://pith.science/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/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":"2026-06-05T21:17:48Z","links":{"resolver":"https://pith.science/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS","bundle":"https://pith.science/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/bundle.json","state":"https://pith.science/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHKQ5MGNG5R3MVHAVP7HNYCWBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NHKQ5MGNG5R3MVHAVP7HNYCWBS","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":"53067211ea6274b7d4b815f8028891adb23242d9a37beb08795a4dc09630b2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-25T10:50:36Z","title_canon_sha256":"f6e3e6f22d169c8af92d10db3c6651d4bfc5abde502dd734bbfb69569734773e"},"schema_version":"1.0","source":{"id":"1903.10232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10232","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10232v1","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10232","created_at":"2026-05-17T23:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"NHKQ5MGNG5R3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NHKQ5MGNG5R3MVHA","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NHKQ5MGN","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:41e9e0881f3b38ada3164b0c7be89c8305593bb79ca55a9c723e8c0bc2938e29","target":"graph","created_at":"2026-05-17T23:50:30Z","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":"We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\\big | |a_{n+1}|-|a_n|\\big |$, for $f$ belonging to the family of $\\gamma$-spirallike functions of order $\\alpha$. Our particular results include the case of starlike and convex functions of order $\\alpha$\n  and other related class of functions.","authors_text":"Saminathan Ponnusamy, Swadesh Kumar Sahoo, Vibhuti Arora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-25T10:50:36Z","title":"Successive coefficients for spirallike and related functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10232","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:e32c833e36fb32e7db257728e880d585bcc8241f174a29c387e6cd548960dd8a","target":"record","created_at":"2026-05-17T23:50:30Z","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":"53067211ea6274b7d4b815f8028891adb23242d9a37beb08795a4dc09630b2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-25T10:50:36Z","title_canon_sha256":"f6e3e6f22d169c8af92d10db3c6651d4bfc5abde502dd734bbfb69569734773e"},"schema_version":"1.0","source":{"id":"1903.10232","kind":"arxiv","version":1}},"canonical_sha256":"69d50eb0cd3763b654e0abfe76e0560cac41ac599824e144eed807bc30fe6700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69d50eb0cd3763b654e0abfe76e0560cac41ac599824e144eed807bc30fe6700","first_computed_at":"2026-05-17T23:50:30.232070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:30.232070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NEUiy9hNhH9UpkpTXK5AlCEJdM5bcSEq0Bz2x7GIyTAAN499Vcpp5gOjbpfgYbrD2EOkOg7dyV9shrhc6t9TAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:30.232820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e32c833e36fb32e7db257728e880d585bcc8241f174a29c387e6cd548960dd8a","sha256:41e9e0881f3b38ada3164b0c7be89c8305593bb79ca55a9c723e8c0bc2938e29"],"state_sha256":"53360ad07c7651be870fcf0ced8ed081aa08f6fbf57f80f591c4bf1ecb239129"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ltW8pYmPt9ShIZ4rZBqPVRemvnhHpvYJYaaAgzE0JbzIGvZPqRn38J7eYSWSaAEQ6gBwteGuZtHsJng/yZUKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:17:48.180479Z","bundle_sha256":"82f76565e8cca8c2cddf87e95eb765f03292184a6c6d59104f81595e4502cf96"}}