{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FVVC2XZSVOSRM7DIU73E3QC3I6","short_pith_number":"pith:FVVC2XZS","canonical_record":{"source":{"id":"1310.6703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-24T18:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"3a000a818930911be6ac9b32137511ed769038cdca47fb36deb1acf1b51dfe73","abstract_canon_sha256":"e412040d47f63caa2c82fec5f17a21bdd977a12d949ab3574767326417fbccba"},"schema_version":"1.0"},"canonical_sha256":"2d6a2d5f32aba5167c68a7f64dc05b4784a10596ffd525e9d8f4a3bbdc20d139","source":{"kind":"arxiv","id":"1310.6703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6703","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6703v1","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6703","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVC2XZSVOSR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVVC2XZSVOSRM7DI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVVC2XZS","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FVVC2XZSVOSRM7DIU73E3QC3I6","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-24T18:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"3a000a818930911be6ac9b32137511ed769038cdca47fb36deb1acf1b51dfe73","abstract_canon_sha256":"e412040d47f63caa2c82fec5f17a21bdd977a12d949ab3574767326417fbccba"},"schema_version":"1.0"},"canonical_sha256":"2d6a2d5f32aba5167c68a7f64dc05b4784a10596ffd525e9d8f4a3bbdc20d139","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:00.398568Z","signature_b64":"ma/GyLncHPVsXl8ehfkLuPJ871MWFr74nsuqq/h1Y4pOyVp7wSfz24mua+gKGsF2iRn8ZXIRasQdLKZumzW9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d6a2d5f32aba5167c68a7f64dc05b4784a10596ffd525e9d8f4a3bbdc20d139","last_reissued_at":"2026-05-18T03:09:00.398004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:00.398004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6703","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":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwXZ9OV0SsXwA9diepHpjq4/L0xU1OKNwylGrcPCY4E4YsK2BszdhP29B+2A8dWKYWQnBY7Vz+Fj3qsB/k/YDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:05:52.545650Z"},"content_sha256":"a372b054de655d65aa579916e834adbc30d86ade44625529d66c6ebced37d709","schema_version":"1.0","event_id":"sha256:a372b054de655d65aa579916e834adbc30d86ade44625529d66c6ebced37d709"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FVVC2XZSVOSRM7DIU73E3QC3I6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Injectivity and univalence of complex functions via monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Szil\\'ard L\\'aszl\\'o","submitted_at":"2013-10-24T18:49:20Z","abstract_excerpt":"In this paper we provide sufficient conditions that ensure the monotonicity, respectively the global injectivity of an operator. Further, some new analytical conditions that assure the injectivity/univalence of a complex function of one complex variable are obtained. We also show that some classical results, such as Alexander-Noshiro-Warschawski and Wolff theorem or Mocanu theorem, are easy consequences of our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6703","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":"2026-05-18T03:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUf6pIPtrs/3RI05de+1rU6Qm8PfhzfjphaZ56nyzWLC5gTDm/JE72FrauQEfWl9HFUiZcmMfW1xS/n/01r1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:05:52.545989Z"},"content_sha256":"10ba3c5e6e4d5be87e3f843ecb57e02187f2e77cda56cfce766b66dfda0e000b","schema_version":"1.0","event_id":"sha256:10ba3c5e6e4d5be87e3f843ecb57e02187f2e77cda56cfce766b66dfda0e000b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/bundle.json","state_url":"https://pith.science/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/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":"2026-06-20T05:05:52Z","links":{"resolver":"https://pith.science/pith/FVVC2XZSVOSRM7DIU73E3QC3I6","bundle":"https://pith.science/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/bundle.json","state":"https://pith.science/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVVC2XZSVOSRM7DIU73E3QC3I6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FVVC2XZSVOSRM7DIU73E3QC3I6","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":"e412040d47f63caa2c82fec5f17a21bdd977a12d949ab3574767326417fbccba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-24T18:49:20Z","title_canon_sha256":"3a000a818930911be6ac9b32137511ed769038cdca47fb36deb1acf1b51dfe73"},"schema_version":"1.0","source":{"id":"1310.6703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6703","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6703v1","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6703","created_at":"2026-05-18T03:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVC2XZSVOSR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVVC2XZSVOSRM7DI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVVC2XZS","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:10ba3c5e6e4d5be87e3f843ecb57e02187f2e77cda56cfce766b66dfda0e000b","target":"graph","created_at":"2026-05-18T03:09:00Z","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":"In this paper we provide sufficient conditions that ensure the monotonicity, respectively the global injectivity of an operator. Further, some new analytical conditions that assure the injectivity/univalence of a complex function of one complex variable are obtained. We also show that some classical results, such as Alexander-Noshiro-Warschawski and Wolff theorem or Mocanu theorem, are easy consequences of our results.","authors_text":"Szil\\'ard L\\'aszl\\'o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-24T18:49:20Z","title":"Injectivity and univalence of complex functions via monotonicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6703","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:a372b054de655d65aa579916e834adbc30d86ade44625529d66c6ebced37d709","target":"record","created_at":"2026-05-18T03:09:00Z","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":"e412040d47f63caa2c82fec5f17a21bdd977a12d949ab3574767326417fbccba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-24T18:49:20Z","title_canon_sha256":"3a000a818930911be6ac9b32137511ed769038cdca47fb36deb1acf1b51dfe73"},"schema_version":"1.0","source":{"id":"1310.6703","kind":"arxiv","version":1}},"canonical_sha256":"2d6a2d5f32aba5167c68a7f64dc05b4784a10596ffd525e9d8f4a3bbdc20d139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d6a2d5f32aba5167c68a7f64dc05b4784a10596ffd525e9d8f4a3bbdc20d139","first_computed_at":"2026-05-18T03:09:00.398004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:00.398004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ma/GyLncHPVsXl8ehfkLuPJ871MWFr74nsuqq/h1Y4pOyVp7wSfz24mua+gKGsF2iRn8ZXIRasQdLKZumzW9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:00.398568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a372b054de655d65aa579916e834adbc30d86ade44625529d66c6ebced37d709","sha256:10ba3c5e6e4d5be87e3f843ecb57e02187f2e77cda56cfce766b66dfda0e000b"],"state_sha256":"22f2b881d66bf29be1a8071d4f5317328b1244926cedb05bc2bccadab440a1c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V8z6pm2RROfyGEZyUneWk2z5YPtU9tbu56NI0BBCSK4Y3mAfWYK4pnlcQSGlMGCDq9TK3eAOOznzFBus2yWHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:05:52.547984Z","bundle_sha256":"63dfef09471f2a6f269423a84b2d4316718c02a2bd60c29a724fb864085c4085"}}