{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XJUZH6NUHEOKSXONS5QW62CDBN","short_pith_number":"pith:XJUZH6NU","canonical_record":{"source":{"id":"1807.11162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-30T04:06:04Z","cross_cats_sorted":[],"title_canon_sha256":"fa03300165f224c1c5f5e9d26ecd0e3fbd61a9a059a48cac14eab90a92f1905b","abstract_canon_sha256":"f7086b5358fbc94c8120333a993873b39f26c15819a6b313ac7029f556b1934c"},"schema_version":"1.0"},"canonical_sha256":"ba6993f9b4391ca95dcd97616f68430b66b4b859603451ddef311d31513ba4f0","source":{"kind":"arxiv","id":"1807.11162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11162","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11162v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11162","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"XJUZH6NUHEOK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XJUZH6NUHEOKSXON","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XJUZH6NU","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XJUZH6NUHEOKSXONS5QW62CDBN","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-30T04:06:04Z","cross_cats_sorted":[],"title_canon_sha256":"fa03300165f224c1c5f5e9d26ecd0e3fbd61a9a059a48cac14eab90a92f1905b","abstract_canon_sha256":"f7086b5358fbc94c8120333a993873b39f26c15819a6b313ac7029f556b1934c"},"schema_version":"1.0"},"canonical_sha256":"ba6993f9b4391ca95dcd97616f68430b66b4b859603451ddef311d31513ba4f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.773053Z","signature_b64":"F/cegirxuLVb4k3EAAD1IzL9aefLRGJM+LbNjAgkdLLzCKCDQ4QnY6WsnJofjFYS2b4PncdvA0KV47hZzrCOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba6993f9b4391ca95dcd97616f68430b66b4b859603451ddef311d31513ba4f0","last_reissued_at":"2026-05-18T00:09:32.772651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.772651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11162","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6vt80+kitusU/qiMxw2w3Fx2y37I008Zx9N3wnEwSVFUMSZ440Y8DEbKDwTbkFKq1V3/BpTw1sFeOASlJ3JMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:19:59.179807Z"},"content_sha256":"06c14b574a9055f82e9e1a95dda7540510b0d71a6e2f99cb721fd5f3ac1c38be","schema_version":"1.0","event_id":"sha256:06c14b574a9055f82e9e1a95dda7540510b0d71a6e2f99cb721fd5f3ac1c38be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XJUZH6NUHEOKSXONS5QW62CDBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial estimates over exponential curves in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Shirali Kadyrov, Yershat Sapazhanov","submitted_at":"2018-07-30T04:06:04Z","abstract_excerpt":"For any complex $\\alpha$ with non-zero imaginary part we show that Bernstein-Walsh type inequality holds on the piece of the curve $\\{(e^z,e^{\\alpha z}) : z \\in \\mathbb C\\}$. Our result extends a theorem of Coman-Poletsky \\cite{CP10} where they considered real-valued $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11162","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFklTHImANy2K4iGmnufem9Z5eXKmBCR1wMnIsc18ugLfpXOvV1UhQgu09dk6fAhRKHyYwswzs2Bb+QtLfQVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:19:59.180465Z"},"content_sha256":"b21afeef1f47504e15ad39412eb0247db6402b773ee87ef9be4946db7ca05604","schema_version":"1.0","event_id":"sha256:b21afeef1f47504e15ad39412eb0247db6402b773ee87ef9be4946db7ca05604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJUZH6NUHEOKSXONS5QW62CDBN/bundle.json","state_url":"https://pith.science/pith/XJUZH6NUHEOKSXONS5QW62CDBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJUZH6NUHEOKSXONS5QW62CDBN/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":"2026-05-30T18:19:59Z","links":{"resolver":"https://pith.science/pith/XJUZH6NUHEOKSXONS5QW62CDBN","bundle":"https://pith.science/pith/XJUZH6NUHEOKSXONS5QW62CDBN/bundle.json","state":"https://pith.science/pith/XJUZH6NUHEOKSXONS5QW62CDBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJUZH6NUHEOKSXONS5QW62CDBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XJUZH6NUHEOKSXONS5QW62CDBN","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":"f7086b5358fbc94c8120333a993873b39f26c15819a6b313ac7029f556b1934c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-30T04:06:04Z","title_canon_sha256":"fa03300165f224c1c5f5e9d26ecd0e3fbd61a9a059a48cac14eab90a92f1905b"},"schema_version":"1.0","source":{"id":"1807.11162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11162","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11162v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11162","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"XJUZH6NUHEOK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XJUZH6NUHEOKSXON","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XJUZH6NU","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:b21afeef1f47504e15ad39412eb0247db6402b773ee87ef9be4946db7ca05604","target":"graph","created_at":"2026-05-18T00:09:32Z","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":"For any complex $\\alpha$ with non-zero imaginary part we show that Bernstein-Walsh type inequality holds on the piece of the curve $\\{(e^z,e^{\\alpha z}) : z \\in \\mathbb C\\}$. Our result extends a theorem of Coman-Poletsky \\cite{CP10} where they considered real-valued $\\alpha$.","authors_text":"Shirali Kadyrov, Yershat Sapazhanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-30T04:06:04Z","title":"Polynomial estimates over exponential curves in $\\mathbb C^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11162","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":"sha256:06c14b574a9055f82e9e1a95dda7540510b0d71a6e2f99cb721fd5f3ac1c38be","target":"record","created_at":"2026-05-18T00:09:32Z","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":"f7086b5358fbc94c8120333a993873b39f26c15819a6b313ac7029f556b1934c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-30T04:06:04Z","title_canon_sha256":"fa03300165f224c1c5f5e9d26ecd0e3fbd61a9a059a48cac14eab90a92f1905b"},"schema_version":"1.0","source":{"id":"1807.11162","kind":"arxiv","version":1}},"canonical_sha256":"ba6993f9b4391ca95dcd97616f68430b66b4b859603451ddef311d31513ba4f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba6993f9b4391ca95dcd97616f68430b66b4b859603451ddef311d31513ba4f0","first_computed_at":"2026-05-18T00:09:32.772651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.772651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F/cegirxuLVb4k3EAAD1IzL9aefLRGJM+LbNjAgkdLLzCKCDQ4QnY6WsnJofjFYS2b4PncdvA0KV47hZzrCOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.773053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06c14b574a9055f82e9e1a95dda7540510b0d71a6e2f99cb721fd5f3ac1c38be","sha256:b21afeef1f47504e15ad39412eb0247db6402b773ee87ef9be4946db7ca05604"],"state_sha256":"1923ba1b16fb71ab5eeeb608dd6067024e72299832e72ec16a78cec4416aa786"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8c5gLlcpnqflCJjbWHpJ+hJHagfroTWkq3Q6xdTE/j/QJkc8vNjwzpCICv+poJgTimWbguudsUA5/xf8+mfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:19:59.183839Z","bundle_sha256":"b485e64587438b4302e51197e99fb37dfe4626b0f43fd0db8389f5e9fbdcbecb"}}