{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7BSLIJLZJQICOZ65XNZQCZHZFX","short_pith_number":"pith:7BSLIJLZ","canonical_record":{"source":{"id":"1610.06706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-21T09:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"8eaa40e8c62738937f3c844e2f7dfbadac2995dd8cb9485a9788e7238cdf9f35","abstract_canon_sha256":"18a4a5bc8e8bd425ef372817536acfbbd063f71aa85a3edd74fb0d108f32cbd5"},"schema_version":"1.0"},"canonical_sha256":"f864b425794c102767ddbb730164f92dc451cb6462e7632b132bd41bf754d66f","source":{"kind":"arxiv","id":"1610.06706","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06706","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06706v1","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06706","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"7BSLIJLZJQIC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7BSLIJLZJQICOZ65","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7BSLIJLZ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7BSLIJLZJQICOZ65XNZQCZHZFX","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-21T09:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"8eaa40e8c62738937f3c844e2f7dfbadac2995dd8cb9485a9788e7238cdf9f35","abstract_canon_sha256":"18a4a5bc8e8bd425ef372817536acfbbd063f71aa85a3edd74fb0d108f32cbd5"},"schema_version":"1.0"},"canonical_sha256":"f864b425794c102767ddbb730164f92dc451cb6462e7632b132bd41bf754d66f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.928950Z","signature_b64":"b9eBSFPj7KTCf1WmQVTu3+X3eoP7Bcw5o/RuglCDNvU2StbHpxr2PC7sKQHOIPR4tMxz3wzps4ag8ufAkTF4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f864b425794c102767ddbb730164f92dc451cb6462e7632b132bd41bf754d66f","last_reissued_at":"2026-05-18T01:01:36.928496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.928496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06706","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":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XUoSuXQfDVHNmwQumpwUdzgVPLpirK/0PiSGTB2Ltx/G9IldEva2WRiux+GEfvJUvfeHd3ODIilMlnLLbWCvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:23:30.502305Z"},"content_sha256":"a95d0e074a46fafefccc27d276539d7c819c33e0bce02481f9bc80eca06c47c0","schema_version":"1.0","event_id":"sha256:a95d0e074a46fafefccc27d276539d7c819c33e0bce02481f9bc80eca06c47c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7BSLIJLZJQICOZ65XNZQCZHZFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein- and Markov-type inequalities for rational functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"B\\'ela Nagy, Sergei Kalmykov, Vilmos Totik","submitted_at":"2016-10-21T09:01:00Z","abstract_excerpt":"Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on $C^2$ smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green's functions with poles at the poles of the rational functions in question. As a special case (when all the poles are at infinity) the corresponding results for polynomials are recaptured."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06706","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":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFOUhpGbbSsMtQZg1oVlcB5gi9dtxZbVDX35v6uAilq3BWFH2qkkzoCgZt4zOFbs38iXyiQ0r5T9rcqZb7CfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:23:30.502911Z"},"content_sha256":"27a77bc39a06d345118c11d20c1e26b1d3f3a779ea39a2b803d1770175d5e5e5","schema_version":"1.0","event_id":"sha256:27a77bc39a06d345118c11d20c1e26b1d3f3a779ea39a2b803d1770175d5e5e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/bundle.json","state_url":"https://pith.science/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/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":"2026-05-31T01:23:30Z","links":{"resolver":"https://pith.science/pith/7BSLIJLZJQICOZ65XNZQCZHZFX","bundle":"https://pith.science/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/bundle.json","state":"https://pith.science/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BSLIJLZJQICOZ65XNZQCZHZFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7BSLIJLZJQICOZ65XNZQCZHZFX","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":"18a4a5bc8e8bd425ef372817536acfbbd063f71aa85a3edd74fb0d108f32cbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-21T09:01:00Z","title_canon_sha256":"8eaa40e8c62738937f3c844e2f7dfbadac2995dd8cb9485a9788e7238cdf9f35"},"schema_version":"1.0","source":{"id":"1610.06706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06706","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06706v1","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06706","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"7BSLIJLZJQIC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7BSLIJLZJQICOZ65","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7BSLIJLZ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:27a77bc39a06d345118c11d20c1e26b1d3f3a779ea39a2b803d1770175d5e5e5","target":"graph","created_at":"2026-05-18T01:01:36Z","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":"Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on $C^2$ smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green's functions with poles at the poles of the rational functions in question. As a special case (when all the poles are at infinity) the corresponding results for polynomials are recaptured.","authors_text":"B\\'ela Nagy, Sergei Kalmykov, Vilmos Totik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-21T09:01:00Z","title":"Bernstein- and Markov-type inequalities for rational functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06706","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:a95d0e074a46fafefccc27d276539d7c819c33e0bce02481f9bc80eca06c47c0","target":"record","created_at":"2026-05-18T01:01:36Z","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":"18a4a5bc8e8bd425ef372817536acfbbd063f71aa85a3edd74fb0d108f32cbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-21T09:01:00Z","title_canon_sha256":"8eaa40e8c62738937f3c844e2f7dfbadac2995dd8cb9485a9788e7238cdf9f35"},"schema_version":"1.0","source":{"id":"1610.06706","kind":"arxiv","version":1}},"canonical_sha256":"f864b425794c102767ddbb730164f92dc451cb6462e7632b132bd41bf754d66f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f864b425794c102767ddbb730164f92dc451cb6462e7632b132bd41bf754d66f","first_computed_at":"2026-05-18T01:01:36.928496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:36.928496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9eBSFPj7KTCf1WmQVTu3+X3eoP7Bcw5o/RuglCDNvU2StbHpxr2PC7sKQHOIPR4tMxz3wzps4ag8ufAkTF4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:36.928950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a95d0e074a46fafefccc27d276539d7c819c33e0bce02481f9bc80eca06c47c0","sha256:27a77bc39a06d345118c11d20c1e26b1d3f3a779ea39a2b803d1770175d5e5e5"],"state_sha256":"b2a6978fa80b52fd06d401661b5ddac548c82b25281a598b66ce833a6cc3a686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ss4dUnyrq3sove10Fpnq5Mmy1aIoMu1dmNq4eAcskxhMam4Nslo5LNvV/3hirmusFtn5J+gfQcu1NeNjQfZxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:23:30.506056Z","bundle_sha256":"835e6b8cf6d28ef61aa95d41ef348577a33aebd725d38676bf081e85817b7e36"}}