{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F6V7OCLJFQ3AXVKYWTPZNQGZYM","short_pith_number":"pith:F6V7OCLJ","canonical_record":{"source":{"id":"1503.06620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-23T12:32:23Z","cross_cats_sorted":[],"title_canon_sha256":"a598b47e74277b68484b3e2f420032d49436ff0cb2440737b7ff4c3d20ac2ac2","abstract_canon_sha256":"da0273d867b6799994d97683957b37b92a3932f5502f607c9690a2ec86896dce"},"schema_version":"1.0"},"canonical_sha256":"2fabf709692c360bd558b4df96c0d9c30481c30df384dcb690012ac9d03f61cf","source":{"kind":"arxiv","id":"1503.06620","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06620","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06620v1","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06620","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"F6V7OCLJFQ3A","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F6V7OCLJFQ3AXVKY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F6V7OCLJ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F6V7OCLJFQ3AXVKYWTPZNQGZYM","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-23T12:32:23Z","cross_cats_sorted":[],"title_canon_sha256":"a598b47e74277b68484b3e2f420032d49436ff0cb2440737b7ff4c3d20ac2ac2","abstract_canon_sha256":"da0273d867b6799994d97683957b37b92a3932f5502f607c9690a2ec86896dce"},"schema_version":"1.0"},"canonical_sha256":"2fabf709692c360bd558b4df96c0d9c30481c30df384dcb690012ac9d03f61cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:20.823163Z","signature_b64":"YO7mXPoWrdtEsnr/M9PyANpDGLAyeeRhGuk0kYSRAXJ6y1dcYAFXTn3+6N7patFTGMzANLizM1rt12ylHF+PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fabf709692c360bd558b4df96c0d9c30481c30df384dcb690012ac9d03f61cf","last_reissued_at":"2026-05-18T00:54:20.822801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:20.822801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06620","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ogo8F6tYZ4KO1GZFfY63G5AtaILOPNXY2dASPYuNw/k6k4mZeKqyMQQ+HBiVUUW13vLjdNY47O+bc7eS6k39Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:31:56.699722Z"},"content_sha256":"c4b02723e941c9873d93ca7351a30b310d88217c049a5951f25b05d5b2cad6f3","schema_version":"1.0","event_id":"sha256:c4b02723e941c9873d93ca7351a30b310d88217c049a5951f25b05d5b2cad6f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F6V7OCLJFQ3AXVKYWTPZNQGZYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gonchar-Stahl's $\\rho^2$-theorem and associated directions in the theory of rational approximation of analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"E. A. Rakhmanov","submitted_at":"2015-03-23T12:32:23Z","abstract_excerpt":"Gonchar-Stahl's $\\rho^2$-theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions. The theorem itself, its modifications and generalizations, methods involved in the proof and other related details constitute an important subfield in the theory of rational approximations of analytic functions and complex analysis.\n  The paper briefly outlines essentials of the subfield. Fundamental contributions by A. A. Gonchar and H. Stahl are in the center of the exposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06620","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6Qg/M9TSNvJDEmi1cgEpuuQX7sOdwj4fhM8hc8/7z1GBDaBthPjrsGnohHHoGME+j7GmTD6jHIMfyxSSTSVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:31:56.700061Z"},"content_sha256":"f1f673c88937523e2e02d5b3536037cf812b3f0f8025335d8657968281f69f74","schema_version":"1.0","event_id":"sha256:f1f673c88937523e2e02d5b3536037cf812b3f0f8025335d8657968281f69f74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/bundle.json","state_url":"https://pith.science/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/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":"2026-06-08T23:31:56Z","links":{"resolver":"https://pith.science/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM","bundle":"https://pith.science/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/bundle.json","state":"https://pith.science/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6V7OCLJFQ3AXVKYWTPZNQGZYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F6V7OCLJFQ3AXVKYWTPZNQGZYM","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":"da0273d867b6799994d97683957b37b92a3932f5502f607c9690a2ec86896dce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-23T12:32:23Z","title_canon_sha256":"a598b47e74277b68484b3e2f420032d49436ff0cb2440737b7ff4c3d20ac2ac2"},"schema_version":"1.0","source":{"id":"1503.06620","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06620","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06620v1","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06620","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"F6V7OCLJFQ3A","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F6V7OCLJFQ3AXVKY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F6V7OCLJ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:f1f673c88937523e2e02d5b3536037cf812b3f0f8025335d8657968281f69f74","target":"graph","created_at":"2026-05-18T00:54:20Z","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":"Gonchar-Stahl's $\\rho^2$-theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions. The theorem itself, its modifications and generalizations, methods involved in the proof and other related details constitute an important subfield in the theory of rational approximations of analytic functions and complex analysis.\n  The paper briefly outlines essentials of the subfield. Fundamental contributions by A. A. Gonchar and H. Stahl are in the center of the exposition.","authors_text":"E. A. Rakhmanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-23T12:32:23Z","title":"Gonchar-Stahl's $\\rho^2$-theorem and associated directions in the theory of rational approximation of analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06620","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:c4b02723e941c9873d93ca7351a30b310d88217c049a5951f25b05d5b2cad6f3","target":"record","created_at":"2026-05-18T00:54:20Z","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":"da0273d867b6799994d97683957b37b92a3932f5502f607c9690a2ec86896dce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-23T12:32:23Z","title_canon_sha256":"a598b47e74277b68484b3e2f420032d49436ff0cb2440737b7ff4c3d20ac2ac2"},"schema_version":"1.0","source":{"id":"1503.06620","kind":"arxiv","version":1}},"canonical_sha256":"2fabf709692c360bd558b4df96c0d9c30481c30df384dcb690012ac9d03f61cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fabf709692c360bd558b4df96c0d9c30481c30df384dcb690012ac9d03f61cf","first_computed_at":"2026-05-18T00:54:20.822801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:20.822801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YO7mXPoWrdtEsnr/M9PyANpDGLAyeeRhGuk0kYSRAXJ6y1dcYAFXTn3+6N7patFTGMzANLizM1rt12ylHF+PBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:20.823163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06620","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b02723e941c9873d93ca7351a30b310d88217c049a5951f25b05d5b2cad6f3","sha256:f1f673c88937523e2e02d5b3536037cf812b3f0f8025335d8657968281f69f74"],"state_sha256":"071d73f49d855ba42d4e520d3a2d7a86671368ef6a3df36eee9965bcd20604c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6BS9o6uLec8fUSfZfxZUj2ijgWprOWEoBM4FZWEBkmKpNJh9gqvsCxL2OJxwC+R1xLx6pEC9PCBdmt+ZLy/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:31:56.701902Z","bundle_sha256":"620c068ddd3f6f1b83bd4e2306df8ef46f405e0adcb4fc5997432bc1509ecc02"}}