{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WMWH5PDIUTXAWUQLVCP5IZWSIC","short_pith_number":"pith:WMWH5PDI","canonical_record":{"source":{"id":"1511.05346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-17T10:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"c78bee55bf3e064aea4b9f50cd4929a7660872f7ea09d7a6c60ed476d9577c23","abstract_canon_sha256":"9baa0428ac63880b883bdecdbf337c132fc745f0d33beb49c424fd0bdf9e9800"},"schema_version":"1.0"},"canonical_sha256":"b32c7ebc68a4ee0b520ba89fd466d240a36ae24ada96e9b508a0ff96dcc2a8a8","source":{"kind":"arxiv","id":"1511.05346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05346","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05346v1","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05346","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"WMWH5PDIUTXA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WMWH5PDIUTXAWUQL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WMWH5PDI","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WMWH5PDIUTXAWUQLVCP5IZWSIC","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-17T10:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"c78bee55bf3e064aea4b9f50cd4929a7660872f7ea09d7a6c60ed476d9577c23","abstract_canon_sha256":"9baa0428ac63880b883bdecdbf337c132fc745f0d33beb49c424fd0bdf9e9800"},"schema_version":"1.0"},"canonical_sha256":"b32c7ebc68a4ee0b520ba89fd466d240a36ae24ada96e9b508a0ff96dcc2a8a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:52.284815Z","signature_b64":"XgFuv9ytXS97sG+Lf8WGKm8tAmUhFAE01EqER3NJy4bsxfUNldufmOWdxZd2+XTfBAcMNbX8tEVy/jqg1ciGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b32c7ebc68a4ee0b520ba89fd466d240a36ae24ada96e9b508a0ff96dcc2a8a8","last_reissued_at":"2026-05-18T00:29:52.284352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:52.284352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05346","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTqwyZSpAQCDXVWAWF3IJsaU0NORfybhdRJ8dEsd8aOm/jf2/AX4Dx6N5/mOkecSqzDz27AzB5Xe7NSfWquNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:46:56.319176Z"},"content_sha256":"09c0c890cd9b32eac2da17e1feee34fe8d9a69e6d01205dffcc542cefebb3053","schema_version":"1.0","event_id":"sha256:09c0c890cd9b32eac2da17e1feee34fe8d9a69e6d01205dffcc542cefebb3053"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WMWH5PDIUTXAWUQLVCP5IZWSIC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How many Zolotarev fractions are there?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei Bogatyrev","submitted_at":"2015-11-17T10:57:43Z","abstract_excerpt":"Known properties of Chebyshev polynomials are the following: they have simple critical points with only two (finite) critical values. Those properties uniquely determine the named polynomials modulo affine transformations of dependent and independent variables. A similar property of Zolotarev fractions: simple critical points and only four critical values generates already many classes of rational functions modulo projective transformations of their dependent and independent variables. They are listed in this note."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05346","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48HAUrsCBbjFzeCf8dIW0arL8vIw8Np5BKVWudGnC1bC/NFGqn3Cuq8NxnIVABDXLlW62GRmkQ5plh/3ctxjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:46:56.319531Z"},"content_sha256":"558129fcd256d979df8876d504d2043f30ed7035380a6801fafc9591d3c96590","schema_version":"1.0","event_id":"sha256:558129fcd256d979df8876d504d2043f30ed7035380a6801fafc9591d3c96590"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/bundle.json","state_url":"https://pith.science/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/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":"2026-06-21T11:46:56Z","links":{"resolver":"https://pith.science/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC","bundle":"https://pith.science/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/bundle.json","state":"https://pith.science/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMWH5PDIUTXAWUQLVCP5IZWSIC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WMWH5PDIUTXAWUQLVCP5IZWSIC","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":"9baa0428ac63880b883bdecdbf337c132fc745f0d33beb49c424fd0bdf9e9800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-17T10:57:43Z","title_canon_sha256":"c78bee55bf3e064aea4b9f50cd4929a7660872f7ea09d7a6c60ed476d9577c23"},"schema_version":"1.0","source":{"id":"1511.05346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05346","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05346v1","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05346","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"WMWH5PDIUTXA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WMWH5PDIUTXAWUQL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WMWH5PDI","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:558129fcd256d979df8876d504d2043f30ed7035380a6801fafc9591d3c96590","target":"graph","created_at":"2026-05-18T00:29:52Z","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":"Known properties of Chebyshev polynomials are the following: they have simple critical points with only two (finite) critical values. Those properties uniquely determine the named polynomials modulo affine transformations of dependent and independent variables. A similar property of Zolotarev fractions: simple critical points and only four critical values generates already many classes of rational functions modulo projective transformations of their dependent and independent variables. They are listed in this note.","authors_text":"Andrei Bogatyrev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-17T10:57:43Z","title":"How many Zolotarev fractions are there?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05346","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":"sha256:09c0c890cd9b32eac2da17e1feee34fe8d9a69e6d01205dffcc542cefebb3053","target":"record","created_at":"2026-05-18T00:29:52Z","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":"9baa0428ac63880b883bdecdbf337c132fc745f0d33beb49c424fd0bdf9e9800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-17T10:57:43Z","title_canon_sha256":"c78bee55bf3e064aea4b9f50cd4929a7660872f7ea09d7a6c60ed476d9577c23"},"schema_version":"1.0","source":{"id":"1511.05346","kind":"arxiv","version":1}},"canonical_sha256":"b32c7ebc68a4ee0b520ba89fd466d240a36ae24ada96e9b508a0ff96dcc2a8a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b32c7ebc68a4ee0b520ba89fd466d240a36ae24ada96e9b508a0ff96dcc2a8a8","first_computed_at":"2026-05-18T00:29:52.284352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:52.284352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XgFuv9ytXS97sG+Lf8WGKm8tAmUhFAE01EqER3NJy4bsxfUNldufmOWdxZd2+XTfBAcMNbX8tEVy/jqg1ciGAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:52.284815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c0c890cd9b32eac2da17e1feee34fe8d9a69e6d01205dffcc542cefebb3053","sha256:558129fcd256d979df8876d504d2043f30ed7035380a6801fafc9591d3c96590"],"state_sha256":"ea22c4f0bcebe10d0b89077813631a488461148a53b9a097b01d94d8626664d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDccCHJsOPET59MoBCoxqmwrroE3EVF3cg1ADsHgvrh9QZmNVLm2l2XOuTW3rwBfvjx82zF4UcjHGQEySZrlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:46:56.321525Z","bundle_sha256":"9a8103ec0f71252b2052b91a8c9e6db870292c59c3c6c76b6d51755c3cb2a452"}}