{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CDF5Q6F7F4NFVG2S7KBFMDFMCL","short_pith_number":"pith:CDF5Q6F7","canonical_record":{"source":{"id":"1801.01985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-06T08:05:43Z","cross_cats_sorted":["math.AG","math.CV","math.NT"],"title_canon_sha256":"be945d8cacc840803d69d27e7d170b3c0f457359192773da1674571a388331d7","abstract_canon_sha256":"b8789058c0b3ef67f6a1b44812eed9eab0082b18ef4c9383f9497a3e750e87e7"},"schema_version":"1.0"},"canonical_sha256":"10cbd878bf2f1a5a9b52fa82560cac12c1a2ea6e3ed9f81f2d70c85ac11952e3","source":{"kind":"arxiv","id":"1801.01985","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01985","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01985v2","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01985","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"CDF5Q6F7F4NF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDF5Q6F7F4NFVG2S","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDF5Q6F7","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CDF5Q6F7F4NFVG2S7KBFMDFMCL","target":"record","payload":{"canonical_record":{"source":{"id":"1801.01985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-06T08:05:43Z","cross_cats_sorted":["math.AG","math.CV","math.NT"],"title_canon_sha256":"be945d8cacc840803d69d27e7d170b3c0f457359192773da1674571a388331d7","abstract_canon_sha256":"b8789058c0b3ef67f6a1b44812eed9eab0082b18ef4c9383f9497a3e750e87e7"},"schema_version":"1.0"},"canonical_sha256":"10cbd878bf2f1a5a9b52fa82560cac12c1a2ea6e3ed9f81f2d70c85ac11952e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:03.134544Z","signature_b64":"jbKI7jIXKIBjqoHoqQRgN7pgll+sGJ7lW6RIlfxf/2DTMvEcbBADejEJZMeen2gBTz17PiiEqjLIVfkRmxLqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10cbd878bf2f1a5a9b52fa82560cac12c1a2ea6e3ed9f81f2d70c85ac11952e3","last_reissued_at":"2026-05-17T23:54:03.134123Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:03.134123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.01985","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5hH8NHObXdgAkbGugccSg15svBXd6CePc2VMJXLbQId9guFm+3lB8+YOzGOo4JBWg8gFgUo44rcrzAMfaNRVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:26:19.648420Z"},"content_sha256":"2821e2d51d6c01931835d0d599920007323f9f9a8bfbd9dd4098dbce1066ba9e","schema_version":"1.0","event_id":"sha256:2821e2d51d6c01931835d0d599920007323f9f9a8bfbd9dd4098dbce1066ba9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CDF5Q6F7F4NFVG2S7KBFMDFMCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic curves $A^{\\circ l}(x)-U(y)=0$ and arithmetic of orbits of rational functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.NT"],"primary_cat":"math.DS","authors_text":"Fedor Pakovich","submitted_at":"2018-01-06T08:05:43Z","abstract_excerpt":"We give a description of pairs of complex rational functions $A$ and $U$ of degree at least two such that for every $d\\geq 1$ the algebraic curve $A^{\\circ d}(x)-U(y)=0$ has a factor of genus zero or one. In particular, we show that if $A$ is not a `generalized Latt\\`es map', then this condition is satisfied if and only if there exists a rational function $V$ such that $U\\circ V=A^{\\circ l}$ for some $l\\geq 1.$ We also prove a version of the dynamical Mordell-Lang conjecture, concerning intersections of orbits of points from $\\mathbb P^1(K)$ under iterates of $A$ with the value set $U(\\mathbb "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01985","kind":"arxiv","version":2},"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":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VoNx44bqbkJarssQ7a1n0dkCRtvutNR/mjysHmroJfKN994t0H6JDyn4Wt4z8Ng+S3PSZK6o/SrrjBDlcegAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:26:19.648801Z"},"content_sha256":"e30ce22be9d2666202257b0bee52bfa1e8bcfa5cb30d12a1bfb131028657b9de","schema_version":"1.0","event_id":"sha256:e30ce22be9d2666202257b0bee52bfa1e8bcfa5cb30d12a1bfb131028657b9de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/bundle.json","state_url":"https://pith.science/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/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":"2026-06-28T15:26:19Z","links":{"resolver":"https://pith.science/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL","bundle":"https://pith.science/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/bundle.json","state":"https://pith.science/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDF5Q6F7F4NFVG2S7KBFMDFMCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CDF5Q6F7F4NFVG2S7KBFMDFMCL","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":"b8789058c0b3ef67f6a1b44812eed9eab0082b18ef4c9383f9497a3e750e87e7","cross_cats_sorted":["math.AG","math.CV","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-06T08:05:43Z","title_canon_sha256":"be945d8cacc840803d69d27e7d170b3c0f457359192773da1674571a388331d7"},"schema_version":"1.0","source":{"id":"1801.01985","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01985","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01985v2","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01985","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"CDF5Q6F7F4NF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDF5Q6F7F4NFVG2S","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDF5Q6F7","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:e30ce22be9d2666202257b0bee52bfa1e8bcfa5cb30d12a1bfb131028657b9de","target":"graph","created_at":"2026-05-17T23:54:03Z","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":"We give a description of pairs of complex rational functions $A$ and $U$ of degree at least two such that for every $d\\geq 1$ the algebraic curve $A^{\\circ d}(x)-U(y)=0$ has a factor of genus zero or one. In particular, we show that if $A$ is not a `generalized Latt\\`es map', then this condition is satisfied if and only if there exists a rational function $V$ such that $U\\circ V=A^{\\circ l}$ for some $l\\geq 1.$ We also prove a version of the dynamical Mordell-Lang conjecture, concerning intersections of orbits of points from $\\mathbb P^1(K)$ under iterates of $A$ with the value set $U(\\mathbb ","authors_text":"Fedor Pakovich","cross_cats":["math.AG","math.CV","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-06T08:05:43Z","title":"Algebraic curves $A^{\\circ l}(x)-U(y)=0$ and arithmetic of orbits of rational functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01985","kind":"arxiv","version":2},"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":"sha256:2821e2d51d6c01931835d0d599920007323f9f9a8bfbd9dd4098dbce1066ba9e","target":"record","created_at":"2026-05-17T23:54:03Z","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":"b8789058c0b3ef67f6a1b44812eed9eab0082b18ef4c9383f9497a3e750e87e7","cross_cats_sorted":["math.AG","math.CV","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-06T08:05:43Z","title_canon_sha256":"be945d8cacc840803d69d27e7d170b3c0f457359192773da1674571a388331d7"},"schema_version":"1.0","source":{"id":"1801.01985","kind":"arxiv","version":2}},"canonical_sha256":"10cbd878bf2f1a5a9b52fa82560cac12c1a2ea6e3ed9f81f2d70c85ac11952e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10cbd878bf2f1a5a9b52fa82560cac12c1a2ea6e3ed9f81f2d70c85ac11952e3","first_computed_at":"2026-05-17T23:54:03.134123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.134123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbKI7jIXKIBjqoHoqQRgN7pgll+sGJ7lW6RIlfxf/2DTMvEcbBADejEJZMeen2gBTz17PiiEqjLIVfkRmxLqAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.134544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01985","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2821e2d51d6c01931835d0d599920007323f9f9a8bfbd9dd4098dbce1066ba9e","sha256:e30ce22be9d2666202257b0bee52bfa1e8bcfa5cb30d12a1bfb131028657b9de"],"state_sha256":"0927273bfe6f79cb4c9498b82ec5bb535b57f5bf19ece7a413bcf84c4d45f440"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6b5qOhrSEz7+3r+6M5CRzue86PARc2sSLPoNSxez9ghBOhEanGXQRLSlZLDgImBpgAEX2RucywrxCEbf5BCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:26:19.651403Z","bundle_sha256":"293954fd42461171dc8226733eb20a9397feea00f68666cdfa5cdcb532ccdd15"}}