{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SN3WL2NFMP3W4NMQAJ2MZ66KOI","short_pith_number":"pith:SN3WL2NF","schema_version":"1.0","canonical_sha256":"937765e9a563f76e35900274ccfbca721d16867122434de13fa312bd7f5a188f","source":{"kind":"arxiv","id":"2605.27058","version":1},"attestation_state":"computed","paper":{"title":"Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO","math.NT"],"primary_cat":"math.DS","authors_text":"Geng-Rui Zhang","submitted_at":"2026-05-26T14:13:28Z","abstract_excerpt":"Let $f,g\\in\\mathbb{C}[z]\\setminus\\mathbb{C}$ and $c\\in\\mathbb{C}[z]$. Suppose that $\\mathrm{deg}(c)=1$ if $\\mathrm{deg}(f)=\\mathrm{deg}(g)=1$. Using the theory of Presburger arithmetic, we prove that the rank-two recurrence set\n  \\[S_{f,g,c}^2:=\\left\\lbrace(m,n)\\in\\mathbb{Z}_{\\geq0}^2\\colon \\exists\\lambda\\in\\mathbb{C}, f^{\\circ m}(\\lambda)=g^{\\circ n}(\\lambda)=c(\\lambda)\\right\\rbrace\\] is semi-linear. This is a generalization of a theorem of Yang and Zhong for the case $m=n$. We also obtain partial results on recurrence sets for rational maps in the case $m=n$. These results are related to hig"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.27058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-26T14:13:28Z","cross_cats_sorted":["math.AG","math.LO","math.NT"],"title_canon_sha256":"7f483d034bec24deee1bf538b7ea47433a94b966cf25621941390ac064b4c09c","abstract_canon_sha256":"2bcd2bdc288aeda156dd65f62b24656c14c67e00927a5cdc8505e4e69217ba5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:06:26.265686Z","signature_b64":"Ql6WB6lk9Z1ick3p+60BUIUUiz9OPmUTF1Ipi43Zo5N+7jh/IBDQ4sLH1IS1Fy/RvSYG5n0DAkhX+yXAyKUqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937765e9a563f76e35900274ccfbca721d16867122434de13fa312bd7f5a188f","last_reissued_at":"2026-05-27T01:06:26.264950Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:06:26.264950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO","math.NT"],"primary_cat":"math.DS","authors_text":"Geng-Rui Zhang","submitted_at":"2026-05-26T14:13:28Z","abstract_excerpt":"Let $f,g\\in\\mathbb{C}[z]\\setminus\\mathbb{C}$ and $c\\in\\mathbb{C}[z]$. Suppose that $\\mathrm{deg}(c)=1$ if $\\mathrm{deg}(f)=\\mathrm{deg}(g)=1$. Using the theory of Presburger arithmetic, we prove that the rank-two recurrence set\n  \\[S_{f,g,c}^2:=\\left\\lbrace(m,n)\\in\\mathbb{Z}_{\\geq0}^2\\colon \\exists\\lambda\\in\\mathbb{C}, f^{\\circ m}(\\lambda)=g^{\\circ n}(\\lambda)=c(\\lambda)\\right\\rbrace\\] is semi-linear. This is a generalization of a theorem of Yang and Zhong for the case $m=n$. We also obtain partial results on recurrence sets for rational maps in the case $m=n$. These results are related to hig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.27058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.27058","created_at":"2026-05-27T01:06:26.265058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.27058v1","created_at":"2026-05-27T01:06:26.265058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27058","created_at":"2026-05-27T01:06:26.265058+00:00"},{"alias_kind":"pith_short_12","alias_value":"SN3WL2NFMP3W","created_at":"2026-05-27T01:06:26.265058+00:00"},{"alias_kind":"pith_short_16","alias_value":"SN3WL2NFMP3W4NMQ","created_at":"2026-05-27T01:06:26.265058+00:00"},{"alias_kind":"pith_short_8","alias_value":"SN3WL2NF","created_at":"2026-05-27T01:06:26.265058+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI","json":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI.json","graph_json":"https://pith.science/api/pith-number/SN3WL2NFMP3W4NMQAJ2MZ66KOI/graph.json","events_json":"https://pith.science/api/pith-number/SN3WL2NFMP3W4NMQAJ2MZ66KOI/events.json","paper":"https://pith.science/paper/SN3WL2NF"},"agent_actions":{"view_html":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI","download_json":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI.json","view_paper":"https://pith.science/paper/SN3WL2NF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.27058&json=true","fetch_graph":"https://pith.science/api/pith-number/SN3WL2NFMP3W4NMQAJ2MZ66KOI/graph.json","fetch_events":"https://pith.science/api/pith-number/SN3WL2NFMP3W4NMQAJ2MZ66KOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI/action/storage_attestation","attest_author":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI/action/author_attestation","sign_citation":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI/action/citation_signature","submit_replication":"https://pith.science/pith/SN3WL2NFMP3W4NMQAJ2MZ66KOI/action/replication_record"}},"created_at":"2026-05-27T01:06:26.265058+00:00","updated_at":"2026-05-27T01:06:26.265058+00:00"}