{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WE3X32HMK54EBCFCWMXZ4NIEJS","short_pith_number":"pith:WE3X32HM","schema_version":"1.0","canonical_sha256":"b1377de8ec57784088a2b32f9e35044cbe5710384bf76d6f69023ccfaade40bc","source":{"kind":"arxiv","id":"2412.15141","version":1},"attestation_state":"computed","paper":{"title":"Towards Common Zeros of Iterated Morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Chatchai Noytaptim, Xiao Zhong","submitted_at":"2024-12-19T18:24:59Z","abstract_excerpt":"Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance towards a question of Hsia and Tucker on a Zariski non-density of common zeros of iterated morphisms on a variety. More precisely, we provide an affirmative answer in the case of H\\'{e}non type maps on $\\mathbb{A}^2$, endomorphisms on $(\\mathbb{P}^1)^n$, and polynomial skew products on $\\mathbb{A}^2$ defined over $\\overline{\\mathbb{Q}}$. As a by-product, we prove a Tits' alternative analogy for semigroups generated by two "},"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":"2412.15141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-19T18:24:59Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"71aa5dc65e99547631f379a699663a9a282e32571770ac442a9a857b99a6a34a","abstract_canon_sha256":"8aed65007cf6ffa7401e6efde55d25c8607b62db2a4e6e0a9c20d8dc328bbfaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:51:58.432150Z","signature_b64":"o28nJijSN8QAfC7Il1OsG7F+cFFeJaQcPHHri31dczHpnYyLnJyFLs+EK1UKLvhVflby2/vkOLCmq8aOATIvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1377de8ec57784088a2b32f9e35044cbe5710384bf76d6f69023ccfaade40bc","last_reissued_at":"2026-07-05T09:51:58.431687Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:51:58.431687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Common Zeros of Iterated Morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Chatchai Noytaptim, Xiao Zhong","submitted_at":"2024-12-19T18:24:59Z","abstract_excerpt":"Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance towards a question of Hsia and Tucker on a Zariski non-density of common zeros of iterated morphisms on a variety. More precisely, we provide an affirmative answer in the case of H\\'{e}non type maps on $\\mathbb{A}^2$, endomorphisms on $(\\mathbb{P}^1)^n$, and polynomial skew products on $\\mathbb{A}^2$ defined over $\\overline{\\mathbb{Q}}$. As a by-product, we prove a Tits' alternative analogy for semigroups generated by two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15141","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/2412.15141/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":"2412.15141","created_at":"2026-07-05T09:51:58.431751+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.15141v1","created_at":"2026-07-05T09:51:58.431751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15141","created_at":"2026-07-05T09:51:58.431751+00:00"},{"alias_kind":"pith_short_12","alias_value":"WE3X32HMK54E","created_at":"2026-07-05T09:51:58.431751+00:00"},{"alias_kind":"pith_short_16","alias_value":"WE3X32HMK54EBCFC","created_at":"2026-07-05T09:51:58.431751+00:00"},{"alias_kind":"pith_short_8","alias_value":"WE3X32HM","created_at":"2026-07-05T09:51:58.431751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.04881","citing_title":"Unlikely intersections in families of polynomial skew products","ref_index":53,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS","json":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS.json","graph_json":"https://pith.science/api/pith-number/WE3X32HMK54EBCFCWMXZ4NIEJS/graph.json","events_json":"https://pith.science/api/pith-number/WE3X32HMK54EBCFCWMXZ4NIEJS/events.json","paper":"https://pith.science/paper/WE3X32HM"},"agent_actions":{"view_html":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS","download_json":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS.json","view_paper":"https://pith.science/paper/WE3X32HM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.15141&json=true","fetch_graph":"https://pith.science/api/pith-number/WE3X32HMK54EBCFCWMXZ4NIEJS/graph.json","fetch_events":"https://pith.science/api/pith-number/WE3X32HMK54EBCFCWMXZ4NIEJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS/action/storage_attestation","attest_author":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS/action/author_attestation","sign_citation":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS/action/citation_signature","submit_replication":"https://pith.science/pith/WE3X32HMK54EBCFCWMXZ4NIEJS/action/replication_record"}},"created_at":"2026-07-05T09:51:58.431751+00:00","updated_at":"2026-07-05T09:51:58.431751+00:00"}