{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AV6IGMTFNUHY5PFZY3JSYPEYJA","short_pith_number":"pith:AV6IGMTF","schema_version":"1.0","canonical_sha256":"057c8332656d0f8ebcb9c6d32c3c984809629cbee0ff55abc6f47c433cf0d0dc","source":{"kind":"arxiv","id":"1603.04459","version":1},"attestation_state":"computed","paper":{"title":"Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2016-03-14T20:28:19Z","abstract_excerpt":"Let $K$ be a global function field and let $\\phi\\in K[x]$. For all wandering basepoints $b\\in K$, we show that there is a bound on the size of the elements of the dynamical Zsigmondy set $\\mathcal{Z}(\\phi,b)$ that depends only on $\\phi$, the poles of the $b$, and $K$. Moreover, when we order $b\\in\\mathcal{O}_{K,S}$ by height, we show that $\\mathcal{Z}(\\phi,b)$ is empty on average. As an application, we prove that the inverse limit of the Galois groups of iterates of $\\phi(x)=x^d+f$ is a finite index subgroup of an iterated wreath product of cyclic groups. Finally, we establish similar results "},"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":"1603.04459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-14T20:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"31c522de2c9dbf28c965b13e82685453a72194836d8259f27d732fbb9581326f","abstract_canon_sha256":"99760fdce70684d2fcb9dedfbb9be97f4dd8c7e527c93fb1f6bfc24d9867c550"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:04.892168Z","signature_b64":"kgde3R2GP+FfR6ixHEvkM9BOF2kYRsg+/t6miBV7iwi5I+27meKG5SuMbW9etXevTWFZqW+b+hBzXH+SjOYfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"057c8332656d0f8ebcb9c6d32c3c984809629cbee0ff55abc6f47c433cf0d0dc","last_reissued_at":"2026-05-18T01:19:04.891599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:04.891599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2016-03-14T20:28:19Z","abstract_excerpt":"Let $K$ be a global function field and let $\\phi\\in K[x]$. For all wandering basepoints $b\\in K$, we show that there is a bound on the size of the elements of the dynamical Zsigmondy set $\\mathcal{Z}(\\phi,b)$ that depends only on $\\phi$, the poles of the $b$, and $K$. Moreover, when we order $b\\in\\mathcal{O}_{K,S}$ by height, we show that $\\mathcal{Z}(\\phi,b)$ is empty on average. As an application, we prove that the inverse limit of the Galois groups of iterates of $\\phi(x)=x^d+f$ is a finite index subgroup of an iterated wreath product of cyclic groups. Finally, we establish similar results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04459","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.04459","created_at":"2026-05-18T01:19:04.891663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04459v1","created_at":"2026-05-18T01:19:04.891663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04459","created_at":"2026-05-18T01:19:04.891663+00:00"},{"alias_kind":"pith_short_12","alias_value":"AV6IGMTFNUHY","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AV6IGMTFNUHY5PFZ","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AV6IGMTF","created_at":"2026-05-18T12:30:07.202191+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/AV6IGMTFNUHY5PFZY3JSYPEYJA","json":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA.json","graph_json":"https://pith.science/api/pith-number/AV6IGMTFNUHY5PFZY3JSYPEYJA/graph.json","events_json":"https://pith.science/api/pith-number/AV6IGMTFNUHY5PFZY3JSYPEYJA/events.json","paper":"https://pith.science/paper/AV6IGMTF"},"agent_actions":{"view_html":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA","download_json":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA.json","view_paper":"https://pith.science/paper/AV6IGMTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04459&json=true","fetch_graph":"https://pith.science/api/pith-number/AV6IGMTFNUHY5PFZY3JSYPEYJA/graph.json","fetch_events":"https://pith.science/api/pith-number/AV6IGMTFNUHY5PFZY3JSYPEYJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA/action/storage_attestation","attest_author":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA/action/author_attestation","sign_citation":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA/action/citation_signature","submit_replication":"https://pith.science/pith/AV6IGMTFNUHY5PFZY3JSYPEYJA/action/replication_record"}},"created_at":"2026-05-18T01:19:04.891663+00:00","updated_at":"2026-05-18T01:19:04.891663+00:00"}