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Following Silverman, consider $\\delta := \\lim_{n \\in \\mathbb{N}} (\\deg{F^{n}})^{1/n}$ the dynamic degree of $F$ and $\\alpha(P) := \\limsup_{n \\in \\mathbb{N}} h_K(F^{n}P)^{1/n}$ the arithmetic degree of $F$ at $P$. We have $\\alpha(P) \\leq \\delta$, and extending a conjecture of Silverman from the number field case, it is expected that equality holds if the orbit of $P$ is Zariski-dense.\n  We prove a weaker form of this conjec"},"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":"1511.04061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-12T20:36:10Z","cross_cats_sorted":[],"title_canon_sha256":"8c80d693f43fa38fa52f8489aee94e65a99c687f9bc287c16951efae667c2ac7","abstract_canon_sha256":"ca7ba56d195b090e1e82b2cfc00f6e1da9fecc284900aa5aad7333957be21a59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:06.061540Z","signature_b64":"2dLpvl5FWT+TDFON+/qXcg4jq/2WghyYBn3aL0nGIOoLNax1EgBr3SWMB+thZ3ASVS3K78uOGEsa3eLsYj2zCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87c46654513cc287cdce044e883f16bf69f9c1c0c2984a3150ddfabdb182f4dc","last_reissued_at":"2026-05-18T01:27:06.060854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:06.060854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Silverman's conjecture for additive polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2015-11-12T20:36:10Z","abstract_excerpt":"Let $F : \\mathrm{End}_{\\mathbb{F_p}}(\\mathbb{G}_{a/K}^d)$ be an additive polynomial mapping over a global function field $K/\\mathbb{F}_q$, and let $P \\in \\mathbb{G}_a^d(K)$. Following Silverman, consider $\\delta := \\lim_{n \\in \\mathbb{N}} (\\deg{F^{n}})^{1/n}$ the dynamic degree of $F$ and $\\alpha(P) := \\limsup_{n \\in \\mathbb{N}} h_K(F^{n}P)^{1/n}$ the arithmetic degree of $F$ at $P$. We have $\\alpha(P) \\leq \\delta$, and extending a conjecture of Silverman from the number field case, it is expected that equality holds if the orbit of $P$ is Zariski-dense.\n  We prove a weaker form of this conjec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04061","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":"1511.04061","created_at":"2026-05-18T01:27:06.060968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04061v1","created_at":"2026-05-18T01:27:06.060968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04061","created_at":"2026-05-18T01:27:06.060968+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q7CGMVCRHTBI","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q7CGMVCRHTBIPTOO","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q7CGMVCR","created_at":"2026-05-18T12:29:37.295048+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/Q7CGMVCRHTBIPTOOARHIQPYWX5","json":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5.json","graph_json":"https://pith.science/api/pith-number/Q7CGMVCRHTBIPTOOARHIQPYWX5/graph.json","events_json":"https://pith.science/api/pith-number/Q7CGMVCRHTBIPTOOARHIQPYWX5/events.json","paper":"https://pith.science/paper/Q7CGMVCR"},"agent_actions":{"view_html":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5","download_json":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5.json","view_paper":"https://pith.science/paper/Q7CGMVCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04061&json=true","fetch_graph":"https://pith.science/api/pith-number/Q7CGMVCRHTBIPTOOARHIQPYWX5/graph.json","fetch_events":"https://pith.science/api/pith-number/Q7CGMVCRHTBIPTOOARHIQPYWX5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5/action/storage_attestation","attest_author":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5/action/author_attestation","sign_citation":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5/action/citation_signature","submit_replication":"https://pith.science/pith/Q7CGMVCRHTBIPTOOARHIQPYWX5/action/replication_record"}},"created_at":"2026-05-18T01:27:06.060968+00:00","updated_at":"2026-05-18T01:27:06.060968+00:00"}