{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GWYQB2SPBA4NLTJZEXCAUHKMAF","short_pith_number":"pith:GWYQB2SP","schema_version":"1.0","canonical_sha256":"35b100ea4f0838d5cd3925c40a1d4c01567ddb870f5759c89b0f832b21780755","source":{"kind":"arxiv","id":"1704.04292","version":2},"attestation_state":"computed","paper":{"title":"Explicit bounds for composite lacunary polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christina Karolus","submitted_at":"2017-04-13T22:26:11Z","abstract_excerpt":"Let $f, g, h\\in \\mathbb{C}\\left[x\\right]$ be non-constant complex polynomials satisfying $f(x)=g(h(x))$ and let $f$ be lacunary in the sense that it has at most $l$ non-constant terms. Zannier proved that there exists a function $B_1(l)$ on $\\mathbb{N}$, depending only on $l$ and with the property that $h(x)$ can be written as the ratio of two polynomials having each at most $B_1(l)$ terms. Here, we give explicit estimates for this function or, more precicely, we prove that one may take for instance \\[B_1(l)=(4l)^{(2l)^{(3l)^{l+1}}}.\\] Moreover, in the case $l=2$, a better result is obtained u"},"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":"1704.04292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-13T22:26:11Z","cross_cats_sorted":[],"title_canon_sha256":"7ffbf736a0143bc2b841d180e1a0b683f32f0dd4c6a229bdbbfa58e222fc33da","abstract_canon_sha256":"3ac6cdff1cd3be2223d942d33388d23dcefd9834cfa2c417a81c19b536d72de8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:22.238668Z","signature_b64":"RNSQEoSfscyiNVRw898CaPBH9hRhStg27Yf8q5/fFb9PjUFBEZ5I6ahejN0Wa4eJYHI2aVv4AVuqI9L/omKIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35b100ea4f0838d5cd3925c40a1d4c01567ddb870f5759c89b0f832b21780755","last_reissued_at":"2026-05-18T00:30:22.238112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:22.238112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit bounds for composite lacunary polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christina Karolus","submitted_at":"2017-04-13T22:26:11Z","abstract_excerpt":"Let $f, g, h\\in \\mathbb{C}\\left[x\\right]$ be non-constant complex polynomials satisfying $f(x)=g(h(x))$ and let $f$ be lacunary in the sense that it has at most $l$ non-constant terms. Zannier proved that there exists a function $B_1(l)$ on $\\mathbb{N}$, depending only on $l$ and with the property that $h(x)$ can be written as the ratio of two polynomials having each at most $B_1(l)$ terms. Here, we give explicit estimates for this function or, more precicely, we prove that one may take for instance \\[B_1(l)=(4l)^{(2l)^{(3l)^{l+1}}}.\\] Moreover, in the case $l=2$, a better result is obtained u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04292","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1704.04292","created_at":"2026-05-18T00:30:22.238209+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04292v2","created_at":"2026-05-18T00:30:22.238209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04292","created_at":"2026-05-18T00:30:22.238209+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWYQB2SPBA4N","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWYQB2SPBA4NLTJZ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWYQB2SP","created_at":"2026-05-18T12:31:18.294218+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/GWYQB2SPBA4NLTJZEXCAUHKMAF","json":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF.json","graph_json":"https://pith.science/api/pith-number/GWYQB2SPBA4NLTJZEXCAUHKMAF/graph.json","events_json":"https://pith.science/api/pith-number/GWYQB2SPBA4NLTJZEXCAUHKMAF/events.json","paper":"https://pith.science/paper/GWYQB2SP"},"agent_actions":{"view_html":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF","download_json":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF.json","view_paper":"https://pith.science/paper/GWYQB2SP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04292&json=true","fetch_graph":"https://pith.science/api/pith-number/GWYQB2SPBA4NLTJZEXCAUHKMAF/graph.json","fetch_events":"https://pith.science/api/pith-number/GWYQB2SPBA4NLTJZEXCAUHKMAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF/action/storage_attestation","attest_author":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF/action/author_attestation","sign_citation":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF/action/citation_signature","submit_replication":"https://pith.science/pith/GWYQB2SPBA4NLTJZEXCAUHKMAF/action/replication_record"}},"created_at":"2026-05-18T00:30:22.238209+00:00","updated_at":"2026-05-18T00:30:22.238209+00:00"}