{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P3CKAJHM5PHPEE6XAPKKZRQISS","short_pith_number":"pith:P3CKAJHM","schema_version":"1.0","canonical_sha256":"7ec4a024ecebcef213d703d4acc60894af9ab7d5039743e2309222b666ea61a1","source":{"kind":"arxiv","id":"1906.03864","version":1},"attestation_state":"computed","paper":{"title":"The dependence of Lyapunov exponents of polynomials on its coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Atma Ram Tiwari, Shrihari Sridharan","submitted_at":"2019-06-10T09:30:05Z","abstract_excerpt":"In this paper, we consider the family of hyperbolic quadratic polynomials parametrised by a complex constant; namely $P_{c}(z) = z^{2} + c$ with $|c| < 1$ and the family of hyperbolic cubic polynomials parametrised by two complex constants; namely $P_{(a_{1},a_{0})}(z) = z^{3} + a_{1}z + a_{0}$ with $|a_{i}| < 1$, restricted on their respective Julia sets. We compute the Lyapunov characteristic exponents for these polynomial maps over corresponding Julia sets, with respect to various Bernoulli measures and obtain results pertaining to the dependence of the behaviour of these exponents on the p"},"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":"1906.03864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-10T09:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"a73f835439b1603804e4d47bc10090dcb8a8a064fd58d29fe7557bfeb082db6d","abstract_canon_sha256":"975e757dca07808b89bbb32e604900ca914d5717067f3aee81775f387524bbd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:44.693255Z","signature_b64":"IzRvbQikkIxqIRjqRHIipIi2jLvQOoNwUCWg3xxh89qr9xITK5Etf5384NzdJC1RP85hwTbuRliDkBIE8qf0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ec4a024ecebcef213d703d4acc60894af9ab7d5039743e2309222b666ea61a1","last_reissued_at":"2026-05-17T23:43:44.692544Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:44.692544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dependence of Lyapunov exponents of polynomials on its coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Atma Ram Tiwari, Shrihari Sridharan","submitted_at":"2019-06-10T09:30:05Z","abstract_excerpt":"In this paper, we consider the family of hyperbolic quadratic polynomials parametrised by a complex constant; namely $P_{c}(z) = z^{2} + c$ with $|c| < 1$ and the family of hyperbolic cubic polynomials parametrised by two complex constants; namely $P_{(a_{1},a_{0})}(z) = z^{3} + a_{1}z + a_{0}$ with $|a_{i}| < 1$, restricted on their respective Julia sets. We compute the Lyapunov characteristic exponents for these polynomial maps over corresponding Julia sets, with respect to various Bernoulli measures and obtain results pertaining to the dependence of the behaviour of these exponents on the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03864","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":"1906.03864","created_at":"2026-05-17T23:43:44.692651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.03864v1","created_at":"2026-05-17T23:43:44.692651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03864","created_at":"2026-05-17T23:43:44.692651+00:00"},{"alias_kind":"pith_short_12","alias_value":"P3CKAJHM5PHP","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"P3CKAJHM5PHPEE6X","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"P3CKAJHM","created_at":"2026-05-18T12:33:24.271573+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/P3CKAJHM5PHPEE6XAPKKZRQISS","json":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS.json","graph_json":"https://pith.science/api/pith-number/P3CKAJHM5PHPEE6XAPKKZRQISS/graph.json","events_json":"https://pith.science/api/pith-number/P3CKAJHM5PHPEE6XAPKKZRQISS/events.json","paper":"https://pith.science/paper/P3CKAJHM"},"agent_actions":{"view_html":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS","download_json":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS.json","view_paper":"https://pith.science/paper/P3CKAJHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.03864&json=true","fetch_graph":"https://pith.science/api/pith-number/P3CKAJHM5PHPEE6XAPKKZRQISS/graph.json","fetch_events":"https://pith.science/api/pith-number/P3CKAJHM5PHPEE6XAPKKZRQISS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS/action/storage_attestation","attest_author":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS/action/author_attestation","sign_citation":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS/action/citation_signature","submit_replication":"https://pith.science/pith/P3CKAJHM5PHPEE6XAPKKZRQISS/action/replication_record"}},"created_at":"2026-05-17T23:43:44.692651+00:00","updated_at":"2026-05-17T23:43:44.692651+00:00"}