{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4VAKDBX2TFZV3CGDHSVL7EAFCZ","short_pith_number":"pith:4VAKDBX2","schema_version":"1.0","canonical_sha256":"e540a186fa99735d88c33caabf90051674012309a6f26236271c4522354d8dc4","source":{"kind":"arxiv","id":"1106.5914","version":2},"attestation_state":"computed","paper":{"title":"On products of skew rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. N. Rybko, E. I. Dinaburg, G. B. Dobrushina, M. D. Arnold, S. A. Pirogov","submitted_at":"2011-06-29T11:48:28Z","abstract_excerpt":"Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\\{S_1^t\\}$, $\\{S_2^t\\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$."},"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":"1106.5914","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-29T11:48:28Z","cross_cats_sorted":[],"title_canon_sha256":"277301e29b5ae45e953ecd8e68224c1fbf824d79be93007119d4dc94b5a5e738","abstract_canon_sha256":"ff6ba261d5adb2b209c6c8452ddf44ef9697f1195403ad2798f2a112edae9361"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:35.829469Z","signature_b64":"Ou45gOl8ee3gudB5Zp8JbUMPvlIYIvcX0/ww3xPQtxkRvT2alZvtVMwRioohaOgJmiunEKj0WO0Z99U5CoFVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e540a186fa99735d88c33caabf90051674012309a6f26236271c4522354d8dc4","last_reissued_at":"2026-05-18T03:20:35.828656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:35.828656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On products of skew rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. N. Rybko, E. I. Dinaburg, G. B. Dobrushina, M. D. Arnold, S. A. Pirogov","submitted_at":"2011-06-29T11:48:28Z","abstract_excerpt":"Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\\{S_1^t\\}$, $\\{S_2^t\\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5914","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":"1106.5914","created_at":"2026-05-18T03:20:35.828783+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5914v2","created_at":"2026-05-18T03:20:35.828783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5914","created_at":"2026-05-18T03:20:35.828783+00:00"},{"alias_kind":"pith_short_12","alias_value":"4VAKDBX2TFZV","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4VAKDBX2TFZV3CGD","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4VAKDBX2","created_at":"2026-05-18T12:26:20.644004+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/4VAKDBX2TFZV3CGDHSVL7EAFCZ","json":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ.json","graph_json":"https://pith.science/api/pith-number/4VAKDBX2TFZV3CGDHSVL7EAFCZ/graph.json","events_json":"https://pith.science/api/pith-number/4VAKDBX2TFZV3CGDHSVL7EAFCZ/events.json","paper":"https://pith.science/paper/4VAKDBX2"},"agent_actions":{"view_html":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ","download_json":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ.json","view_paper":"https://pith.science/paper/4VAKDBX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5914&json=true","fetch_graph":"https://pith.science/api/pith-number/4VAKDBX2TFZV3CGDHSVL7EAFCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4VAKDBX2TFZV3CGDHSVL7EAFCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ/action/storage_attestation","attest_author":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ/action/author_attestation","sign_citation":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ/action/citation_signature","submit_replication":"https://pith.science/pith/4VAKDBX2TFZV3CGDHSVL7EAFCZ/action/replication_record"}},"created_at":"2026-05-18T03:20:35.828783+00:00","updated_at":"2026-05-18T03:20:35.828783+00:00"}