{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:APBBDPAILTUH3UDIVZWEK5HJKX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"acf52184096575f2bcc08b8ca64266aeec7e1a971f9ac7c0cf5c58c5291600b5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1996-04-05T00:00:00Z","title_canon_sha256":"6753876e71382e3a3c8dc6b1fb80551845c7692a237669b3f259938f823f87a8"},"schema_version":"1.0","source":{"id":"math/9604233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9604233","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9604233v1","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9604233","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"APBBDPAILTUH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"APBBDPAILTUH3UDI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"APBBDPAI","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:81473103525f6a369335b30125c2635ad79b52b141bbcc2562397c00c67e4af5","target":"graph","created_at":"2026-05-18T04:42:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the characteristic exponents of the Hamiltonian system of $n$ ($\\ge 2$) point masses $m_1,\\dots,m_n$ freely falling in the vertical half line $\\{q|\\, q\\ge 0\\}$ under constant gravitation and colliding with each other and the solid floor $q=0$ elastically. This model was introduced and first studied by M. Wojtkowski. Hereby we prove his conjecture: All relevant characteristic (Lyapunov) exponents of the above dynamical system are nonzero, provided that $m_1\\ge\\dots\\ge m_n$ (i. e. the masses do not increase as we go up) and $m_1\\ne m_2$.","authors_text":"Nandor Simanyi","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1996-04-05T00:00:00Z","title":"The characteristic exponents of the falling ball model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9604233","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9b18cfeaa4b29dad506eede0114a71713b472b3bcdfacdfc397fd9553c4efc4d","target":"record","created_at":"2026-05-18T04:42:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"acf52184096575f2bcc08b8ca64266aeec7e1a971f9ac7c0cf5c58c5291600b5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1996-04-05T00:00:00Z","title_canon_sha256":"6753876e71382e3a3c8dc6b1fb80551845c7692a237669b3f259938f823f87a8"},"schema_version":"1.0","source":{"id":"math/9604233","kind":"arxiv","version":1}},"canonical_sha256":"03c211bc085ce87dd068ae6c4574e955f3dbbcc7221e2f78bf8e99cbd0e04539","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03c211bc085ce87dd068ae6c4574e955f3dbbcc7221e2f78bf8e99cbd0e04539","first_computed_at":"2026-05-18T04:42:22.377001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:22.377001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QpHLvfIojHpoOZlA6CxQOIsfcDqh8jJXVstHbMAAlHsiVYlmXBl1fc9PM5qHhUkSveGWteLIMXn4J0jRZb3bBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:22.377652Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9604233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b18cfeaa4b29dad506eede0114a71713b472b3bcdfacdfc397fd9553c4efc4d","sha256:81473103525f6a369335b30125c2635ad79b52b141bbcc2562397c00c67e4af5"],"state_sha256":"f870bf41b01cc1a4fe0ca32ee0e009e443e1eeb81a714bccbe9dbd23dcd5f629"}