{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:CH2YH2JMJDU42CCKRUTUAPBZG6","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":"b58e7dfb4b8a60c49d025156874dff1aa60bde03b814086685d6b9b05ea30fc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-05-14T05:00:40Z","title_canon_sha256":"ed1b0de1453710f29b86d359d0c38d65eaeb4b75b3f1191e511fb6e82ba933ad"},"schema_version":"1.0","source":{"id":"math/0605358","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605358","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605358v6","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605358","created_at":"2026-05-18T04:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"CH2YH2JMJDU4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CH2YH2JMJDU42CCK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CH2YH2JM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7d6bf9cefb1c93b64318b3508d417f9ca74ce99bfa8106ccff1098ed64ffbcd3","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 consider the system of $N$ ($\\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\\Bbb T^\\nu$, $\\nu\\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters, provided that almost every singular orbit is geometrically hyperbolic (sufficient), i. e. the so called Chernov-Sinai Ansatz is true. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs ","authors_text":"Nandor Simanyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-05-14T05:00:40Z","title":"Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605358","kind":"arxiv","version":6},"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":"sha256:5c92c245e053262b8902f1cc0534272c68dcb976b566c5bef2a723baf6299e54","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":"b58e7dfb4b8a60c49d025156874dff1aa60bde03b814086685d6b9b05ea30fc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-05-14T05:00:40Z","title_canon_sha256":"ed1b0de1453710f29b86d359d0c38d65eaeb4b75b3f1191e511fb6e82ba933ad"},"schema_version":"1.0","source":{"id":"math/0605358","kind":"arxiv","version":6}},"canonical_sha256":"11f583e92c48e9cd084a8d27403c393789a30c062526201516b80e50f123468b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11f583e92c48e9cd084a8d27403c393789a30c062526201516b80e50f123468b","first_computed_at":"2026-05-18T04:42:22.384375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:22.384375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iX9dJo8eVlGj+pLVoemnng3Ywq2SMremYCjYM4wRxtq++mRu5HrjuWZLnK7hc5WMGXIx6wA0rqhT6DjP1oPiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:22.385038Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605358","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c92c245e053262b8902f1cc0534272c68dcb976b566c5bef2a723baf6299e54","sha256:7d6bf9cefb1c93b64318b3508d417f9ca74ce99bfa8106ccff1098ed64ffbcd3"],"state_sha256":"b9fcb08594b2759717adb2aaa5a2b483784f2424840a676d8b0f3bd5b896ed1e"}