{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:EFWKIABBJZDYJ4EXHZJZ5CNLDL","short_pith_number":"pith:EFWKIABB","canonical_record":{"source":{"id":"math/0510022","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-10-02T20:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"81e36462e0c84a8bc283626a5f887ee5ecf497c5763089dfcb15b1ada5c6f8c6","abstract_canon_sha256":"9c44c68089b41a4890b6bb34c8500405d572d97145d47685ea136b5099ffafd1"},"schema_version":"1.0"},"canonical_sha256":"216ca400214e4784f0973e539e89ab1acfb3feefc80e094090ca84ed2c095d0b","source":{"kind":"arxiv","id":"math/0510022","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510022","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510022v3","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510022","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"EFWKIABBJZDY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EFWKIABBJZDYJ4EX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EFWKIABB","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:EFWKIABBJZDYJ4EXHZJZ5CNLDL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0510022","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-10-02T20:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"81e36462e0c84a8bc283626a5f887ee5ecf497c5763089dfcb15b1ada5c6f8c6","abstract_canon_sha256":"9c44c68089b41a4890b6bb34c8500405d572d97145d47685ea136b5099ffafd1"},"schema_version":"1.0"},"canonical_sha256":"216ca400214e4784f0973e539e89ab1acfb3feefc80e094090ca84ed2c095d0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:23.297857Z","signature_b64":"a0shx6LI/P+MQ3t9ExAiRE/SbH+ITseA3jKirbTBy/gqTDzg+IRyWFxdCoVS8iNfnUQzWjgw6vnJLyVwkA7bBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"216ca400214e4784f0973e539e89ab1acfb3feefc80e094090ca84ed2c095d0b","last_reissued_at":"2026-05-18T04:42:23.297339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:23.297339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0510022","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lNzY0LnMVnZxATLwqcCFXkhBxo8RQS9wwyCVqDYB2wIbKoA2H350YQ5ikihW4utoy5opomsB20vd+zK3rN1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:06:43.249575Z"},"content_sha256":"4ec4e2133a8fa25ed1431ab675fe5c824293741b1680f18b45511c7efd64b07a","schema_version":"1.0","event_id":"sha256:4ec4e2133a8fa25ed1431ab675fe5c824293741b1680f18b45511c7efd64b07a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:EFWKIABBJZDYJ4EXHZJZ5CNLDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nandor Simanyi","submitted_at":"2005-10-02T20:22:39Z","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, without exceptional values. The present proof does not use at all the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools of geometric analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510022","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SML23YBh199BG8GI/3XJGfbga86Rw0GdToktz7VD78w8ueteg5VIni9qTLCzxq6vkVkfFPcFsUCSJ5UIP+A0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:06:43.249954Z"},"content_sha256":"3923fd1f5893984865fe4c7cfc424e4be3c5b7eb2ac7592d556605594146b282","schema_version":"1.0","event_id":"sha256:3923fd1f5893984865fe4c7cfc424e4be3c5b7eb2ac7592d556605594146b282"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/bundle.json","state_url":"https://pith.science/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T09:06:43Z","links":{"resolver":"https://pith.science/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL","bundle":"https://pith.science/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/bundle.json","state":"https://pith.science/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFWKIABBJZDYJ4EXHZJZ5CNLDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:EFWKIABBJZDYJ4EXHZJZ5CNLDL","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":"9c44c68089b41a4890b6bb34c8500405d572d97145d47685ea136b5099ffafd1","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-10-02T20:22:39Z","title_canon_sha256":"81e36462e0c84a8bc283626a5f887ee5ecf497c5763089dfcb15b1ada5c6f8c6"},"schema_version":"1.0","source":{"id":"math/0510022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510022","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510022v3","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510022","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"EFWKIABBJZDY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EFWKIABBJZDYJ4EX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EFWKIABB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:3923fd1f5893984865fe4c7cfc424e4be3c5b7eb2ac7592d556605594146b282","target":"graph","created_at":"2026-05-18T04:42:23Z","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, without exceptional values. The present proof does not use at all the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools of geometric analysis.","authors_text":"Nandor Simanyi","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-10-02T20:22:39Z","title":"The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510022","kind":"arxiv","version":3},"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":"sha256:4ec4e2133a8fa25ed1431ab675fe5c824293741b1680f18b45511c7efd64b07a","target":"record","created_at":"2026-05-18T04:42:23Z","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":"9c44c68089b41a4890b6bb34c8500405d572d97145d47685ea136b5099ffafd1","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-10-02T20:22:39Z","title_canon_sha256":"81e36462e0c84a8bc283626a5f887ee5ecf497c5763089dfcb15b1ada5c6f8c6"},"schema_version":"1.0","source":{"id":"math/0510022","kind":"arxiv","version":3}},"canonical_sha256":"216ca400214e4784f0973e539e89ab1acfb3feefc80e094090ca84ed2c095d0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216ca400214e4784f0973e539e89ab1acfb3feefc80e094090ca84ed2c095d0b","first_computed_at":"2026-05-18T04:42:23.297339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:23.297339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a0shx6LI/P+MQ3t9ExAiRE/SbH+ITseA3jKirbTBy/gqTDzg+IRyWFxdCoVS8iNfnUQzWjgw6vnJLyVwkA7bBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:23.297857Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ec4e2133a8fa25ed1431ab675fe5c824293741b1680f18b45511c7efd64b07a","sha256:3923fd1f5893984865fe4c7cfc424e4be3c5b7eb2ac7592d556605594146b282"],"state_sha256":"c58ecbcc286cafdc513e5a56a5a5d4c699fb3dfd73968451cfc322d8ba81489a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4huUFB83+te+6XQPyKKKLMFMVCkThvkhrxiu0Uctp2uoMkPiBrHojaAv2VnYIy5gEiX2r+LIz4yTj1uxkWNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:06:43.251891Z","bundle_sha256":"97637d0fe47c37fa4175f0f0f802815de53a923fa12c07ca288010d90b8e32b4"}}