{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AAA3KQGQDC5JPA7HWNXJS32X4X","short_pith_number":"pith:AAA3KQGQ","canonical_record":{"source":{"id":"1108.1901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-08-09T11:22:23Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"title_canon_sha256":"26a768aa9da18d02a67ff35a24ef0e4f0d06f1d05aaf68531188bbde8750963d","abstract_canon_sha256":"7cb7b0a440190670565ee6b01a1154f7a103c7fdc437b1a9fd43a09a0bf46e03"},"schema_version":"1.0"},"canonical_sha256":"0001b540d018ba9783e7b36e996f57e5eb8de04ce43dba2635df2ef96c9f9bab","source":{"kind":"arxiv","id":"1108.1901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1901","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1901v1","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1901","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"AAA3KQGQDC5J","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AAA3KQGQDC5JPA7H","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AAA3KQGQ","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AAA3KQGQDC5JPA7HWNXJS32X4X","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-08-09T11:22:23Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"title_canon_sha256":"26a768aa9da18d02a67ff35a24ef0e4f0d06f1d05aaf68531188bbde8750963d","abstract_canon_sha256":"7cb7b0a440190670565ee6b01a1154f7a103c7fdc437b1a9fd43a09a0bf46e03"},"schema_version":"1.0"},"canonical_sha256":"0001b540d018ba9783e7b36e996f57e5eb8de04ce43dba2635df2ef96c9f9bab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:47.187659Z","signature_b64":"SXPeRzXD3Td0dv9GmFM2jL6f6dHqv+FYNzLcHyH6CJiYE13JKOaYpufj8538ujL0wLvyeXoGoobvPkrC7C29Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0001b540d018ba9783e7b36e996f57e5eb8de04ce43dba2635df2ef96c9f9bab","last_reissued_at":"2026-05-18T04:05:47.187277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:47.187277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1901","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GiTK6neYvQtJVbf71if8swvuMTIO+Sk08H2xYE0yMBoGs0XO8/XRq1GRJKxxNQtEi9xg9F/f9uZ+C6uSi460BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:19:03.968183Z"},"content_sha256":"05b107d38e3f73c88ec037fa6ec53d0e427ca3a5216ad517bb95f7ff53bb0dfa","schema_version":"1.0","event_id":"sha256:05b107d38e3f73c88ec037fa6ec53d0e427ca3a5216ad517bb95f7ff53bb0dfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AAA3KQGQDC5JPA7HWNXJS32X4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Nonlinear Map for the Decay to Equilibrium of Ideal Gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS"],"primary_cat":"nlin.AO","authors_text":"Elyas Shivanian, Ricardo Lopez-Ruiz","submitted_at":"2011-08-09T11:22:23Z","abstract_excerpt":"An operator that governs the discrete time evolution of the velocity distribution of an out-of-equilibrium ideal gas will be presented. This nonlinear map, which conserves the momentum and the energy of the ideal gas, has the Maxwellian Velocity Distribution (MVD) as an asymptotic equilibrium. Moreover, the system displays the increasing of the entropy during the decay to the MVD."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1901","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kbRAHc0MlteD3W1jLQALwQOg2LYE2F0vcrNaPg9Nh+t4DwDmsswuBp1F5rzmNomvlLk2IF85qpZ9rpXa6NcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:19:03.968546Z"},"content_sha256":"a9648374aa82fb9a8d209f1d9886407877215703a5dae8ff50c144a56af3ff29","schema_version":"1.0","event_id":"sha256:a9648374aa82fb9a8d209f1d9886407877215703a5dae8ff50c144a56af3ff29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/bundle.json","state_url":"https://pith.science/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/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":"2026-06-23T16:19:03Z","links":{"resolver":"https://pith.science/pith/AAA3KQGQDC5JPA7HWNXJS32X4X","bundle":"https://pith.science/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/bundle.json","state":"https://pith.science/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAA3KQGQDC5JPA7HWNXJS32X4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AAA3KQGQDC5JPA7HWNXJS32X4X","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":"7cb7b0a440190670565ee6b01a1154f7a103c7fdc437b1a9fd43a09a0bf46e03","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-08-09T11:22:23Z","title_canon_sha256":"26a768aa9da18d02a67ff35a24ef0e4f0d06f1d05aaf68531188bbde8750963d"},"schema_version":"1.0","source":{"id":"1108.1901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1901","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1901v1","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1901","created_at":"2026-05-18T04:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"AAA3KQGQDC5J","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AAA3KQGQDC5JPA7H","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AAA3KQGQ","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:a9648374aa82fb9a8d209f1d9886407877215703a5dae8ff50c144a56af3ff29","target":"graph","created_at":"2026-05-18T04:05:47Z","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":"An operator that governs the discrete time evolution of the velocity distribution of an out-of-equilibrium ideal gas will be presented. This nonlinear map, which conserves the momentum and the energy of the ideal gas, has the Maxwellian Velocity Distribution (MVD) as an asymptotic equilibrium. Moreover, the system displays the increasing of the entropy during the decay to the MVD.","authors_text":"Elyas Shivanian, Ricardo Lopez-Ruiz","cross_cats":["cond-mat.stat-mech","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-08-09T11:22:23Z","title":"A Nonlinear Map for the Decay to Equilibrium of Ideal Gases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1901","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":"sha256:05b107d38e3f73c88ec037fa6ec53d0e427ca3a5216ad517bb95f7ff53bb0dfa","target":"record","created_at":"2026-05-18T04:05:47Z","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":"7cb7b0a440190670565ee6b01a1154f7a103c7fdc437b1a9fd43a09a0bf46e03","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2011-08-09T11:22:23Z","title_canon_sha256":"26a768aa9da18d02a67ff35a24ef0e4f0d06f1d05aaf68531188bbde8750963d"},"schema_version":"1.0","source":{"id":"1108.1901","kind":"arxiv","version":1}},"canonical_sha256":"0001b540d018ba9783e7b36e996f57e5eb8de04ce43dba2635df2ef96c9f9bab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0001b540d018ba9783e7b36e996f57e5eb8de04ce43dba2635df2ef96c9f9bab","first_computed_at":"2026-05-18T04:05:47.187277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:47.187277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SXPeRzXD3Td0dv9GmFM2jL6f6dHqv+FYNzLcHyH6CJiYE13JKOaYpufj8538ujL0wLvyeXoGoobvPkrC7C29Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:47.187659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05b107d38e3f73c88ec037fa6ec53d0e427ca3a5216ad517bb95f7ff53bb0dfa","sha256:a9648374aa82fb9a8d209f1d9886407877215703a5dae8ff50c144a56af3ff29"],"state_sha256":"c75a1ec6da48ce4b84762035e39c0909fc7c4f7a3389d42a9181e6811991fc25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"343CvLPi5b07LBtjkwCNGkv6JmfI/G8kiopOgPcybfgS/HS/IZzUZjCANCvOAQmBtEnm/KBTKeNdnVSCnde1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:19:03.970807Z","bundle_sha256":"c4d5e275530e3c87a68b646617926210a931a8bf7184254c27bc67e57ed872bb"}}