{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:73UWF6MASNEIKBTHW5VFGVKOMU","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":"bed1123b0bb13f1faba6f24a1ff0336303602cab557279e83a1531829d5a2435","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-07T11:27:39Z","title_canon_sha256":"198c2119aad8ecec15a44afa25c7ba7ed2ecfb8d2f777e4ba06e5a11f77071a5"},"schema_version":"1.0","source":{"id":"1512.01986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01986","created_at":"2026-05-18T01:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01986v1","created_at":"2026-05-18T01:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01986","created_at":"2026-05-18T01:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"73UWF6MASNEI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"73UWF6MASNEIKBTH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"73UWF6MA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:ca02b8d7da205d770cf008ed3a1f8121c4ee4288e6315f825f4cb15a34eee7f6","target":"graph","created_at":"2026-05-18T01:18:39Z","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 here a very popular 1D jump model introduced by Kac: it consists of $N$ velocities encountering random binary collisions at which they randomly exchange energy. We show the uniform (in $N$) exponential contractivity of the dynamics in a non-standard Monge-Kantorovich-Wasserstein: precisely the MKW metric of order 2 on the energy. The result is optimal in the sense that for each $N$, the contractivity constant is equal to the $L^2$ spectral gap of the generator associated to Kac's dynamic. As a corollary, we get an uniform but non optimal contractivity in the MKW metric of order $4$. W","authors_text":"Maxime Hauray","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-07T11:27:39Z","title":"Uniform contractivity in Wasserstein metric for the original 1D Kac's model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01986","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":"sha256:5c8987adc7d2650d1fa7ddf02aa49ceb7df0a3e6e0c5259959a9582013b74d80","target":"record","created_at":"2026-05-18T01:18:39Z","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":"bed1123b0bb13f1faba6f24a1ff0336303602cab557279e83a1531829d5a2435","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-07T11:27:39Z","title_canon_sha256":"198c2119aad8ecec15a44afa25c7ba7ed2ecfb8d2f777e4ba06e5a11f77071a5"},"schema_version":"1.0","source":{"id":"1512.01986","kind":"arxiv","version":1}},"canonical_sha256":"fee962f9809348850667b76a53554e651951fa15d164e8a9e521768cc5d76a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fee962f9809348850667b76a53554e651951fa15d164e8a9e521768cc5d76a94","first_computed_at":"2026-05-18T01:18:39.382475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:39.382475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIiLCtdZIozSQjKhn0ekc8sv47h0T1tiaCcFJVVX28ewAjANVfinZ4ZKCgWdAZtpsbKGMZMNgrwcCzv3ypRBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:39.383049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c8987adc7d2650d1fa7ddf02aa49ceb7df0a3e6e0c5259959a9582013b74d80","sha256:ca02b8d7da205d770cf008ed3a1f8121c4ee4288e6315f825f4cb15a34eee7f6"],"state_sha256":"c895342e6b8e063c53d3c2304f05ddac9c59751a7f72bebda203bde1e2f4d870"}