{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JFC3C7FUINDTLULKY3YOHJEWEG","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":"ca677de8e6fe9ec36409878cb04e46b1628d64e9ccc7d3e499585e7a3cd57fbe","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T03:38:05Z","title_canon_sha256":"ed7d5768b535aff39e49745a449fdd8f155c5da1eb5271cd7ecdc326fd15802e"},"schema_version":"1.0","source":{"id":"1610.09601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09601","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09601v2","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09601","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"JFC3C7FUINDT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JFC3C7FUINDTLULK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JFC3C7FU","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:15398fb0ada758f6a87d6ee856d24e28d5edc7263dec2e5ec405c9de7b70dfdc","target":"graph","created_at":"2026-05-18T00:35:24Z","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 use the Fourier based Gabetta-Toscani-Wennberg (GTW) metric $d_2$ to study the rate of convergence to equilibrium for the Kac model in $1$ dimension. We take the initial velocity distribution of the particles to be a Borel probability measure $\\mu$ on $\\mathbb{R}^n$ that is symmetric in all its variables, has mean $\\vec{0}$ and finite second moment. Let $\\mu_t(dv)$ denote the Kac-evolved distribution at time $t$, and let $R_\\mu$ be the angular average of $\\mu$. We give an upper bound to $d_2(\\mu_t, R_\\mu)$ of the form $\\min\\{ B e^{-\\frac{4 \\lambda_1}{n+3}t}, d_2(\\mu,R_\\mu)\\}$, where $\\lambd","authors_text":"Hagop Tossounian","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T03:38:05Z","title":"Equilibration in the Kac Model using the GTW Metric $d_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09601","kind":"arxiv","version":2},"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:a1bfdb4e9e4e14066159708e6917c2e10e8d23a29278a9f298e650bdc50a5cfa","target":"record","created_at":"2026-05-18T00:35:24Z","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":"ca677de8e6fe9ec36409878cb04e46b1628d64e9ccc7d3e499585e7a3cd57fbe","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T03:38:05Z","title_canon_sha256":"ed7d5768b535aff39e49745a449fdd8f155c5da1eb5271cd7ecdc326fd15802e"},"schema_version":"1.0","source":{"id":"1610.09601","kind":"arxiv","version":2}},"canonical_sha256":"4945b17cb4434735d16ac6f0e3a4962199025928c7374388b6b7bc4cf2e6b3cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4945b17cb4434735d16ac6f0e3a4962199025928c7374388b6b7bc4cf2e6b3cf","first_computed_at":"2026-05-18T00:35:24.399343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:24.399343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NsExvSsBWL/cBlSrK8mnHbhI76Zh9qqDsWXIEYaZ5Ulrxe+qyrAbxqE+K6x0F3NuOR6zq4EUFT208wZJwEpABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:24.399864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1bfdb4e9e4e14066159708e6917c2e10e8d23a29278a9f298e650bdc50a5cfa","sha256:15398fb0ada758f6a87d6ee856d24e28d5edc7263dec2e5ec405c9de7b70dfdc"],"state_sha256":"c268667e6d116dd283732ff8699ee45c8e1c4b476fbb66f750bc22933c939430"}