{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2HTJBMCAA4W2RIEAFFZXB44ADZ","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":"cc6ed5bcb5b5487a97140b9d0bf4049216237ce8950729012a41acc5c762c5be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-30T03:24:34Z","title_canon_sha256":"3dcd8b89d847edf091fa9dc7f6e5bc66cde2b9926310aa92b005ef3958b1feea"},"schema_version":"1.0","source":{"id":"1410.8241","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8241","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8241v3","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8241","created_at":"2026-05-18T01:23:58Z"},{"alias_kind":"pith_short_12","alias_value":"2HTJBMCAA4W2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2HTJBMCAA4W2RIEA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2HTJBMCA","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:efe1f77ea8ed604406f5083bdcebc8f8d17c131880a2463fb4c60b0996babc93","target":"graph","created_at":"2026-05-18T01:23:58Z","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":"In this paper we introduce a notion of asymptotic stability of a probability kernel, which we call dynamic uniqueness. We say that a kernel exhibits dynamic uniqueness if all the stochastic chains starting from a fixed past coincide on the future tail $\\sigma$-algebra. We prove that the dynamic uniqueness is generally stronger than the usual notion of uniqueness for $g$-measures. Our main result shows that dynamic uniqueness is equivalent to the weak-$\\ell^2$ summability condition on the kernel. This generalizes and strengthens the Johansson-\\\"Oberg $\\ell^2$ criterion for uniqueness of $g$-mea","authors_text":"Christophe Gallesco, Daniel Yasumasa Takahashi, Sandro Gallo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-30T03:24:34Z","title":"Characterization of the stability of chains associated with $g$-measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8241","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":"sha256:754a17732c541b4eea6f60e3d1f605524b16592f92d5e8a09014ec9ea03909ff","target":"record","created_at":"2026-05-18T01:23:58Z","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":"cc6ed5bcb5b5487a97140b9d0bf4049216237ce8950729012a41acc5c762c5be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-30T03:24:34Z","title_canon_sha256":"3dcd8b89d847edf091fa9dc7f6e5bc66cde2b9926310aa92b005ef3958b1feea"},"schema_version":"1.0","source":{"id":"1410.8241","kind":"arxiv","version":3}},"canonical_sha256":"d1e690b040072da8a080297370f3801e7a8e10aec345347b6a3c1310c8314f01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e690b040072da8a080297370f3801e7a8e10aec345347b6a3c1310c8314f01","first_computed_at":"2026-05-18T01:23:58.803339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:58.803339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wriMLGTp1HmZBYDhpDEtANwYOIC9w2XroKHiceVkWBzZx44t/F8Zk+RKF/NkPowHr2B5xgFBdnts4mbWtr2qAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:58.803974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8241","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:754a17732c541b4eea6f60e3d1f605524b16592f92d5e8a09014ec9ea03909ff","sha256:efe1f77ea8ed604406f5083bdcebc8f8d17c131880a2463fb4c60b0996babc93"],"state_sha256":"3214646df1d6182375d3595d5b56daa7288b7e7ded1891f02310e29e2a232701"}