{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3IT2SJDYZWO5CBIPDOKH3LHNS5","short_pith_number":"pith:3IT2SJDY","schema_version":"1.0","canonical_sha256":"da27a92478cd9dd1050f1b947daced97782fb6882eea805b9df1865d0dc4cc5b","source":{"kind":"arxiv","id":"1004.0650","version":1},"attestation_state":"computed","paper":{"title":"Unique Bernoulli g-measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Anders Johansson, Anders \\\"Oberg, Mark Pollicott","submitted_at":"2010-04-05T15:27:11Z","abstract_excerpt":"We improve and subsume the conditions of Johansson and \\\"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.  In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular, we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely many states under any one of the following additional assumptions. (1) $$\\sum_{n=1}^\\infty (\\var_n \\log g)^2<\\infty,$$ (2) For any fixed $\\epsilon>0$, $$\\sum_{n=1}^\\infty e^{-(\\{1}{2}+\\epsilon) (\\var_1 \\log g+...+\\var_n \\l"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1004.0650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-05T15:27:11Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"26269b78a2d22ff82d24598af3cf0c3f4b8422dd6443302013d53da7747bd8bc","abstract_canon_sha256":"ff7e6b17f2bea215414f7327e96ad1d0b3922888315f0368a70b03b7006f38d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:31.307115Z","signature_b64":"3p5rlRR9MqClZ6iMIMC/r2fFx4QpV/wDrrPDVgZjDbEN4hgLQQ2l57tPqqljXEJwYmL8Z63QwQZgBsp/gVx/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da27a92478cd9dd1050f1b947daced97782fb6882eea805b9df1865d0dc4cc5b","last_reissued_at":"2026-05-18T02:32:31.306763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:31.306763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unique Bernoulli g-measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Anders Johansson, Anders \\\"Oberg, Mark Pollicott","submitted_at":"2010-04-05T15:27:11Z","abstract_excerpt":"We improve and subsume the conditions of Johansson and \\\"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.  In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular, we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely many states under any one of the following additional assumptions. (1) $$\\sum_{n=1}^\\infty (\\var_n \\log g)^2<\\infty,$$ (2) For any fixed $\\epsilon>0$, $$\\sum_{n=1}^\\infty e^{-(\\{1}{2}+\\epsilon) (\\var_1 \\log g+...+\\var_n \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0650","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1004.0650","created_at":"2026-05-18T02:32:31.306811+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.0650v1","created_at":"2026-05-18T02:32:31.306811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0650","created_at":"2026-05-18T02:32:31.306811+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IT2SJDYZWO5","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IT2SJDYZWO5CBIP","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IT2SJDY","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5","json":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5.json","graph_json":"https://pith.science/api/pith-number/3IT2SJDYZWO5CBIPDOKH3LHNS5/graph.json","events_json":"https://pith.science/api/pith-number/3IT2SJDYZWO5CBIPDOKH3LHNS5/events.json","paper":"https://pith.science/paper/3IT2SJDY"},"agent_actions":{"view_html":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5","download_json":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5.json","view_paper":"https://pith.science/paper/3IT2SJDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.0650&json=true","fetch_graph":"https://pith.science/api/pith-number/3IT2SJDYZWO5CBIPDOKH3LHNS5/graph.json","fetch_events":"https://pith.science/api/pith-number/3IT2SJDYZWO5CBIPDOKH3LHNS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5/action/storage_attestation","attest_author":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5/action/author_attestation","sign_citation":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5/action/citation_signature","submit_replication":"https://pith.science/pith/3IT2SJDYZWO5CBIPDOKH3LHNS5/action/replication_record"}},"created_at":"2026-05-18T02:32:31.306811+00:00","updated_at":"2026-05-18T02:32:31.306811+00:00"}