{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JPRZFPJSWMRHKLA2Z7PAXLQ3LQ","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":"298131add6aeab0aa1f191317d00954a9eccfb709d50125fee63d2f448c1711d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-14T20:11:32Z","title_canon_sha256":"aa05f00dddb77088ec7e07e103e6da5177354ee10ea99c2d8f2d58a372fb18cf"},"schema_version":"1.0","source":{"id":"1611.04547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04547","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04547v2","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04547","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"JPRZFPJSWMRH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JPRZFPJSWMRHKLA2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JPRZFPJS","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:abf1fd8025294bc8722a07ad22865fa32eb99b7efb2c5cb8719fcf33b16a5bfb","target":"graph","created_at":"2026-05-18T00:43:09Z","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 weaken the assumption of summable variations in a paper by Verbitskiy \\cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) of the full shift space on finitely many symbols to have a $g$-measure with a continuous $g$-function. But we also prove by means of a counterexample, that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is an inverse critical temperature in a one-sided long-range Ising model which is at most 8 times the critical inverse ","authors_text":"Anders Johansson, Anders \\\"Oberg, Mark Pollicott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-14T20:11:32Z","title":"Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04547","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":"sha256:471e8fedf8bf92d6b14c3323234f5d6a37e519a4931018a8f8a249b5204de2d7","target":"record","created_at":"2026-05-18T00:43:09Z","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":"298131add6aeab0aa1f191317d00954a9eccfb709d50125fee63d2f448c1711d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-14T20:11:32Z","title_canon_sha256":"aa05f00dddb77088ec7e07e103e6da5177354ee10ea99c2d8f2d58a372fb18cf"},"schema_version":"1.0","source":{"id":"1611.04547","kind":"arxiv","version":2}},"canonical_sha256":"4be392bd32b322752c1acfde0bae1b5c0fb69082de0dcdff03abad31f082cb4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be392bd32b322752c1acfde0bae1b5c0fb69082de0dcdff03abad31f082cb4f","first_computed_at":"2026-05-18T00:43:09.040675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:09.040675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2idWcH1jZXZDbRlBxpGPtbXZ8Nj2q0dKIyK95gEHHgse6wfHXSWvZeucN+shIRkgIk2vEZxiWMICvuEtwZpvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:09.041258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:471e8fedf8bf92d6b14c3323234f5d6a37e519a4931018a8f8a249b5204de2d7","sha256:abf1fd8025294bc8722a07ad22865fa32eb99b7efb2c5cb8719fcf33b16a5bfb"],"state_sha256":"e877c8fee094001bf84bd2baeb456ffb4fec176d67b3b0673cbf537d54047fd6"}