{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3EDSVEDMYMWH2NCUQQIB67GEHM","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":"c3c4012fdd042f8ef86741bf556c8806b5aa76ccfe27b6398e6c664c774c76e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-19T09:26:13Z","title_canon_sha256":"2fe7903a6f99ec6a8d046cea6338d12a9c5fc14491fbd46e7c8cd1e38ea2e037"},"schema_version":"1.0","source":{"id":"1902.06962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06962","created_at":"2026-05-17T23:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06962v2","created_at":"2026-05-17T23:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06962","created_at":"2026-05-17T23:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"3EDSVEDMYMWH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3EDSVEDMYMWH2NCU","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3EDSVEDM","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:530dba9dcb6d62b40efc980c612434a6fd6845fe38454de644fb07f7a630142f","target":"graph","created_at":"2026-05-17T23:51:41Z","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 refine the multifractal formalism for the local dimension of a Gibbs measure $\\mu$ supported on the attractor $\\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\\alpha\\in \\mathbb{R}$, we establish the formalism for the Hausdorff dimension of level sets of points $x\\in\\Lambda$ for which the $\\mu$-measure of a ball of radius $r_{n}$ centered at $x$ obeys a power law $r_{n}{}^{\\alpha}$, for a sequence $r_{n}\\rightarrow0$. This allows us to investigate the H\\\"older regularity of various fractal functions, such as distribution functions and conjugacy maps ass","authors_text":"Hiroki Sumi, Johannes Jaerisch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-19T09:26:13Z","title":"Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06962","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":"sha256:4a17c56d4a15f78968aad639b2ff4d817834fdbe0fe495cb18e5e76dd616c169","target":"record","created_at":"2026-05-17T23:51:41Z","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":"c3c4012fdd042f8ef86741bf556c8806b5aa76ccfe27b6398e6c664c774c76e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-19T09:26:13Z","title_canon_sha256":"2fe7903a6f99ec6a8d046cea6338d12a9c5fc14491fbd46e7c8cd1e38ea2e037"},"schema_version":"1.0","source":{"id":"1902.06962","kind":"arxiv","version":2}},"canonical_sha256":"d9072a906cc32c7d345484101f7cc43b331d40639554c42cf701bd8ad8e2d505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9072a906cc32c7d345484101f7cc43b331d40639554c42cf701bd8ad8e2d505","first_computed_at":"2026-05-17T23:51:41.690789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:41.690789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RR19at+LtrR5eBRoBdr06zRssNmcokpqXhtAT4/WolrquNlUTg+yiiu+NcT3/BeiwiJiECuMSn0ZmY0R4FOlCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:41.691286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a17c56d4a15f78968aad639b2ff4d817834fdbe0fe495cb18e5e76dd616c169","sha256:530dba9dcb6d62b40efc980c612434a6fd6845fe38454de644fb07f7a630142f"],"state_sha256":"42c21977e56cbe95878c8302a82c21192ffb74af0e7ab85af43118a33c537dba"}