{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:E3P66GZ432UT6DLD6QFXKKIPYA","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":"b43701c2ae858ee4839809cfa4a2d4696c742d9c001a7e32b97ae894247f0b5b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-12-24T14:02:36Z","title_canon_sha256":"f68593ba9eaad872253eb165115f31072baa14b2cddcc4dec1fcc2c42b8f6bb8"},"schema_version":"1.0","source":{"id":"1012.5399","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5399","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5399v2","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5399","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"E3P66GZ432UT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E3P66GZ432UT6DLD","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E3P66GZ4","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:40e5fe5b2a175f256bd2f3918cc01d7e642648b07815f38fa32b23a2da2eee43","target":"graph","created_at":"2026-05-18T00:33:33Z","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 show that the fractal curvature measures of invariant sets of one-dimensional conformal iterated function systems satisfying the open set condition exist, if and only if the associated geometric potential function is nonlattice. Moreover, in the nonlattice situation we obtain that the Minkowski content exists and prove that the fractal curvature measures are constant multiples of the $\\delta$-conformal measure, where $\\delta$ denotes the Minkowski dimension of the invariant set. For the first fractal curvature measure, this constant factor coincides with the Minkowski content of the invaria","authors_text":"Marc Kesseb\\\"ohmer, Sabrina Kombrink","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-12-24T14:02:36Z","title":"Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5399","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":"sha256:7150dcc82e92a78bfd1e76236a3bcd8cd144905a59b0912a35233b77365f743f","target":"record","created_at":"2026-05-18T00:33:33Z","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":"b43701c2ae858ee4839809cfa4a2d4696c742d9c001a7e32b97ae894247f0b5b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-12-24T14:02:36Z","title_canon_sha256":"f68593ba9eaad872253eb165115f31072baa14b2cddcc4dec1fcc2c42b8f6bb8"},"schema_version":"1.0","source":{"id":"1012.5399","kind":"arxiv","version":2}},"canonical_sha256":"26dfef1b3cdea93f0d63f40b75290fc00d381da7125897f49ce4b62ff4aa9f94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26dfef1b3cdea93f0d63f40b75290fc00d381da7125897f49ce4b62ff4aa9f94","first_computed_at":"2026-05-18T00:33:33.141071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:33.141071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WZ448HhwF9oP/k4DZ+Iq7GRtdEiHU06Hyi3i7PwdCK+5RLV+cY7xLw5CT4ZML9UlGlvpPgIx4xstUmxxLMWBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:33.141556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5399","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7150dcc82e92a78bfd1e76236a3bcd8cd144905a59b0912a35233b77365f743f","sha256:40e5fe5b2a175f256bd2f3918cc01d7e642648b07815f38fa32b23a2da2eee43"],"state_sha256":"cfe36bd36eb8cd5f2e1d252956bcf96db0e9e0cb49e77de3705b0bcded40b9a2"}