{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PY6ORCG2A5TRR3U44F7J5C4WP3","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":"34bdb08ef6d5f6798bfa00a2d7173ba3536d1fe7f309e49c298f3bd15d633059","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-12-08T17:45:14Z","title_canon_sha256":"eeb0c5a407291dd141237247fd45ba2ab45dc96e102fa998d9b58881c3eb5d72"},"schema_version":"1.0","source":{"id":"2412.06008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.06008","created_at":"2026-07-05T11:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.06008v2","created_at":"2026-07-05T11:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06008","created_at":"2026-07-05T11:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"PY6ORCG2A5TR","created_at":"2026-07-05T11:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"PY6ORCG2A5TRR3U4","created_at":"2026-07-05T11:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"PY6ORCG2","created_at":"2026-07-05T11:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:63a3f3cc938b453cda6456d5e2c6d4fba821c974eaa4e05549bb3638dee0fb41","target":"graph","created_at":"2026-07-05T11:04:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.06008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than 1 at every point is absolutely continuous with H\\\"older continuous density almost surely. In particular, if the similarity dimension is greater than 1 then the random self-similar set on the line contains an interior point almost surely.","authors_text":"Bal\\'azs B\\'ar\\'any, Micha{\\l} Rams","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-12-08T17:45:14Z","title":"Smoothness of random self-similar measures on the line and the existence of interior points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06008","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":"sha256:64c2298bafc42a8ee87e1859e024be4aec2a49d10610e16725ac548db4587a0e","target":"record","created_at":"2026-07-05T11:04:42Z","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":"34bdb08ef6d5f6798bfa00a2d7173ba3536d1fe7f309e49c298f3bd15d633059","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-12-08T17:45:14Z","title_canon_sha256":"eeb0c5a407291dd141237247fd45ba2ab45dc96e102fa998d9b58881c3eb5d72"},"schema_version":"1.0","source":{"id":"2412.06008","kind":"arxiv","version":2}},"canonical_sha256":"7e3ce888da076718ee9ce17e9e8b967ef79d6d0bf5fddc2feb661d571c2c4cec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e3ce888da076718ee9ce17e9e8b967ef79d6d0bf5fddc2feb661d571c2c4cec","first_computed_at":"2026-07-05T11:04:42.540595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:42.540595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gwoO8Ts3UuN+RXkEsoF3LX34tGtw0bC3XugCsDRUcmtKs/EdU8vcq77reVJ5uc2WNpOWVCXTcSL2TLYttWmXCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:42.541081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.06008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64c2298bafc42a8ee87e1859e024be4aec2a49d10610e16725ac548db4587a0e","sha256:63a3f3cc938b453cda6456d5e2c6d4fba821c974eaa4e05549bb3638dee0fb41"],"state_sha256":"e2c5d5cffb9f53a88e1e2032e91e9ddd31aa38058dc0058fa0a1c42f2f4abd13"}