{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7KGKPQBNY6NQBCH3TVWR6AVKQ4","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":"4a50ef686bfd1656e3b1db64cea15577598caa1b072c29c9e745b168a67fc05d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-06T15:14:31Z","title_canon_sha256":"93367ae74d09520b95cd760b0ec0d26f502cfaf57359a6fd8cf4b8a89d7dca67"},"schema_version":"1.0","source":{"id":"1212.1345","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1345","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1345v4","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1345","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"7KGKPQBNY6NQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7KGKPQBNY6NQBCH3","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7KGKPQBN","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:46179ff45f31993805d7367bfd4d06815dc6c13f0b403aedf908b86472d41d8b","target":"graph","created_at":"2026-05-18T00:44:30Z","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 study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact-dimensional, generalizing Feng and Hu's result \\cite{FeHu09} for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures \\cite{HoSh12} to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and ","authors_text":"Kenneth Falconer, Xiong Jin","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-06T15:14:31Z","title":"Exact dimensionality and projections of random self-similar measures and sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1345","kind":"arxiv","version":4},"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:ac34794767d9a115eafdbd631b94764f5872130f8516cfae0ebf42f44d15157d","target":"record","created_at":"2026-05-18T00:44:30Z","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":"4a50ef686bfd1656e3b1db64cea15577598caa1b072c29c9e745b168a67fc05d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-06T15:14:31Z","title_canon_sha256":"93367ae74d09520b95cd760b0ec0d26f502cfaf57359a6fd8cf4b8a89d7dca67"},"schema_version":"1.0","source":{"id":"1212.1345","kind":"arxiv","version":4}},"canonical_sha256":"fa8ca7c02dc79b0088fb9d6d1f02aa872b51e580428237741ac04758a441e069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa8ca7c02dc79b0088fb9d6d1f02aa872b51e580428237741ac04758a441e069","first_computed_at":"2026-05-18T00:44:30.162279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.162279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xOPkwAyYyiMBZ7FkPgTrz3hCcL7OsecbuZzrsxn2EysrqCvWNM+5DIkbyYktDdpSokqIfznZwx1GfI6av1fuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.162836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1345","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac34794767d9a115eafdbd631b94764f5872130f8516cfae0ebf42f44d15157d","sha256:46179ff45f31993805d7367bfd4d06815dc6c13f0b403aedf908b86472d41d8b"],"state_sha256":"9cc30f303b738bf5499f156e95400908f190bba9b0cdfc6014c8685c98f2ac27"}