{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FCPBT5IMQQ2AIRIAUOOALGX24","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":"450540f57023af175149dda78accf03ecc5f81ff9ffa9fa74d610a2611f108ee","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-31T13:46:44Z","title_canon_sha256":"8faeb1f7fd9c420790576d0b0e56493ad4e5482fce6a637d81edd1a7e79eb527"},"schema_version":"1.0","source":{"id":"1503.09043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09043","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09043v2","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09043","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"3FCPBT5IMQQ2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FCPBT5IMQQ2AIRI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FCPBT5I","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:137186a400dec31914e92b98be5009765f012f6d69b903b98e7b20152d9750b5","target":"graph","created_at":"2026-05-18T00:43:03Z","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 self-similar sets and measures on $\\mathbb{R}^{d}$. Assuming that the defining iterated function system $\\Phi$ does not preserve a proper affine subspace, we show that one of the following holds: (1) the dimension is equal to the trivial bound (the minimum of $d$ and the similarity dimension $s$); (2) for all large $n$ there are $n$-fold compositions of maps from $\\Phi$ which are super-exponentially close in $n$; (3) there is a non-trivial linear subspace of $\\mathbb{R}^{d}$ that is preserved by the linearization of $\\Phi$ and whose translates typically meet the set or measure in full","authors_text":"Michael Hochman","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-31T13:46:44Z","title":"On self-similar sets with overlaps and inverse theorems for entropy in $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09043","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":"sha256:938db85060fecf85e86fcb2ea060c7d9b0086b4c7bd0675fd38d9621f059eb61","target":"record","created_at":"2026-05-18T00:43:03Z","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":"450540f57023af175149dda78accf03ecc5f81ff9ffa9fa74d610a2611f108ee","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-31T13:46:44Z","title_canon_sha256":"8faeb1f7fd9c420790576d0b0e56493ad4e5482fce6a637d81edd1a7e79eb527"},"schema_version":"1.0","source":{"id":"1503.09043","kind":"arxiv","version":2}},"canonical_sha256":"d944f0cfa86421a02228051ce02cd7d7052ab5fcba459503b3e4021b79f67293","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d944f0cfa86421a02228051ce02cd7d7052ab5fcba459503b3e4021b79f67293","first_computed_at":"2026-05-18T00:43:03.300496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:03.300496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aq37hrEZjDJt2azvC9XVswMA+Kr7/WJusj60jUAufPolp1PxLHtVtZpFFI2zpF7tpkCKF0kBYAHUQh9YvPHvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:03.301269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.09043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:938db85060fecf85e86fcb2ea060c7d9b0086b4c7bd0675fd38d9621f059eb61","sha256:137186a400dec31914e92b98be5009765f012f6d69b903b98e7b20152d9750b5"],"state_sha256":"0ca6cb36ca23071cf49c83a7af8c3f24652e48bc3905ac0dc2f588fc9b4c53d8"}