{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UKCPHJ6UV74EZKK7CWF267HCOS","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":"d650303fff1ab236381d1172e1b2feb8cb998b54bcad16998ba7952643f6df89","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-25T15:53:56Z","title_canon_sha256":"45ef0b1a0c47f547ffcbc0b5924fe69e3ae73cb504d4763fd59fbd28b54dd1be"},"schema_version":"1.0","source":{"id":"2410.19648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19648","created_at":"2026-07-05T09:25:59Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19648v1","created_at":"2026-07-05T09:25:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19648","created_at":"2026-07-05T09:25:59Z"},{"alias_kind":"pith_short_12","alias_value":"UKCPHJ6UV74E","created_at":"2026-07-05T09:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"UKCPHJ6UV74EZKK7","created_at":"2026-07-05T09:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"UKCPHJ6U","created_at":"2026-07-05T09:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8eaf72d60b24dd49ebdc156def4f863113df5280b7b2c93b3509a83ba7f04f72","target":"graph","created_at":"2026-07-05T09:25:59Z","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/2410.19648/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For self-similar sets $X,Y\\subseteq \\mathbb{R}$, we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of $X,Y$ have algebraic contraction ratios, and also for arbitrary $Y$ when the maps defining $X$ have algebraic-contraction ratios and there are sufficiently many of them relative to the number of maps defining $Y$. We also show that it holds for a.e. choice of the corresponding contraction ratios, and obtain bounds on the packing dimension of the exce","authors_text":"Amir Algom, Meng Wu, Michael Hochman","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-25T15:53:56Z","title":"New results on embeddings of self-similar sets via renormalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19648","kind":"arxiv","version":1},"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:d96e5afe61ef9bb1a44b82c9144f1878fdcbd75c2d07362115cd1c23dc35bb04","target":"record","created_at":"2026-07-05T09:25:59Z","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":"d650303fff1ab236381d1172e1b2feb8cb998b54bcad16998ba7952643f6df89","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-25T15:53:56Z","title_canon_sha256":"45ef0b1a0c47f547ffcbc0b5924fe69e3ae73cb504d4763fd59fbd28b54dd1be"},"schema_version":"1.0","source":{"id":"2410.19648","kind":"arxiv","version":1}},"canonical_sha256":"a284f3a7d4aff84ca95f158baf7ce274926b801e0f7de7abfc765f59e6652f81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a284f3a7d4aff84ca95f158baf7ce274926b801e0f7de7abfc765f59e6652f81","first_computed_at":"2026-07-05T09:25:59.728301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:59.728301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96pS+FvP8xK5mda3LB0GwmHmS+WthXZabJsNduaCbNjuzmDl646dij9EgjFsNrMI2A1D8Ue2+bA+vEqypFwmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:59.728739Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d96e5afe61ef9bb1a44b82c9144f1878fdcbd75c2d07362115cd1c23dc35bb04","sha256:8eaf72d60b24dd49ebdc156def4f863113df5280b7b2c93b3509a83ba7f04f72"],"state_sha256":"66cb5b9aed7d85ef6d6a697a6a97cb92b3e97635d1d61baf8ba91c16901b140d"}