{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5GCSH6NS2QOIMQF26NMAIGTE5H","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":"65c8e1bb06daae1c8548fb5110616925c889809082b63bfeecb5b1d8119c38c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-04T12:48:55Z","title_canon_sha256":"9c802985e3346264e956cdf1374c99add1f772a217bf68b81652e66eb74fb95c"},"schema_version":"1.0","source":{"id":"1806.01080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01080","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01080v2","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01080","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"pith_short_12","alias_value":"5GCSH6NS2QOI","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5GCSH6NS2QOIMQF2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5GCSH6NS","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f31f739643c9c67e7fa001c65a6d0dbfeb6304ad6de70a383845568f6216f83c","target":"graph","created_at":"2026-05-18T00:13:36Z","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":"Let $\\beta>1$. Define a class of similitudes \\[S=\\left\\{f_{i}(x)=\\dfrac{x}{\\beta^{n_i}}+a_i:n_i\\in \\mathbb{N}^{+}, a_i\\in \\mathbb{R}\\right\\}.\\] Let $\\mathcal{A}$ be the collection of all the self-similar sets generated by the similitudes from $S$. In this paper, we prove that for any $\\theta\\in(0,\\pi)$ and $K_1, K_2\\in \\mathcal{A}$, $Proj_{\\theta}(K_1\\times K_2)$ is similar to a self-similar set or an attractor of some infinite iterated function system, where $Proj_{\\theta}$ denotes the orthogonal projection onto $L_{\\theta}$, and $L_{\\theta}$ denotes the line through the origin in direction $","authors_text":"Kan Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-04T12:48:55Z","title":"Projections of cartesian products of the self-similar sets without the irrationality assumption"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01080","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":"sha256:8e8cbc99b3f415c678f663d3e9126fade9fba8853520f176c254478b9bf0d09e","target":"record","created_at":"2026-05-18T00:13:36Z","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":"65c8e1bb06daae1c8548fb5110616925c889809082b63bfeecb5b1d8119c38c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-04T12:48:55Z","title_canon_sha256":"9c802985e3346264e956cdf1374c99add1f772a217bf68b81652e66eb74fb95c"},"schema_version":"1.0","source":{"id":"1806.01080","kind":"arxiv","version":2}},"canonical_sha256":"e98523f9b2d41c8640baf358041a64e9c9beb58e287c6a0303988cfb31ecf111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e98523f9b2d41c8640baf358041a64e9c9beb58e287c6a0303988cfb31ecf111","first_computed_at":"2026-05-18T00:13:36.672869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:36.672869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5W07XYjI/7dq99U+YFJW5y79PF+Jat6FbBUJgS3VTg17Xv3WnCaHC3yr2XE6PHB05A35LvzGtZGicpdufLOtBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:36.673507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e8cbc99b3f415c678f663d3e9126fade9fba8853520f176c254478b9bf0d09e","sha256:f31f739643c9c67e7fa001c65a6d0dbfeb6304ad6de70a383845568f6216f83c"],"state_sha256":"be8fecb45d9568b0d252274ac23353dad1ea88c76fc52fd0ea319d0bb72f313c"}