{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2FD3VYRDVCY2ED4WT4QJ4ZEVXT","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":"be282c0c66a66c6c4a4ef046b61ee407f800760a0fa6c840700dce205641e589","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-01-23T20:03:06Z","title_canon_sha256":"32d4687aa91618e99000ea42791b5db70877ae649059027b826727fb9b6b1317"},"schema_version":"1.0","source":{"id":"1001.4203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4203","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4203v1","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4203","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"2FD3VYRDVCY2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2FD3VYRDVCY2ED4W","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2FD3VYRD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:6c267dbc42352a2814c05fdea1e45edb0853a3a37fe411908866b29b94b0b810","target":"graph","created_at":"2026-05-18T04:07:16Z","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":"In 1994, Martin Gardner stated a set of questions concerning the dissection of a square or an equilateral triangle in three similar parts. Meanwhile, Gardner's questions have been generalized and some of them are already solved. In the present paper, we solve more of his questions and treat them in a much more general context. Let $D\\subset \\mathbb{R}^d$ be a given set and let $f_1,...,f_k$ be injective continuous mappings. Does there exist a set $X$ such that $D = X \\cup f_1(X) \\cup ... \\cup f_k(X)$ is satisfied with a non-overlapping union? We prove that such a set $X$ exists for certain cho","authors_text":"J\\\"org Thuswaldner, Jun Luo, Ryotaro Okazaki, Shigeki Akiyama, Wolfgang Steiner (LIAFA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-01-23T20:03:06Z","title":"Similar dissection of sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4203","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":"sha256:1bed0689800ca3b413bf27dd9a019a14bd1ce1a9d07c5c3a0b7a00dbc936205f","target":"record","created_at":"2026-05-18T04:07:16Z","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":"be282c0c66a66c6c4a4ef046b61ee407f800760a0fa6c840700dce205641e589","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-01-23T20:03:06Z","title_canon_sha256":"32d4687aa91618e99000ea42791b5db70877ae649059027b826727fb9b6b1317"},"schema_version":"1.0","source":{"id":"1001.4203","kind":"arxiv","version":1}},"canonical_sha256":"d147bae223a8b1a20f969f209e6495bccce19b0bff7cd3daeae9d0be5c906e81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d147bae223a8b1a20f969f209e6495bccce19b0bff7cd3daeae9d0be5c906e81","first_computed_at":"2026-05-18T04:07:16.077745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:16.077745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GG/a+EUpR+C78D8FZNmu8LjKZhZQLauMPTIwQJffZr0fMC59JFhce0V5L2Y52Y3AcpgS47RMKl3K44tHWDLLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:16.078254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bed0689800ca3b413bf27dd9a019a14bd1ce1a9d07c5c3a0b7a00dbc936205f","sha256:6c267dbc42352a2814c05fdea1e45edb0853a3a37fe411908866b29b94b0b810"],"state_sha256":"1b6933b2536ab0100e2abe80317b9c5d5eb95806fded0096d21fafac0d745234"}