{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H76B3A7K4TLRJ4SRFVL277CP2N","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":"23d9f2a4a7028276ce36a0423bf46fc3b6d65342b7692802802faa8ded06b50b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-16T09:40:21Z","title_canon_sha256":"daee02d03f1a3445f6fc6bd4d4253428984ef381d22dc6d3a72205a1fbb77f31"},"schema_version":"1.0","source":{"id":"1702.04901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04901","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04901v2","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04901","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"pith_short_12","alias_value":"H76B3A7K4TLR","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H76B3A7K4TLRJ4SR","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H76B3A7K","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:1c001d862c3808556311b9e1d5714cd7d726be0ffd4c45afd413ffd0d6834818","target":"graph","created_at":"2026-05-18T00:30:05Z","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 obtain a nature generalization for an affine Sierpinski carpet and Sierpinski triangle to $n$-dimensional space, by using the generations and characterizations of affinely-equivalent Sierpinski carpet. Exactly, in this paper, a Menger sponge and Sierpinski simplex in $4$-dimensional space could be drawn out clearly under an affine transformation. Furthermore, the method could be used to a much broader class in fractals.","authors_text":"Yanhua Yu, Yun Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-16T09:40:21Z","title":"The generalization of Sierpinski carpet and Sierpinski triangle in $n$-dimensional space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04901","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:a1912ea34aa2603fdfb791b25b98734b8c47b58c5fa3b9d222c6ba2bb0cc7f65","target":"record","created_at":"2026-05-18T00:30:05Z","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":"23d9f2a4a7028276ce36a0423bf46fc3b6d65342b7692802802faa8ded06b50b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-16T09:40:21Z","title_canon_sha256":"daee02d03f1a3445f6fc6bd4d4253428984ef381d22dc6d3a72205a1fbb77f31"},"schema_version":"1.0","source":{"id":"1702.04901","kind":"arxiv","version":2}},"canonical_sha256":"3ffc1d83eae4d714f2512d57affc4fd362f1250d53a21a06d4c454e467505f4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ffc1d83eae4d714f2512d57affc4fd362f1250d53a21a06d4c454e467505f4b","first_computed_at":"2026-05-18T00:30:05.606474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:05.606474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bk6JoYlHSvsgEtoAw3EalsjllCl6M/fNxdyPad8iXMRhl3ziZuCTXeH2gNx4kHPGz/U+H330aGGHtRAQUJCTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:05.606926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1912ea34aa2603fdfb791b25b98734b8c47b58c5fa3b9d222c6ba2bb0cc7f65","sha256:1c001d862c3808556311b9e1d5714cd7d726be0ffd4c45afd413ffd0d6834818"],"state_sha256":"0ec0d27386ba7fa3abf76e6290b6a1e006927a9d9afbb92546638cdce6788540"}