{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VVVKDB7TWTKWFLK2UODXRJJSX4","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":"b2d5c8359e1e8f20084f50f1f4b9f4b7535cb0a617590aeb340323713d3aed43","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-27T11:35:52Z","title_canon_sha256":"ac3efb39556bc6fa5b9f109a27400033047eaf608a87bd9c46732b096be8212b"},"schema_version":"1.0","source":{"id":"1812.00766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00766","created_at":"2026-05-17T23:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00766v1","created_at":"2026-05-17T23:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00766","created_at":"2026-05-17T23:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"VVVKDB7TWTKW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VVVKDB7TWTKWFLK2","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VVVKDB7T","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:2a8ecd8fa79d63c55cfc496be1ecf7ab72f3950fa6c3a586ef10d341ab43db47","target":"graph","created_at":"2026-05-17T23:59:19Z","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":"One of the most startling mathematical discoveries of the nineteen century was the existence of plane-filling curves. As is well known, the first example of such a curve was given by the Italian mathematician Giuseppe Peano in 1890. Subsequently, other examples of plane-filling curves appeared, with some of them having $n$-dimensional analogues. However, the expressions of the coordinates of the Peano curve are not easily extendable to arbitrary $n$ dimensions. In fact, the only known extension of the Peano curve to an $n$-dimensional space-filling curve, made by Stephen Milne in 1982, is rath","authors_text":"Daniel T. dos Santos, Jaquim E. DE Freitas, Ronaldo F. de Lima","cross_cats":["math.HO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-27T11:35:52Z","title":"The $n$-dimensional Peano Curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00766","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:d9b67fd0d55e25a4062ca8a43465b8b9a415c70059d3f1ab8107b8182c648acf","target":"record","created_at":"2026-05-17T23:59:19Z","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":"b2d5c8359e1e8f20084f50f1f4b9f4b7535cb0a617590aeb340323713d3aed43","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-27T11:35:52Z","title_canon_sha256":"ac3efb39556bc6fa5b9f109a27400033047eaf608a87bd9c46732b096be8212b"},"schema_version":"1.0","source":{"id":"1812.00766","kind":"arxiv","version":1}},"canonical_sha256":"ad6aa187f3b4d562ad5aa38778a532bf2ab354cabf9173ddfa427fd13b455c9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad6aa187f3b4d562ad5aa38778a532bf2ab354cabf9173ddfa427fd13b455c9c","first_computed_at":"2026-05-17T23:59:19.053237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:19.053237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/psyNTQ62y+FLA0+/NFjvU8QCKOeHmX1eug7BZ7J1aH6E0R0G3KdRu6iAGQ5DmPnDDoFJVHwZAl82sjbbFIUBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:19.053623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9b67fd0d55e25a4062ca8a43465b8b9a415c70059d3f1ab8107b8182c648acf","sha256:2a8ecd8fa79d63c55cfc496be1ecf7ab72f3950fa6c3a586ef10d341ab43db47"],"state_sha256":"2a03158769881f7bfd4dd872565b1d64920ed6cdcfccde0805ae090f85e66034"}