{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AGMZIU22YG7S2BAPHAK5T67PQZ","short_pith_number":"pith:AGMZIU22","canonical_record":{"source":{"id":"1601.01274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T18:53:04Z","cross_cats_sorted":[],"title_canon_sha256":"fe17dd77944a4b681ecac4d1e7e72fabadf41d9548a65a314279ecd81f6532fc","abstract_canon_sha256":"2f511516da7bb7b413c5f9fcd326f0eec149dcda5301c99a3d0200495ee44f34"},"schema_version":"1.0"},"canonical_sha256":"019994535ac1bf2d040f3815d9fbef865f2b8464824e283bfb0415c6d53daf67","source":{"kind":"arxiv","id":"1601.01274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01274","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01274v1","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01274","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"AGMZIU22YG7S","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGMZIU22YG7S2BAP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGMZIU22","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AGMZIU22YG7S2BAPHAK5T67PQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T18:53:04Z","cross_cats_sorted":[],"title_canon_sha256":"fe17dd77944a4b681ecac4d1e7e72fabadf41d9548a65a314279ecd81f6532fc","abstract_canon_sha256":"2f511516da7bb7b413c5f9fcd326f0eec149dcda5301c99a3d0200495ee44f34"},"schema_version":"1.0"},"canonical_sha256":"019994535ac1bf2d040f3815d9fbef865f2b8464824e283bfb0415c6d53daf67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:17.283583Z","signature_b64":"/VtQeSEjSmOZuYXdr+65QSC37aL1m2pfMZ9cp3n3Yfw5DXfWqLyZGTb5nUxbQR6ptcHLMY0YGd+tqLZH1BMABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"019994535ac1bf2d040f3815d9fbef865f2b8464824e283bfb0415c6d53daf67","last_reissued_at":"2026-05-18T01:23:17.283008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:17.283008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01274","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDmSpzGB9Bpzr0B4jQBf2ilBxcCmcw7MEAyNwG6IaGA9QU88ETyF8GQYD+xVFKikSko/eQRb1viSmLjliodUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:23:57.881834Z"},"content_sha256":"890ee7ddcff831ff11e69d4dfcde209d7e201592deaccc7e0b62195c7303578f","schema_version":"1.0","event_id":"sha256:890ee7ddcff831ff11e69d4dfcde209d7e201592deaccc7e0b62195c7303578f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AGMZIU22YG7S2BAPHAK5T67PQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Encoding and Decoding Algorithms for Arbitrary Dimensional Hilbert Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Hui Liu, Linbo Zhang, Tao Cui, Wei Leng","submitted_at":"2016-01-06T18:53:04Z","abstract_excerpt":"Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms are proposed. Four algorithms are based on arithmetic operations and the other four algorithms are based on bit operations. For the algorithms complexities, four of them are linear and the other four are constant for given inputs. In the end of the paper, algorithms for two dimensional Hilbert order are presented to demonstrate the usage of the algorithms intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01274","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3XE5XTucP19O4Ua609Ylat9ali3fRDtNB3veejTV+xjXQ81J8hyPrDF9tKknDyGbRB7y0z95/aCdJEEoOXNkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:23:57.882523Z"},"content_sha256":"7b65447dc115f3b7773f8c138bd98bb32002b22f990a9dd92946f69bf1da3ecd","schema_version":"1.0","event_id":"sha256:7b65447dc115f3b7773f8c138bd98bb32002b22f990a9dd92946f69bf1da3ecd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/bundle.json","state_url":"https://pith.science/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T19:23:57Z","links":{"resolver":"https://pith.science/pith/AGMZIU22YG7S2BAPHAK5T67PQZ","bundle":"https://pith.science/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/bundle.json","state":"https://pith.science/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGMZIU22YG7S2BAPHAK5T67PQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AGMZIU22YG7S2BAPHAK5T67PQZ","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":"2f511516da7bb7b413c5f9fcd326f0eec149dcda5301c99a3d0200495ee44f34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T18:53:04Z","title_canon_sha256":"fe17dd77944a4b681ecac4d1e7e72fabadf41d9548a65a314279ecd81f6532fc"},"schema_version":"1.0","source":{"id":"1601.01274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01274","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01274v1","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01274","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"AGMZIU22YG7S","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGMZIU22YG7S2BAP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGMZIU22","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:7b65447dc115f3b7773f8c138bd98bb32002b22f990a9dd92946f69bf1da3ecd","target":"graph","created_at":"2026-05-18T01:23:17Z","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":"Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms are proposed. Four algorithms are based on arithmetic operations and the other four algorithms are based on bit operations. For the algorithms complexities, four of them are linear and the other four are constant for given inputs. In the end of the paper, algorithms for two dimensional Hilbert order are presented to demonstrate the usage of the algorithms intr","authors_text":"Hui Liu, Linbo Zhang, Tao Cui, Wei Leng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T18:53:04Z","title":"Encoding and Decoding Algorithms for Arbitrary Dimensional Hilbert Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01274","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":"sha256:890ee7ddcff831ff11e69d4dfcde209d7e201592deaccc7e0b62195c7303578f","target":"record","created_at":"2026-05-18T01:23:17Z","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":"2f511516da7bb7b413c5f9fcd326f0eec149dcda5301c99a3d0200495ee44f34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T18:53:04Z","title_canon_sha256":"fe17dd77944a4b681ecac4d1e7e72fabadf41d9548a65a314279ecd81f6532fc"},"schema_version":"1.0","source":{"id":"1601.01274","kind":"arxiv","version":1}},"canonical_sha256":"019994535ac1bf2d040f3815d9fbef865f2b8464824e283bfb0415c6d53daf67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"019994535ac1bf2d040f3815d9fbef865f2b8464824e283bfb0415c6d53daf67","first_computed_at":"2026-05-18T01:23:17.283008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:17.283008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VtQeSEjSmOZuYXdr+65QSC37aL1m2pfMZ9cp3n3Yfw5DXfWqLyZGTb5nUxbQR6ptcHLMY0YGd+tqLZH1BMABw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:17.283583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:890ee7ddcff831ff11e69d4dfcde209d7e201592deaccc7e0b62195c7303578f","sha256:7b65447dc115f3b7773f8c138bd98bb32002b22f990a9dd92946f69bf1da3ecd"],"state_sha256":"d12eda5ac9d72878f9d0598d8bec473b13dfd22a9153948a48bf8280e92c71a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/WaidIxnyLqHNlcFIV65SE76UqkS8EIcr0/Ow2qLVwEWFBAiqsESY8f0thG68WgS/t/0AFlmK8u5bqe4ugUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:23:57.886125Z","bundle_sha256":"0c5c1be3cbdd6262bd16f135b8033c8499a238faeb795500275f7e3e086a1852"}}