{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LLAUQWZT7JDK7MM5HHDXLVPB3T","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":"42d5be7e99b692da82db69cca68db711d4dce5088216bec15529a416ee4928be","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-04T13:37:01Z","title_canon_sha256":"60ca8f3d616241e6db5fc5c7506625d6640dd822ddb1c24af879f742f179de6f"},"schema_version":"1.0","source":{"id":"0804.0733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0733","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0733v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0733","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"LLAUQWZT7JDK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LLAUQWZT7JDK7MM5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LLAUQWZT","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e29c8537f5aeabc1814e9c5f5cc13af350214c5092783addb2bfa00fb80392ac","target":"graph","created_at":"2026-05-18T04:14:36Z","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":"Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by other authors are correct. In fact it turns out that the complement operation does not have significant influence on the performance of the algorithm and can therefore be omitted.","authors_text":"Clemens Heuberger, Helmut Prodinger","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-04T13:37:01Z","title":"Complements and signed digit representations: Analysis of a multi-exponentiation-algorithm of Wu, Lou, Lai and Chang"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0733","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":"sha256:67d948f28b1519de286bb102f477f7960628116f6635399027bf24d3a14fa831","target":"record","created_at":"2026-05-18T04:14:36Z","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":"42d5be7e99b692da82db69cca68db711d4dce5088216bec15529a416ee4928be","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-04T13:37:01Z","title_canon_sha256":"60ca8f3d616241e6db5fc5c7506625d6640dd822ddb1c24af879f742f179de6f"},"schema_version":"1.0","source":{"id":"0804.0733","kind":"arxiv","version":1}},"canonical_sha256":"5ac1485b33fa46afb19d39c775d5e1dcdb90a0e2c5ccdb5d89bee13d218a7dd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ac1485b33fa46afb19d39c775d5e1dcdb90a0e2c5ccdb5d89bee13d218a7dd6","first_computed_at":"2026-05-18T04:14:36.565273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.565273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aJjulUzqpU3RUqDUgSi9rsBE9bWP5HCfMu6J3Ap/bnpsx02K68Re/4LS3ZnQ0vTWlDBMLPBv1czHNIq7ZSRDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.566252Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67d948f28b1519de286bb102f477f7960628116f6635399027bf24d3a14fa831","sha256:e29c8537f5aeabc1814e9c5f5cc13af350214c5092783addb2bfa00fb80392ac"],"state_sha256":"1b0a5cd9b49821f7009e26e67d9f9721965e187ee753152eef06aee8bb4bb191"}