{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RHDG23EVVM5PE4KJ6S2UMRGBWA","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":"f7ffa1c8109a48b26618f5bb1d30ef615c7f2e76c829a41121930acb20140e0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-24T10:00:46Z","title_canon_sha256":"4296648aa92555aabdefc4cb20c1c2db329e5de08966f50f200c8bbcd06df860"},"schema_version":"1.0","source":{"id":"1210.6474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6474","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6474v1","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6474","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"RHDG23EVVM5P","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RHDG23EVVM5PE4KJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RHDG23EV","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4b5edd0619a9485173aed94a14f288c787954a18cf46aaec8deb23279a52883b","target":"graph","created_at":"2026-05-18T03:42:24Z","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 use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.","authors_text":"B. Girard, I. Sh. Averbukh, S. W\\\"olk, W. Merkel, W. P. Schleich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-24T10:00:46Z","title":"Factorization of numbers with Gauss sums: I. Mathematical background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6474","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":"sha256:2affb139e3395a5adf702492379acd8be310cd1016e0a2fe0adb3aeb8867be7e","target":"record","created_at":"2026-05-18T03:42:24Z","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":"f7ffa1c8109a48b26618f5bb1d30ef615c7f2e76c829a41121930acb20140e0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-24T10:00:46Z","title_canon_sha256":"4296648aa92555aabdefc4cb20c1c2db329e5de08966f50f200c8bbcd06df860"},"schema_version":"1.0","source":{"id":"1210.6474","kind":"arxiv","version":1}},"canonical_sha256":"89c66d6c95ab3af27149f4b54644c1b03b1c52c72c63ac065e64b756a7f855fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89c66d6c95ab3af27149f4b54644c1b03b1c52c72c63ac065e64b756a7f855fc","first_computed_at":"2026-05-18T03:42:24.684554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:24.684554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ptY4W4rOaI9QDbxhh5PC+xejgmXZBjnN+PyZsWPOq4FhWF7HJtALLiimOKLboWTGktMJOYm5O6QB2Xv4gx0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:24.685306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2affb139e3395a5adf702492379acd8be310cd1016e0a2fe0adb3aeb8867be7e","sha256:4b5edd0619a9485173aed94a14f288c787954a18cf46aaec8deb23279a52883b"],"state_sha256":"d5c580d7b9cb1cbc82d4a834346be49f5dea693014ce7df983a470331f52ef43"}