{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TMPUPBFRAJ7YIGDVS5FNFKTZWY","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":"766748af9549cb40eca0c5bbe369e6a65363d33a5ac11a688839c4717d25b4b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-27T17:28:38Z","title_canon_sha256":"c0024fd7674edb38b7bc95df1402c9a20697a6eff21e79112ca090913497a81b"},"schema_version":"1.0","source":{"id":"1706.08949","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08949","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08949v3","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08949","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"TMPUPBFRAJ7Y","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMPUPBFRAJ7YIGDV","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMPUPBFR","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:329712bbd92c4c0add633ec9f1ed6091407d685370356c3d875a5fb4e4ee9bf7","target":"graph","created_at":"2026-05-18T00:29:01Z","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":"This paper adresses the question whether the $LS$-sequences constructed by Carbone yield indeed a new family of low discrepancy sequences. While it is well known that the case $S=0$ corresponds to van der Corput sequences, we prove here that the case $S=1$ can be traced back to two-sided Kronecker sequences and moreover that for $S \\geq 2$ none of these two types occurs anymore. In addition, our approach allows for an improved discrepancy bound for $S=1$ and $L$ arbitrary.","authors_text":"Christian Wei{\\ss}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-27T17:28:38Z","title":"On the Classification of LS-Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08949","kind":"arxiv","version":3},"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:a141d22342dc045b64176412b7abecfac69b4ad25be1780cc0400a6d1eb0794e","target":"record","created_at":"2026-05-18T00:29:01Z","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":"766748af9549cb40eca0c5bbe369e6a65363d33a5ac11a688839c4717d25b4b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-27T17:28:38Z","title_canon_sha256":"c0024fd7674edb38b7bc95df1402c9a20697a6eff21e79112ca090913497a81b"},"schema_version":"1.0","source":{"id":"1706.08949","kind":"arxiv","version":3}},"canonical_sha256":"9b1f4784b1027f841875974ad2aa79b606f767f4a75c25a94946d88f6b5bf889","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b1f4784b1027f841875974ad2aa79b606f767f4a75c25a94946d88f6b5bf889","first_computed_at":"2026-05-18T00:29:01.386741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:01.386741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JYwt3cCrC6LKG3MeZtB2i+3gbVAIj7g4bJWXDRea56IG02rYDNxz0Et7baRlIvfcS2p4qhxgAlYbMDx53XL2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:01.387384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08949","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a141d22342dc045b64176412b7abecfac69b4ad25be1780cc0400a6d1eb0794e","sha256:329712bbd92c4c0add633ec9f1ed6091407d685370356c3d875a5fb4e4ee9bf7"],"state_sha256":"a52940d0c9e7f99844dbb5afae27d900bbca6d90ae52ebcbc66958ac0049a33a"}