{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I6UNYECF3CC3M6R3YTJLKJL5EY","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":"78adf559ddafe615c018e3cabc067d7435ccba32b67d2dc462f533b9027ce6cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-16T12:48:20Z","title_canon_sha256":"adaadcbf46a0d55da37a8b7c9c0960b27ff72cc24e718f78657dce78e718198f"},"schema_version":"1.0","source":{"id":"1511.04937","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04937","created_at":"2026-05-18T01:17:18Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04937v2","created_at":"2026-05-18T01:17:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04937","created_at":"2026-05-18T01:17:18Z"},{"alias_kind":"pith_short_12","alias_value":"I6UNYECF3CC3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I6UNYECF3CC3M6R3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I6UNYECF","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:dab53dcbafda4c1b4a026e5505187accaf1d9d4e0e05ea5acabc13757bd645cc","target":"graph","created_at":"2026-05-18T01:17:18Z","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":"Two popular and often applied methods to obtain two-dimensional point sets with the optimal order of $L_p$ discrepancy are digit scrambling and symmetrization. In this paper we combine these two techniques and symmetrize $b$-adic Hammersley point sets scrambled with arbitrary permutations. It is already known that these modifications indeed assure that the $L_p$ discrepancy is of optimal order $\\mathcal{O}\\left(\\sqrt{\\log{N}}/N\\right)$ for $p\\in [1,\\infty)$ in contrast to the classical Hammersley point set. We prove an exact formula for the $L_2$ discrepancy of these point sets for special per","authors_text":"Lisa M. Kritzinger, Ralph Kritzinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-16T12:48:20Z","title":"$L_2$ discrepancy of symmetrized generalized Hammersley point sets in base $b$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04937","kind":"arxiv","version":2},"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":"sha256:9ff028f92e27478ac648ef095f0b31740584748ff187123cd9633b59935df84a","target":"record","created_at":"2026-05-18T01:17:18Z","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":"78adf559ddafe615c018e3cabc067d7435ccba32b67d2dc462f533b9027ce6cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-16T12:48:20Z","title_canon_sha256":"adaadcbf46a0d55da37a8b7c9c0960b27ff72cc24e718f78657dce78e718198f"},"schema_version":"1.0","source":{"id":"1511.04937","kind":"arxiv","version":2}},"canonical_sha256":"47a8dc1045d885b67a3bc4d2b5257d2625f843787d4b1500d888c855d0d8c79a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47a8dc1045d885b67a3bc4d2b5257d2625f843787d4b1500d888c855d0d8c79a","first_computed_at":"2026-05-18T01:17:18.359139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:18.359139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aBC0ex6BMf/n+c7PLlw4F8v6v0Xkzqf8YEM/8764g/A9NxLt6yd2kJc4Df9bC/tNRpnv9SZ1xsYuotujCjIZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:18.359785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04937","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ff028f92e27478ac648ef095f0b31740584748ff187123cd9633b59935df84a","sha256:dab53dcbafda4c1b4a026e5505187accaf1d9d4e0e05ea5acabc13757bd645cc"],"state_sha256":"4088c5f180c6e807158372bfa0d0bc0460bc15ef9c526265c88339c7128afac7"}