{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M3B3V7IDQ3RHFL3BIHKOLE445W","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":"a3b2e26d99d9e2a9f30dca263d7e0a93f541bb943f913d354c50c56464db269d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-08T09:39:01Z","title_canon_sha256":"ec254f3f7c99351eb25e2bc66ca5fb71da35d23d7e4e46226b8cc2e10017d43d"},"schema_version":"1.0","source":{"id":"1211.1804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1804","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1804v1","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1804","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"M3B3V7IDQ3RH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M3B3V7IDQ3RHFL3B","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M3B3V7ID","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:e4eb4e1d29d5e2fca014cd1b1e8871918a4804768784db3650a11afa9df35c07","target":"graph","created_at":"2026-05-18T03:41:13Z","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":"For bases $\\mathbf{b}=(b_1,..., b_s)$ of $s$ not necessarily distinct integers $b_i\\ge 2$, we prove a version of the inequality of \\etk \\ for the hybrid function system composed of the Walsh functions in base $\\bfb^{(1)}=(b_1,..., b_{s_1})$ and, as second component, the $\\bfb^{(2)}$-adic functions, $\\bfb^{(2)}=(b_{s_1+1},..., b_s)$, with $s=s_1+s_2$, $s_1$ and $s_2$ not both equal to 0. Further, we point out why this choice of a hybrid function system covers all possible cases of sequences that employ addition of digit vectors as their main construction principle.","authors_text":"Peter Hellekalek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-08T09:39:01Z","title":"A hybrid inequality of Erd\\\"os-Tur\\'an-Koksma for digital sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1804","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":"sha256:6a28ba7861eac26a10343ad1e65d5fe0e33546e24bd22e1fec61d9deff391b73","target":"record","created_at":"2026-05-18T03:41:13Z","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":"a3b2e26d99d9e2a9f30dca263d7e0a93f541bb943f913d354c50c56464db269d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-08T09:39:01Z","title_canon_sha256":"ec254f3f7c99351eb25e2bc66ca5fb71da35d23d7e4e46226b8cc2e10017d43d"},"schema_version":"1.0","source":{"id":"1211.1804","kind":"arxiv","version":1}},"canonical_sha256":"66c3bafd0386e272af6141d4e5939ced96978612af0f6eb6428e0f6f9c837e4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66c3bafd0386e272af6141d4e5939ced96978612af0f6eb6428e0f6f9c837e4b","first_computed_at":"2026-05-18T03:41:13.418254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:13.418254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNLpLgrht7d5BeTNv6cYsS6qFfzkwTBNL1l0z1n+m7SEZUgTmyLMO1ISezeDSdOXVlye8BXmQdjB7DBUrTZjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:13.418733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a28ba7861eac26a10343ad1e65d5fe0e33546e24bd22e1fec61d9deff391b73","sha256:e4eb4e1d29d5e2fca014cd1b1e8871918a4804768784db3650a11afa9df35c07"],"state_sha256":"a212a6a3b8588bef84a77cd1411a1fa0eac25d8564114c3666459a493687ff1f"}