{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EHS7ZI32Q4ZDEW2QOPBQECXOZ5","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":"d0a1b6d478b0578a4f25ba9235b377a4f1da46453a83ff2c11a7c21c20102844","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-10T12:24:30Z","title_canon_sha256":"2ad1345ef3caf985ef4d657317d9395f25b9498f7a7d9f769d50f3db52739aca"},"schema_version":"1.0","source":{"id":"1402.2125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2125","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2125v3","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2125","created_at":"2026-05-18T02:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"EHS7ZI32Q4ZD","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EHS7ZI32Q4ZDEW2Q","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EHS7ZI32","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:a79dd7f04feed4fcb49fbb20c9e46eb4dea4fc30464221916d2705f4637536a4","target":"graph","created_at":"2026-05-18T02:37:58Z","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 any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient condition of Rauzy, of an infinite family of non-trivial bounded remainder sets for any totally irrational toral rotation in any dimension.","authors_text":"Alan Haynes, Henna Koivusalo","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-10T12:24:30Z","title":"Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2125","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":"sha256:59ca46c0447083d90c6e0603d25b52ca18c29b0131540eab8f4807e3e3956d42","target":"record","created_at":"2026-05-18T02:37:58Z","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":"d0a1b6d478b0578a4f25ba9235b377a4f1da46453a83ff2c11a7c21c20102844","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-10T12:24:30Z","title_canon_sha256":"2ad1345ef3caf985ef4d657317d9395f25b9498f7a7d9f769d50f3db52739aca"},"schema_version":"1.0","source":{"id":"1402.2125","kind":"arxiv","version":3}},"canonical_sha256":"21e5fca37a8732325b5073c3020aeecf64458f44e664b4f6908fe10bc4e23856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21e5fca37a8732325b5073c3020aeecf64458f44e664b4f6908fe10bc4e23856","first_computed_at":"2026-05-18T02:37:58.815799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:58.815799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFxWe/k9gpHvCp3zfTfqPoqmmb47H+e4l+Fg1+fEj7Fa5KYrb/1UC5c6jEwlzqlZtRcp3CpMoCKPsc5cqqqVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:58.816214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59ca46c0447083d90c6e0603d25b52ca18c29b0131540eab8f4807e3e3956d42","sha256:a79dd7f04feed4fcb49fbb20c9e46eb4dea4fc30464221916d2705f4637536a4"],"state_sha256":"b3e232a5e9fce462bf6c1c778ef72ed3b40e6d2c59832ca0290ec1e99ff2d297"}