{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z2VYO7FYXJJUC4MED4LWYO2F23","short_pith_number":"pith:Z2VYO7FY","canonical_record":{"source":{"id":"1702.04041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-14T01:31:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f6a7a70528c738e34868772864d1a90e12bcc1c4bb0f50626ce22f3114a54347","abstract_canon_sha256":"68bacbaaac9e41c01c347ffd07af52a94c73cd5c80cb757103d84a4236c301bc"},"schema_version":"1.0"},"canonical_sha256":"ceab877cb8ba534171841f176c3b45d6c80c1445dd8b4916475b107c18d1d7f5","source":{"kind":"arxiv","id":"1702.04041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04041","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04041v1","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04041","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z2VYO7FYXJJU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2VYO7FYXJJUC4ME","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2VYO7FY","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z2VYO7FYXJJUC4MED4LWYO2F23","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-14T01:31:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f6a7a70528c738e34868772864d1a90e12bcc1c4bb0f50626ce22f3114a54347","abstract_canon_sha256":"68bacbaaac9e41c01c347ffd07af52a94c73cd5c80cb757103d84a4236c301bc"},"schema_version":"1.0"},"canonical_sha256":"ceab877cb8ba534171841f176c3b45d6c80c1445dd8b4916475b107c18d1d7f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:49.162372Z","signature_b64":"3n+UhZMb5xyEUQau5JWWbpdr2wZhy6Po5bR1Sr3v7RyCQC+8Yl5LAaJHun2x4NX/knEC+kal+t5g3hVBelO+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceab877cb8ba534171841f176c3b45d6c80c1445dd8b4916475b107c18d1d7f5","last_reissued_at":"2026-05-18T00:50:49.161710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:49.161710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04041","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5r0MQqv5M7lW1N+OU0JBtUVUlL0MNJaecXhM3ct/nfkBQMlcIRn/tGlrcDRFYkUDRVh4curH/EIXvRWuSj+WCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:32:45.458295Z"},"content_sha256":"de9e801e03252c45f3f0ef0e705561cd87125f5c8aa602398026502211aa5dd2","schema_version":"1.0","event_id":"sha256:de9e801e03252c45f3f0ef0e705561cd87125f5c8aa602398026502211aa5dd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z2VYO7FYXJJUC4MED4LWYO2F23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistics of patterns in typical cut and project sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alan Haynes, Antoine Julien, Henna Koivusalo, James Walton","submitted_at":"2017-02-14T01:31:51Z","abstract_excerpt":"In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in discrepancy theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04041","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuaImHHQeXrZfUJlpVuGGeMEOpwVbhkp8d0qWHA1OZAgTIBh2eAS8yU2x1ckF5Xfi+dXurD6QP2M+HOwh/ZhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:32:45.458647Z"},"content_sha256":"b95cddb624d108a8662d57df2b59bab397ae710a130c66ed8d4613f720d9e948","schema_version":"1.0","event_id":"sha256:b95cddb624d108a8662d57df2b59bab397ae710a130c66ed8d4613f720d9e948"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/bundle.json","state_url":"https://pith.science/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T13:32:45Z","links":{"resolver":"https://pith.science/pith/Z2VYO7FYXJJUC4MED4LWYO2F23","bundle":"https://pith.science/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/bundle.json","state":"https://pith.science/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2VYO7FYXJJUC4MED4LWYO2F23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z2VYO7FYXJJUC4MED4LWYO2F23","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":"68bacbaaac9e41c01c347ffd07af52a94c73cd5c80cb757103d84a4236c301bc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-14T01:31:51Z","title_canon_sha256":"f6a7a70528c738e34868772864d1a90e12bcc1c4bb0f50626ce22f3114a54347"},"schema_version":"1.0","source":{"id":"1702.04041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04041","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04041v1","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04041","created_at":"2026-05-18T00:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z2VYO7FYXJJU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2VYO7FYXJJUC4ME","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2VYO7FY","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:b95cddb624d108a8662d57df2b59bab397ae710a130c66ed8d4613f720d9e948","target":"graph","created_at":"2026-05-18T00:50:49Z","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":"In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in discrepancy theory.","authors_text":"Alan Haynes, Antoine Julien, Henna Koivusalo, James Walton","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-14T01:31:51Z","title":"Statistics of patterns in typical cut and project sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04041","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:de9e801e03252c45f3f0ef0e705561cd87125f5c8aa602398026502211aa5dd2","target":"record","created_at":"2026-05-18T00:50:49Z","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":"68bacbaaac9e41c01c347ffd07af52a94c73cd5c80cb757103d84a4236c301bc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-14T01:31:51Z","title_canon_sha256":"f6a7a70528c738e34868772864d1a90e12bcc1c4bb0f50626ce22f3114a54347"},"schema_version":"1.0","source":{"id":"1702.04041","kind":"arxiv","version":1}},"canonical_sha256":"ceab877cb8ba534171841f176c3b45d6c80c1445dd8b4916475b107c18d1d7f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceab877cb8ba534171841f176c3b45d6c80c1445dd8b4916475b107c18d1d7f5","first_computed_at":"2026-05-18T00:50:49.161710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:49.161710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3n+UhZMb5xyEUQau5JWWbpdr2wZhy6Po5bR1Sr3v7RyCQC+8Yl5LAaJHun2x4NX/knEC+kal+t5g3hVBelO+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:49.162372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de9e801e03252c45f3f0ef0e705561cd87125f5c8aa602398026502211aa5dd2","sha256:b95cddb624d108a8662d57df2b59bab397ae710a130c66ed8d4613f720d9e948"],"state_sha256":"c4387787152bcc2b9d120f5fab7a2301f8d518f1dbc86fc8ca988f6b2c9b1ef4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxVSyzv9bA67uBZKMObG1lSe0Oq/29rEFc1epJ9lSBTnMSOj9Mq4s0P2OS0Batvmvj9VSv00Dqh6lW3ieCSpDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:32:45.460473Z","bundle_sha256":"9a4260ce27f4ed57072f2f83bb16158d2b93a9858be3458859581fab7c9e5be1"}}