{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VCUECQAXPCPI2TN5H5OBP35ORU","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":"a0d3de3a14c5fd3c13bbeb7d63af0bff1c44acd15afae930c187e5075d06d71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-07T10:01:42Z","title_canon_sha256":"badae2f6c76cd01ad5710d2e5b9cd7c4ecefbd8ed79221ec8a64ad53b2a0f1ea"},"schema_version":"1.0","source":{"id":"1802.02370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02370","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02370v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02370","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"VCUECQAXPCPI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VCUECQAXPCPI2TN5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VCUECQAX","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:d6b79005a2248c0c71c112703df0749581c015b7c5ab62adc280a6c8998bf727","target":"graph","created_at":"2026-05-18T00:24:08Z","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 these expository notes we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems.","authors_text":"Boris Solomyak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-07T10:01:42Z","title":"Delone sets and dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02370","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:e38259d9e48588da5c73f5f07c17dc93b27084a7dd1a04eaec0535201115c4f6","target":"record","created_at":"2026-05-18T00:24:08Z","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":"a0d3de3a14c5fd3c13bbeb7d63af0bff1c44acd15afae930c187e5075d06d71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-07T10:01:42Z","title_canon_sha256":"badae2f6c76cd01ad5710d2e5b9cd7c4ecefbd8ed79221ec8a64ad53b2a0f1ea"},"schema_version":"1.0","source":{"id":"1802.02370","kind":"arxiv","version":1}},"canonical_sha256":"a8a8414017789e8d4dbd3f5c17efae8d203bc46f461e9e810ea8930876b81ef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8a8414017789e8d4dbd3f5c17efae8d203bc46f461e9e810ea8930876b81ef9","first_computed_at":"2026-05-18T00:24:08.458215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:08.458215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9hPHNS0ymCE8Fr8rZshgKj1+iIFZtZltAXUqGR64lXVYheTOzSyMFMb9GmPpFc0N2rX+ZUJdrfIlejdGlOUbBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:08.458707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e38259d9e48588da5c73f5f07c17dc93b27084a7dd1a04eaec0535201115c4f6","sha256:d6b79005a2248c0c71c112703df0749581c015b7c5ab62adc280a6c8998bf727"],"state_sha256":"93f568b4e1c33c2eaec6baac70c125404f0ab1854c5705c9b89815af20c12a7e"}