{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DVL6R2VIIDXXZKE4TO3MSYF7HP","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":"0cc7e5656d06a6da8f090480cecf699803cc6f14c2b2a177f44e0014adb2805e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-10-31T14:56:29Z","title_canon_sha256":"fd9e74d5919749eebabe47cc7ccb5faf68e9818807f15822baf7c8517425acb3"},"schema_version":"1.0","source":{"id":"2310.20517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.20517","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2310.20517v2","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20517","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"DVL6R2VIIDXX","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"DVL6R2VIIDXXZKE4","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"DVL6R2VI","created_at":"2026-06-02T02:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:8f6db134cb06f41b8eb00778f889be420a64e46b0b847ffda684a9a3f85651e1","target":"graph","created_at":"2026-06-02T02:04:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.20517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study hyperuniformity of self-similar point processes arising from substitution rules in two dimensions. In particular, we derive a sufficient condition for hyperuniformity of these point processes only in terms of the associated substitution matrix. This condition applies to a wide class of examples for which hyperuniformity had not yet been established, including most well-known examples of planar self-similar tilings. In particular, we show that the Godr\\`eche-Lan\\c{c}on-Billard substitution rule gives rise to hyperuniform point processes with singular continuous diffraction. Furthermore","authors_text":"Daniel Roca","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-10-31T14:56:29Z","title":"Hyperuniformity of self-similar point processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20517","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":"sha256:8699e684126d04ed7327b47fad8759ae3047daa42c5f3bc7c86f83d32ae725b3","target":"record","created_at":"2026-06-02T02:04:44Z","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":"0cc7e5656d06a6da8f090480cecf699803cc6f14c2b2a177f44e0014adb2805e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-10-31T14:56:29Z","title_canon_sha256":"fd9e74d5919749eebabe47cc7ccb5faf68e9818807f15822baf7c8517425acb3"},"schema_version":"1.0","source":{"id":"2310.20517","kind":"arxiv","version":2}},"canonical_sha256":"1d57e8eaa840ef7ca89c9bb6c960bf3be988a9667ea8403a338e9dfbb0b48ba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d57e8eaa840ef7ca89c9bb6c960bf3be988a9667ea8403a338e9dfbb0b48ba2","first_computed_at":"2026-06-02T02:04:44.724636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:44.724636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZitAVVbjJLfZL2SC5sdiQ31s5zDUMvbt90SDIq42DZolWD3GNVgWAETfVqKQflEk/15ACWfGwzMVPyanUDLfBQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:44.725087Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.20517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8699e684126d04ed7327b47fad8759ae3047daa42c5f3bc7c86f83d32ae725b3","sha256:8f6db134cb06f41b8eb00778f889be420a64e46b0b847ffda684a9a3f85651e1"],"state_sha256":"fbfebc3395d510988cda44b42b85ec00b527d7e621a8595b7851458d010f95a1"}