{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:C5DDGAA7DB2WL7DRTK6DJIDGRP","short_pith_number":"pith:C5DDGAA7","canonical_record":{"source":{"id":"2405.19881","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-30T09:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"b94564fec045dfd738984f4ce0ddadba8997b5e2b09c8ce570dcde4c7634cfc3","abstract_canon_sha256":"79203716dab0baa6abea8afe92ee5d02bd6ddc21d064e1f314cab078ac735c6b"},"schema_version":"1.0"},"canonical_sha256":"174633001f187565fc719abc34a0668bcccb5c09c31abdc222df910a2da500f8","source":{"kind":"arxiv","id":"2405.19881","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19881","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19881v3","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19881","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"C5DDGAA7DB2W","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_16","alias_value":"C5DDGAA7DB2WL7DR","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_8","alias_value":"C5DDGAA7","created_at":"2026-06-12T01:09:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:C5DDGAA7DB2WL7DRTK6DJIDGRP","target":"record","payload":{"canonical_record":{"source":{"id":"2405.19881","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-30T09:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"b94564fec045dfd738984f4ce0ddadba8997b5e2b09c8ce570dcde4c7634cfc3","abstract_canon_sha256":"79203716dab0baa6abea8afe92ee5d02bd6ddc21d064e1f314cab078ac735c6b"},"schema_version":"1.0"},"canonical_sha256":"174633001f187565fc719abc34a0668bcccb5c09c31abdc222df910a2da500f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:04.688473Z","signature_b64":"2shUNR41TS3NXBfEU8tuK2QVxiwsk/4EDsygzum1TV5l766vkjeabU7wROzu3p0hX7bioSW4aRinNq3Nb95yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"174633001f187565fc719abc34a0668bcccb5c09c31abdc222df910a2da500f8","last_reissued_at":"2026-06-12T01:09:04.687416Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:04.687416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.19881","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-12T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFEdYj4Xx+GhzAYr69GFcKJWEfLJdKDfKHreQUTuVF+uCF6Lb9AYIlOxIDmCxTf2zLqtuF8OEL/DNQXscB5rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:51:32.775899Z"},"content_sha256":"8caa1c4c30e112f626de0fccb140ac64e9156404b71bbc202b007f1294eabb6f","schema_version":"1.0","event_id":"sha256:8caa1c4c30e112f626de0fccb140ac64e9156404b71bbc202b007f1294eabb6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:C5DDGAA7DB2WL7DRTK6DJIDGRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"(Non)-hyperuniformity of perturbed lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniela Flimmel, David Dereudre, Martin Huesmann, Thomas Lebl\\'e","submitted_at":"2024-05-30T09:40:32Z","abstract_excerpt":"We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have a finite $d$-moment, and that this condition is sharp. When $d \\geq 3$, we construct arbitrarily small perturbations such that the resulting point process is not hyperuniform. As a side remark of independent interest, we exhibit hyperuniform processes with arbitrarily slow decay of their number variance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19881","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19881/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-12T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFNJ5IfkWeCkenks89l0l8HwBbYnlV5fph2V6RRGd6wEWpbJtcDk0PW4ZVy6PDZUreIh4v1UYjTdCuea01xADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:51:32.776266Z"},"content_sha256":"fa115ec266ab2221afe33be5fb3bf995a3fb95bd3c4d107c2614b59712b9100b","schema_version":"1.0","event_id":"sha256:fa115ec266ab2221afe33be5fb3bf995a3fb95bd3c4d107c2614b59712b9100b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/bundle.json","state_url":"https://pith.science/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/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":"2026-06-21T20:51:32Z","links":{"resolver":"https://pith.science/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP","bundle":"https://pith.science/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/bundle.json","state":"https://pith.science/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5DDGAA7DB2WL7DRTK6DJIDGRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:C5DDGAA7DB2WL7DRTK6DJIDGRP","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":"79203716dab0baa6abea8afe92ee5d02bd6ddc21d064e1f314cab078ac735c6b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-30T09:40:32Z","title_canon_sha256":"b94564fec045dfd738984f4ce0ddadba8997b5e2b09c8ce570dcde4c7634cfc3"},"schema_version":"1.0","source":{"id":"2405.19881","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19881","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19881v3","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19881","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"C5DDGAA7DB2W","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_16","alias_value":"C5DDGAA7DB2WL7DR","created_at":"2026-06-12T01:09:04Z"},{"alias_kind":"pith_short_8","alias_value":"C5DDGAA7","created_at":"2026-06-12T01:09:04Z"}],"graph_snapshots":[{"event_id":"sha256:fa115ec266ab2221afe33be5fb3bf995a3fb95bd3c4d107c2614b59712b9100b","target":"graph","created_at":"2026-06-12T01:09:04Z","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/2405.19881/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have a finite $d$-moment, and that this condition is sharp. When $d \\geq 3$, we construct arbitrarily small perturbations such that the resulting point process is not hyperuniform. As a side remark of independent interest, we exhibit hyperuniform processes with arbitrarily slow decay of their number variance.","authors_text":"Daniela Flimmel, David Dereudre, Martin Huesmann, Thomas Lebl\\'e","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-30T09:40:32Z","title":"(Non)-hyperuniformity of perturbed lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19881","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":"sha256:8caa1c4c30e112f626de0fccb140ac64e9156404b71bbc202b007f1294eabb6f","target":"record","created_at":"2026-06-12T01:09:04Z","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":"79203716dab0baa6abea8afe92ee5d02bd6ddc21d064e1f314cab078ac735c6b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-30T09:40:32Z","title_canon_sha256":"b94564fec045dfd738984f4ce0ddadba8997b5e2b09c8ce570dcde4c7634cfc3"},"schema_version":"1.0","source":{"id":"2405.19881","kind":"arxiv","version":3}},"canonical_sha256":"174633001f187565fc719abc34a0668bcccb5c09c31abdc222df910a2da500f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"174633001f187565fc719abc34a0668bcccb5c09c31abdc222df910a2da500f8","first_computed_at":"2026-06-12T01:09:04.687416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:04.687416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2shUNR41TS3NXBfEU8tuK2QVxiwsk/4EDsygzum1TV5l766vkjeabU7wROzu3p0hX7bioSW4aRinNq3Nb95yDg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:04.688473Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.19881","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8caa1c4c30e112f626de0fccb140ac64e9156404b71bbc202b007f1294eabb6f","sha256:fa115ec266ab2221afe33be5fb3bf995a3fb95bd3c4d107c2614b59712b9100b"],"state_sha256":"f04f48eea4bf517200d449c6bae3e899145d8e50e431afb1f573d47cc28e1160"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZ3RtFs7QO0myMLz5CmWl74mKeiCTQaHDbPydwJ4ZT+v1FfVMO/ZrSHb3xwRMc2l4GnKuGcthl19K35dQizlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:51:32.778285Z","bundle_sha256":"1eab0beb373b11a2d7bcbc273c42c05122b4ba504fa060876278dbabe6d39a9d"}}