{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DWSZJJXJFEKQVJNJ2V3B6T4AHY","short_pith_number":"pith:DWSZJJXJ","canonical_record":{"source":{"id":"2506.19114","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-06-23T20:42:11Z","cross_cats_sorted":["cs.DM","math.FA"],"title_canon_sha256":"7b4065bca60e12ae7c64008ce37f66ec90e7f0e0c5246aca4a1c605c574640a3","abstract_canon_sha256":"b76817858aaeaa3393ddda4de4dc08f9ea88264811a1316ba4a4bf841200db74"},"schema_version":"1.0"},"canonical_sha256":"1da594a6e929150aa5a9d5761f4f803e05f7b6ff86ea36384ab257ffa615fd90","source":{"kind":"arxiv","id":"2506.19114","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19114","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19114v4","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19114","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"DWSZJJXJFEKQ","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_16","alias_value":"DWSZJJXJFEKQVJNJ","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_8","alias_value":"DWSZJJXJ","created_at":"2026-06-19T16:09:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DWSZJJXJFEKQVJNJ2V3B6T4AHY","target":"record","payload":{"canonical_record":{"source":{"id":"2506.19114","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-06-23T20:42:11Z","cross_cats_sorted":["cs.DM","math.FA"],"title_canon_sha256":"7b4065bca60e12ae7c64008ce37f66ec90e7f0e0c5246aca4a1c605c574640a3","abstract_canon_sha256":"b76817858aaeaa3393ddda4de4dc08f9ea88264811a1316ba4a4bf841200db74"},"schema_version":"1.0"},"canonical_sha256":"1da594a6e929150aa5a9d5761f4f803e05f7b6ff86ea36384ab257ffa615fd90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:09:49.772897Z","signature_b64":"3ALXNlg58PucC4Cw2PLL92MNXGqPGOo2sYtFFnHsE8lOqAH1wraB10urfSujNEXkm8zRwypNZwdqjgF4kVvYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1da594a6e929150aa5a9d5761f4f803e05f7b6ff86ea36384ab257ffa615fd90","last_reissued_at":"2026-06-19T16:09:49.772470Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:09:49.772470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.19114","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:09:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zEU0g+K3ZwRYCBu9QjIiv5/5q69h149BMVkpsXET7baPiWAg91VsR5HtZT83JbbVFsrVIKnep0/QYMg0Esb0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:44:42.347037Z"},"content_sha256":"56ec0f784157b9872793c9c13c10b8ad592186da7bafbe5ebf6e83d75c39b0e1","schema_version":"1.0","event_id":"sha256:56ec0f784157b9872793c9c13c10b8ad592186da7bafbe5ebf6e83d75c39b0e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DWSZJJXJFEKQVJNJ2V3B6T4AHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast repetitivity in non-rectifiable Delone sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.FA"],"primary_cat":"math.MG","authors_text":"Ashwin Bhat, Michael Dymond","submitted_at":"2025-06-23T20:42:11Z","abstract_excerpt":"We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\\mathbb{R}^d$ with $d \\geq 2$. We further obtain a close to optimal repetitivity function for such sets. The proof is based on the process of encoding a non-realisable density in a Delone set, due to Burago and Kleiner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19114","kind":"arxiv","version":4},"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/2506.19114/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":"2026-06-19T16:09:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzYITmhvvqwxD5QDUAMh/syhpDSCfr/S6+4DF67fkTKj1gNF7VIso4v6U19DLrOtcnv/+3P/q1PanAqQlmy6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:44:42.347418Z"},"content_sha256":"0567eb900173f7bad690ebe7310498194dbaac46e43cce86b4184f64d67a12ff","schema_version":"1.0","event_id":"sha256:0567eb900173f7bad690ebe7310498194dbaac46e43cce86b4184f64d67a12ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/bundle.json","state_url":"https://pith.science/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/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":"2026-06-20T08:44:42Z","links":{"resolver":"https://pith.science/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY","bundle":"https://pith.science/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/bundle.json","state":"https://pith.science/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWSZJJXJFEKQVJNJ2V3B6T4AHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DWSZJJXJFEKQVJNJ2V3B6T4AHY","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":"b76817858aaeaa3393ddda4de4dc08f9ea88264811a1316ba4a4bf841200db74","cross_cats_sorted":["cs.DM","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-06-23T20:42:11Z","title_canon_sha256":"7b4065bca60e12ae7c64008ce37f66ec90e7f0e0c5246aca4a1c605c574640a3"},"schema_version":"1.0","source":{"id":"2506.19114","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19114","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19114v4","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19114","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_12","alias_value":"DWSZJJXJFEKQ","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_16","alias_value":"DWSZJJXJFEKQVJNJ","created_at":"2026-06-19T16:09:49Z"},{"alias_kind":"pith_short_8","alias_value":"DWSZJJXJ","created_at":"2026-06-19T16:09:49Z"}],"graph_snapshots":[{"event_id":"sha256:0567eb900173f7bad690ebe7310498194dbaac46e43cce86b4184f64d67a12ff","target":"graph","created_at":"2026-06-19T16:09:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.19114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\\mathbb{R}^d$ with $d \\geq 2$. We further obtain a close to optimal repetitivity function for such sets. The proof is based on the process of encoding a non-realisable density in a Delone set, due to Burago and Kleiner.","authors_text":"Ashwin Bhat, Michael Dymond","cross_cats":["cs.DM","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-06-23T20:42:11Z","title":"Fast repetitivity in non-rectifiable Delone sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19114","kind":"arxiv","version":4},"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":"sha256:56ec0f784157b9872793c9c13c10b8ad592186da7bafbe5ebf6e83d75c39b0e1","target":"record","created_at":"2026-06-19T16:09:49Z","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":"b76817858aaeaa3393ddda4de4dc08f9ea88264811a1316ba4a4bf841200db74","cross_cats_sorted":["cs.DM","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-06-23T20:42:11Z","title_canon_sha256":"7b4065bca60e12ae7c64008ce37f66ec90e7f0e0c5246aca4a1c605c574640a3"},"schema_version":"1.0","source":{"id":"2506.19114","kind":"arxiv","version":4}},"canonical_sha256":"1da594a6e929150aa5a9d5761f4f803e05f7b6ff86ea36384ab257ffa615fd90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1da594a6e929150aa5a9d5761f4f803e05f7b6ff86ea36384ab257ffa615fd90","first_computed_at":"2026-06-19T16:09:49.772470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:09:49.772470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ALXNlg58PucC4Cw2PLL92MNXGqPGOo2sYtFFnHsE8lOqAH1wraB10urfSujNEXkm8zRwypNZwdqjgF4kVvYAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:09:49.772897Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.19114","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56ec0f784157b9872793c9c13c10b8ad592186da7bafbe5ebf6e83d75c39b0e1","sha256:0567eb900173f7bad690ebe7310498194dbaac46e43cce86b4184f64d67a12ff"],"state_sha256":"98dc4b6b2f4db6354b4c836fc2372f94f49bc330ebdb853bcc629bb65184b3b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGcwtCYSvG7SE5WQPNhclUU23UwipouoZ8+1c49zRJWeOuCPXXhntqbYv0XyWNICX2Gr7aHjkPwZ4pXMEbPVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:44:42.349324Z","bundle_sha256":"772cace302517f6831947a0d707ec678321137cb0429d45d0d04da2c9e7fbdfa"}}