{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:4HNKX2RAU55YSZQB7UDOOLIPEZ","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":"9905add9e3d8bceb7423ba3ccdee5e0ba1c8a5eef3224e50045943eaac8e1bb0","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-02-21T09:55:49Z","title_canon_sha256":"67932fb5e597bcd88a655f79312da0c367beadca752d050e5f20fb674008205d"},"schema_version":"1.0","source":{"id":"math-ph/0302049","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0302049","created_at":"2026-07-04T15:13:53Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0302049v2","created_at":"2026-07-04T15:13:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0302049","created_at":"2026-07-04T15:13:53Z"},{"alias_kind":"pith_short_12","alias_value":"4HNKX2RAU55Y","created_at":"2026-07-04T15:13:53Z"},{"alias_kind":"pith_short_16","alias_value":"4HNKX2RAU55YSZQB","created_at":"2026-07-04T15:13:53Z"},{"alias_kind":"pith_short_8","alias_value":"4HNKX2RA","created_at":"2026-07-04T15:13:53Z"}],"graph_snapshots":[{"event_id":"sha256:3efeeed28e762688e157b428352f0cb85e8608b1b09cb91b1ea67d56d4fa9501","target":"graph","created_at":"2026-07-04T15:13:53Z","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/math-ph/0302049/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally compact Abelian groups, is the pure pointedness of the diffraction spectrum. We derive an extension of this result, valid for dense point sets in Euclidean space, which is motivated by the study of quasicrystallographic random tilings.","authors_text":"Christoph Richard","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2003-02-21T09:55:49Z","title":"Dense Dirac combs in Euclidean space with pure point diffraction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0302049","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":"sha256:6dcae32577ab23fb44e4741f3246efb0ba523281c90bc8163e5b8654a12386cd","target":"record","created_at":"2026-07-04T15:13:53Z","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":"9905add9e3d8bceb7423ba3ccdee5e0ba1c8a5eef3224e50045943eaac8e1bb0","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-02-21T09:55:49Z","title_canon_sha256":"67932fb5e597bcd88a655f79312da0c367beadca752d050e5f20fb674008205d"},"schema_version":"1.0","source":{"id":"math-ph/0302049","kind":"arxiv","version":2}},"canonical_sha256":"e1daabea20a77b896601fd06e72d0f2673a54cce584777806703cf2c0228b82f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1daabea20a77b896601fd06e72d0f2673a54cce584777806703cf2c0228b82f","first_computed_at":"2026-07-04T15:13:53.611069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:13:53.611069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5PVNOwT/5fi5PD8v99CvUUW7PSZUpEE+vABHijyovMzWrw2sMafW/UjLi1ilDbPb7kTJHs5KGYEb+m06tc0XBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:13:53.611479Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0302049","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dcae32577ab23fb44e4741f3246efb0ba523281c90bc8163e5b8654a12386cd","sha256:3efeeed28e762688e157b428352f0cb85e8608b1b09cb91b1ea67d56d4fa9501"],"state_sha256":"096ac4027da1244ef141aa0d14ff45e7ae6f2070aba40d31a4386b90392bdee5"}