{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KGPBHAAQPG2745NB32GOV2UWIL","short_pith_number":"pith:KGPBHAAQ","schema_version":"1.0","canonical_sha256":"519e13801079b5fe75a1de8ceaea9642f8ed23bea88523d7f4f1cec9abb0f8e7","source":{"kind":"arxiv","id":"1512.00650","version":1},"attestation_state":"computed","paper":{"title":"Model sets, almost periodic patterns, uniform density and linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.MG"],"primary_cat":"math.DS","authors_text":"Pierre-Antoine Guih\\'eneuf","submitted_at":"2015-12-02T11:09:25Z","abstract_excerpt":"This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are stable under discretizations of linear maps."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.00650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-02T11:09:25Z","cross_cats_sorted":["cs.DM","math.MG"],"title_canon_sha256":"16ffc1bbb921707900141eb1edc3517975e7da01692822044b71470d57b5ea56","abstract_canon_sha256":"f505b2b74db9f0de45b01e71804bf6f11bf62301a962ebe47a28a9bfc4dd61ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:25.468631Z","signature_b64":"+NlPZjNvWKJupchbvuCOV0afcgC6CsuBbgzG5YDdzT3xSKHPE6C13zk++d9PTjF3fgv4aRtL/7d/ZexeFLNjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"519e13801079b5fe75a1de8ceaea9642f8ed23bea88523d7f4f1cec9abb0f8e7","last_reissued_at":"2026-05-18T01:25:25.468214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:25.468214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Model sets, almost periodic patterns, uniform density and linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.MG"],"primary_cat":"math.DS","authors_text":"Pierre-Antoine Guih\\'eneuf","submitted_at":"2015-12-02T11:09:25Z","abstract_excerpt":"This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are stable under discretizations of linear maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00650","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.00650","created_at":"2026-05-18T01:25:25.468269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00650v1","created_at":"2026-05-18T01:25:25.468269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00650","created_at":"2026-05-18T01:25:25.468269+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGPBHAAQPG27","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGPBHAAQPG2745NB","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGPBHAAQ","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL","json":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL.json","graph_json":"https://pith.science/api/pith-number/KGPBHAAQPG2745NB32GOV2UWIL/graph.json","events_json":"https://pith.science/api/pith-number/KGPBHAAQPG2745NB32GOV2UWIL/events.json","paper":"https://pith.science/paper/KGPBHAAQ"},"agent_actions":{"view_html":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL","download_json":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL.json","view_paper":"https://pith.science/paper/KGPBHAAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00650&json=true","fetch_graph":"https://pith.science/api/pith-number/KGPBHAAQPG2745NB32GOV2UWIL/graph.json","fetch_events":"https://pith.science/api/pith-number/KGPBHAAQPG2745NB32GOV2UWIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL/action/storage_attestation","attest_author":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL/action/author_attestation","sign_citation":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL/action/citation_signature","submit_replication":"https://pith.science/pith/KGPBHAAQPG2745NB32GOV2UWIL/action/replication_record"}},"created_at":"2026-05-18T01:25:25.468269+00:00","updated_at":"2026-05-18T01:25:25.468269+00:00"}