{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LOFHPUJPICO6UQNCIHY7F4DPGR","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":"153d62b5672e48b73d95360b3b00163a2b94ac0f594fa98b010b23dcc5784ba6","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-27T16:35:41Z","title_canon_sha256":"28f464f9daa7cb2c7b51a9061d47f158b77556e542a02bd73270105910bf2c5d"},"schema_version":"1.0","source":{"id":"1801.10026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10026","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10026v2","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10026","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"pith_short_12","alias_value":"LOFHPUJPICO6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LOFHPUJPICO6UQNC","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LOFHPUJP","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:e01487fc6772654685bc30ca66a488ed173667e74f63d6b58b04ffac4d975c26","target":"graph","created_at":"2026-05-17T23:53:09Z","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"},"paper":{"abstract_excerpt":"We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the connection between model sets and almost periodic functions, as well as Poisson's summations formula for model sets we develop a form of a bracket product that plays a central role in our approach. Furthermore, we show that, if a Gabor system for a model set admits a dual which is of Gabor type, then the density of the model set has to be greater than one.","authors_text":"Ewa Matusiak","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-27T16:35:41Z","title":"Gabor frames for model sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10026","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":"sha256:6764d85f8643b834bb378e83e093f773531403f69bddf60ea02915ddb59a36d2","target":"record","created_at":"2026-05-17T23:53:09Z","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":"153d62b5672e48b73d95360b3b00163a2b94ac0f594fa98b010b23dcc5784ba6","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-27T16:35:41Z","title_canon_sha256":"28f464f9daa7cb2c7b51a9061d47f158b77556e542a02bd73270105910bf2c5d"},"schema_version":"1.0","source":{"id":"1801.10026","kind":"arxiv","version":2}},"canonical_sha256":"5b8a77d12f409dea41a241f1f2f06f347d689d37c6fe96ac536115483aa8c346","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b8a77d12f409dea41a241f1f2f06f347d689d37c6fe96ac536115483aa8c346","first_computed_at":"2026-05-17T23:53:09.715427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:09.715427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WSBeoy+CbGEU4BLrVUxlcs2jDy07q34BJ0PGgGTQSHhglREnBnj6GdKAiIj/cbjRLkppttuKxtNfru0UmBEaBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:09.715948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6764d85f8643b834bb378e83e093f773531403f69bddf60ea02915ddb59a36d2","sha256:e01487fc6772654685bc30ca66a488ed173667e74f63d6b58b04ffac4d975c26"],"state_sha256":"7de400efc17b6cf4a2304d131c885c37768b5c5c445bd09858fc8e134e4a14c5"}