{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O3YHT4UT7LT6KQJTTI7VPH6FF3","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":"3f8ece2ec4b053536eccf04a49aa521d50e09328afef6623d2cd83773c8d7c87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-08T13:16:45Z","title_canon_sha256":"96e46cdb2707ae114c521db2450ac6b89ca7de3a72f34d6e3fd52519196d1238"},"schema_version":"1.0","source":{"id":"1908.03053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03053","created_at":"2026-07-05T04:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03053v2","created_at":"2026-07-05T04:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03053","created_at":"2026-07-05T04:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"O3YHT4UT7LT6","created_at":"2026-07-05T04:19:28Z"},{"alias_kind":"pith_short_16","alias_value":"O3YHT4UT7LT6KQJT","created_at":"2026-07-05T04:19:28Z"},{"alias_kind":"pith_short_8","alias_value":"O3YHT4UT","created_at":"2026-07-05T04:19:28Z"}],"graph_snapshots":[{"event_id":"sha256:94245c26b66142cd10b3e7de73802e98087355a253116d410ddb2fde099dce0b","target":"graph","created_at":"2026-07-05T04:19:28Z","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/1908.03053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(\\pi, \\mathcal{H}_{\\pi})$ be an irreducible, square-integrable representation modulo the center $Z(N)$ of $N$ on a Hilbert space $\\mathcal{H}_{\\pi}$ of formal dimension $d_\\pi $. If $g \\in \\mathcal{H}_{\\pi}$ is an integrable vector and the set $\\{ \\pi (\\lambda )g : \\lambda \\in \\Lambda \\}$ for a discrete subset $\\Lambda \\subseteq N / Z(N)$ forms a frame for $\\mathcal{H}_{\\","authors_text":"David Rottensteiner, Jordy Timo van Velthoven, Jos\\'e Luis Romero, Karlheinz Gr\\\"ochenig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-08T13:16:45Z","title":"Balian-Low type theorems on homogeneous groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03053","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:daac91599c210645776393fc269b47b290a28e5f23063345cc2c35b0efb2ff42","target":"record","created_at":"2026-07-05T04:19:28Z","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":"3f8ece2ec4b053536eccf04a49aa521d50e09328afef6623d2cd83773c8d7c87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-08T13:16:45Z","title_canon_sha256":"96e46cdb2707ae114c521db2450ac6b89ca7de3a72f34d6e3fd52519196d1238"},"schema_version":"1.0","source":{"id":"1908.03053","kind":"arxiv","version":2}},"canonical_sha256":"76f079f293fae7e541339a3f579fc52ee10add86ac421c7f0288438724c07f36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f079f293fae7e541339a3f579fc52ee10add86ac421c7f0288438724c07f36","first_computed_at":"2026-07-05T04:19:28.592916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:19:28.592916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bzHgDrJXu33M/2CTGOF4oOK/JoFh5z/fOQ3zJN5q5y2a8XNyWo806uCIPFxm5378HdBtTwCkmAB7sCnI51VDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:19:28.593473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daac91599c210645776393fc269b47b290a28e5f23063345cc2c35b0efb2ff42","sha256:94245c26b66142cd10b3e7de73802e98087355a253116d410ddb2fde099dce0b"],"state_sha256":"fea2800483c306ad1b3148c379f69f2deb1f113d0da171438c6c81dabc746eae"}