{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EBHBABTZU2L44XYXSVCZUQRD25","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":"56e1b01861ff17390f29059535c8b8451c5a15c142ec8d402a3e258fa1b5bc50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-28T14:27:15Z","title_canon_sha256":"26d8382d68e62170118976a7813b14a271852c611948202047955874c3d32cca"},"schema_version":"1.0","source":{"id":"1801.09237","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09237","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09237v2","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09237","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"EBHBABTZU2L4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBHBABTZU2L44XYX","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBHBABTZ","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:2479559c9696b8940663c38565b75c3faea0309b1f194ee0cb64324dd3a5641f","target":"graph","created_at":"2026-05-18T00:13:21Z","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 extend the Balian-Low theorem to Gabor subspaces of $L^2(\\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace which is invariant under an additional time-frequency shift, then its generator cannot decay fast simultaneously in time and frequency.","authors_text":"A. Caragea, D. Lee, F. Philipp, G.E. Pfander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-28T14:27:15Z","title":"A Balian-Low Theorem for Subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09237","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":"sha256:06a3b3cdfdd9e37ebee6a6b1a689be8e010a689eb447fff5ab46d57633e2a701","target":"record","created_at":"2026-05-18T00:13:21Z","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":"56e1b01861ff17390f29059535c8b8451c5a15c142ec8d402a3e258fa1b5bc50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-28T14:27:15Z","title_canon_sha256":"26d8382d68e62170118976a7813b14a271852c611948202047955874c3d32cca"},"schema_version":"1.0","source":{"id":"1801.09237","kind":"arxiv","version":2}},"canonical_sha256":"204e100679a697ce5f1795459a4223d740b289da65970d3b93934a41a29c186a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"204e100679a697ce5f1795459a4223d740b289da65970d3b93934a41a29c186a","first_computed_at":"2026-05-18T00:13:21.580887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:21.580887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9KdnEdhNJhWimbX3R8ZAcO2ho3ROhVH7RWFEoM7ksqTU8+pI5/rHXD6ma9InntXyaqtLEf6Kgueg+iWZfLUkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:21.581489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09237","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06a3b3cdfdd9e37ebee6a6b1a689be8e010a689eb447fff5ab46d57633e2a701","sha256:2479559c9696b8940663c38565b75c3faea0309b1f194ee0cb64324dd3a5641f"],"state_sha256":"b0a64b249e570bafe0651287740781ae31da7d463f7ab0bdb05001d64dad565f"}