{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AESMT22XXH5M3F4NSXI4VRKGD6","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":"c41f3f53deef5d393aee13b828c7d8e736e04497f6b48d627892c67b2670a4a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-29T06:31:56Z","title_canon_sha256":"07e9c33b952f7ee589c60fdf3cff79784ce762d8b58e1b4edb3c3295afe1f5f5"},"schema_version":"1.0","source":{"id":"1210.0084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0084","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0084v1","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0084","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"AESMT22XXH5M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AESMT22XXH5M3F4N","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AESMT22X","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0a4375c37374798cb6676d1eaf4bbf54825ef25f7654a7071dc813a026540f09","target":"graph","created_at":"2026-05-18T03:25:34Z","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":"Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal transforms allowing for non-uniform and in particular non-linear frequency resolution. Non-uniformity in frequency is realized by applying nonstationary Gabor frames with adaptivity in the frequency domain. The realization of a perfectly invertible constant-Q transform is described in detail. To achieve real-time processing, independent of signal length, sli","authors_text":"Gino Angelo Velasco, Monika D\\\"orfler, Nicki Holighaus, Thomas Grill","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-29T06:31:56Z","title":"A framework for invertible, real-time constant-Q transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0084","kind":"arxiv","version":1},"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:c8f01f47c0cdbd13dd366b7d60f45a9a58f82a9d52c2b1933a016127573da71d","target":"record","created_at":"2026-05-18T03:25:34Z","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":"c41f3f53deef5d393aee13b828c7d8e736e04497f6b48d627892c67b2670a4a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-29T06:31:56Z","title_canon_sha256":"07e9c33b952f7ee589c60fdf3cff79784ce762d8b58e1b4edb3c3295afe1f5f5"},"schema_version":"1.0","source":{"id":"1210.0084","kind":"arxiv","version":1}},"canonical_sha256":"0124c9eb57b9facd978d95d1cac5461f871e83696bab949ced1f13d7bad6e2a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0124c9eb57b9facd978d95d1cac5461f871e83696bab949ced1f13d7bad6e2a8","first_computed_at":"2026-05-18T03:25:34.972287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:34.972287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9j08Y99HO8ejQUHz4iGq5JZVoJTTKzhvOLZnTsWtPN9SyCWoFjZrx9ngmYSNRTwTcWrsrIxDEXZHl2JgHu/ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:34.972767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8f01f47c0cdbd13dd366b7d60f45a9a58f82a9d52c2b1933a016127573da71d","sha256:0a4375c37374798cb6676d1eaf4bbf54825ef25f7654a7071dc813a026540f09"],"state_sha256":"b15c80f572d6f291bea3c3c678be715f43c7be67cbe411ffa5be6d1ab7ed2264"}