{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KHXVHQB75PGW2RLKM5UEBJE5TA","short_pith_number":"pith:KHXVHQB7","canonical_record":{"source":{"id":"1301.1802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T10:28:51Z","cross_cats_sorted":[],"title_canon_sha256":"12555942f8aa1fce3f0ce92e3efdf617f80c30edd60e83bcaa468a57bcf9710c","abstract_canon_sha256":"c2336585db3f4292c3085b6620eb7cdce8b7b0f3b9c2e60741568486209748d4"},"schema_version":"1.0"},"canonical_sha256":"51ef53c03febcd6d456a676840a49d980a7bfb7e19c2c89ae05f2e84fa022eae","source":{"kind":"arxiv","id":"1301.1802","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1802","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1802v1","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1802","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"KHXVHQB75PGW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KHXVHQB75PGW2RLK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KHXVHQB7","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KHXVHQB75PGW2RLKM5UEBJE5TA","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T10:28:51Z","cross_cats_sorted":[],"title_canon_sha256":"12555942f8aa1fce3f0ce92e3efdf617f80c30edd60e83bcaa468a57bcf9710c","abstract_canon_sha256":"c2336585db3f4292c3085b6620eb7cdce8b7b0f3b9c2e60741568486209748d4"},"schema_version":"1.0"},"canonical_sha256":"51ef53c03febcd6d456a676840a49d980a7bfb7e19c2c89ae05f2e84fa022eae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:55.914010Z","signature_b64":"Mi2LSXh6ZgtcHjP34cyRKq0nf0CfUlqOQFFWLIUY/INXUOW2Z6DH03FlTzZrREsZV4oqpoCA8LZlBpt4aFrpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51ef53c03febcd6d456a676840a49d980a7bfb7e19c2c89ae05f2e84fa022eae","last_reissued_at":"2026-05-18T03:36:55.913424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:55.913424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1802","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUOoeI1ZYAu0vWWZ6+GmukYGbHIsm4eFjtlAcVK7IvktlYyGyQZQDNjxIkejResupoUf0EhfPsV55Tq2kOjwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:53:40.953748Z"},"content_sha256":"c0607e9743dee467943be3decd81436d7c8b2b11a68a484e6e07a88fb0d6661c","schema_version":"1.0","event_id":"sha256:c0607e9743dee467943be3decd81436d7c8b2b11a68a484e6e07a88fb0d6661c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KHXVHQB75PGW2RLKM5UEBJE5TA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonstationary Gabor Frames - Approximately Dual Frames and Reconstruction Errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ewa Matusiak, Monika D\\\"orfler","submitted_at":"2013-01-09T10:28:51Z","abstract_excerpt":"Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a complete lattice structure, perfect reconstruction is in general not feasible from coefficients obtained from nonstationary Gabor frames. In this paper it is shown that for nonstationary Gabor frames that are related to some known frames for which dual frames can be computed, good approximate reconstruction can be achieved by resorting to approximately dual fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1802","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CBHw7sfRN7KN+n5Xu48TKkQU9ILwZ8V7CexIyAqIKSW5M/YKUa4s2kn0CrNk+nO0s1bQUGfVHoXNf0vvzTcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:53:40.954101Z"},"content_sha256":"d98b7d2f22550570bc7a07f4b7eaa850d324826045d8178cde95dd1a9f799449","schema_version":"1.0","event_id":"sha256:d98b7d2f22550570bc7a07f4b7eaa850d324826045d8178cde95dd1a9f799449"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/bundle.json","state_url":"https://pith.science/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T04:53:40Z","links":{"resolver":"https://pith.science/pith/KHXVHQB75PGW2RLKM5UEBJE5TA","bundle":"https://pith.science/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/bundle.json","state":"https://pith.science/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHXVHQB75PGW2RLKM5UEBJE5TA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KHXVHQB75PGW2RLKM5UEBJE5TA","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":"c2336585db3f4292c3085b6620eb7cdce8b7b0f3b9c2e60741568486209748d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T10:28:51Z","title_canon_sha256":"12555942f8aa1fce3f0ce92e3efdf617f80c30edd60e83bcaa468a57bcf9710c"},"schema_version":"1.0","source":{"id":"1301.1802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1802","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1802v1","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1802","created_at":"2026-05-18T03:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"KHXVHQB75PGW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KHXVHQB75PGW2RLK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KHXVHQB7","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:d98b7d2f22550570bc7a07f4b7eaa850d324826045d8178cde95dd1a9f799449","target":"graph","created_at":"2026-05-18T03:36:55Z","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":"Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a complete lattice structure, perfect reconstruction is in general not feasible from coefficients obtained from nonstationary Gabor frames. In this paper it is shown that for nonstationary Gabor frames that are related to some known frames for which dual frames can be computed, good approximate reconstruction can be achieved by resorting to approximately dual fr","authors_text":"Ewa Matusiak, Monika D\\\"orfler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T10:28:51Z","title":"Nonstationary Gabor Frames - Approximately Dual Frames and Reconstruction Errors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1802","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:c0607e9743dee467943be3decd81436d7c8b2b11a68a484e6e07a88fb0d6661c","target":"record","created_at":"2026-05-18T03:36:55Z","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":"c2336585db3f4292c3085b6620eb7cdce8b7b0f3b9c2e60741568486209748d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T10:28:51Z","title_canon_sha256":"12555942f8aa1fce3f0ce92e3efdf617f80c30edd60e83bcaa468a57bcf9710c"},"schema_version":"1.0","source":{"id":"1301.1802","kind":"arxiv","version":1}},"canonical_sha256":"51ef53c03febcd6d456a676840a49d980a7bfb7e19c2c89ae05f2e84fa022eae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51ef53c03febcd6d456a676840a49d980a7bfb7e19c2c89ae05f2e84fa022eae","first_computed_at":"2026-05-18T03:36:55.913424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:55.913424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mi2LSXh6ZgtcHjP34cyRKq0nf0CfUlqOQFFWLIUY/INXUOW2Z6DH03FlTzZrREsZV4oqpoCA8LZlBpt4aFrpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:55.914010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0607e9743dee467943be3decd81436d7c8b2b11a68a484e6e07a88fb0d6661c","sha256:d98b7d2f22550570bc7a07f4b7eaa850d324826045d8178cde95dd1a9f799449"],"state_sha256":"2c4b9d1c5cc90925fa13cb41bbab6c944e186c577a8913d408b2e4ffede5069b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/4dprQZRRrfi3d5NMOMNcX4L6LUINhAW6UCzX6Te6YwSDGCXDkHXlQgmuhGVyrL55lU3BoeBIL0FWPoakiUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:53:40.956023Z","bundle_sha256":"652de9e2b7305dd8043098f3026c9638d99ecf342b510bef26effb7696a5e4d8"}}