{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NYI4YM57NZT7LO7KTMZDYEBS5K","short_pith_number":"pith:NYI4YM57","canonical_record":{"source":{"id":"0908.3383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-08-24T15:18:41Z","cross_cats_sorted":["cs.CV","math.IT"],"title_canon_sha256":"96f5b0d12718d46288602414c9018b1e4065ba262a93c94a6bb8385d17b73a3f","abstract_canon_sha256":"4f8deb843e4da59f7979fa2990a7d87f4ed7292167c54c928c5e6fbc3db0d10d"},"schema_version":"1.0"},"canonical_sha256":"6e11cc33bf6e67f5bbea9b323c1032ea8ee2b2c5d562a356155e50ccc4697240","source":{"kind":"arxiv","id":"0908.3383","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3383","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3383v1","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3383","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"NYI4YM57NZT7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"NYI4YM57NZT7LO7K","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"NYI4YM57","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NYI4YM57NZT7LO7KTMZDYEBS5K","target":"record","payload":{"canonical_record":{"source":{"id":"0908.3383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-08-24T15:18:41Z","cross_cats_sorted":["cs.CV","math.IT"],"title_canon_sha256":"96f5b0d12718d46288602414c9018b1e4065ba262a93c94a6bb8385d17b73a3f","abstract_canon_sha256":"4f8deb843e4da59f7979fa2990a7d87f4ed7292167c54c928c5e6fbc3db0d10d"},"schema_version":"1.0"},"canonical_sha256":"6e11cc33bf6e67f5bbea9b323c1032ea8ee2b2c5d562a356155e50ccc4697240","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:57.776720Z","signature_b64":"C97j+NMZAlk5FH+Cv4qagrmRqGvUC4KkpVhkkWGrV4Bk0XM5gqQn+8Fi9LpbGn+ckdb+3Cp5AkuiskLQN+mVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e11cc33bf6e67f5bbea9b323c1032ea8ee2b2c5d562a356155e50ccc4697240","last_reissued_at":"2026-05-18T03:17:57.775926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:57.775926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.3383","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":"2026-05-18T03:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5kUfIXjQG4YPl/0sT6FP9xksQYLrnBmUUpLSjo8offxTBx5TviW+U7EszZr3rMXgi+dsLbZciQDwgj8QOurBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:52:33.812633Z"},"content_sha256":"a1b54e596207ac907ec6c55b880445e3a90e1467abd161d08bc01fd1b84a2f7e","schema_version":"1.0","event_id":"sha256:a1b54e596207ac907ec6c55b880445e3a90e1467abd161d08bc01fd1b84a2f7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NYI4YM57NZT7LO7KTMZDYEBS5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Shiftability of Dual-Tree Complex Wavelet Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.IT"],"primary_cat":"cs.IT","authors_text":"Kunal Narayan Chaudhury, Michael Unser","submitted_at":"2009-08-24T15:18:41Z","abstract_excerpt":"The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a direct explanation for the improvement in the shift-invariance. The representation is based on the shifting action of the group of fractional Hilbert transform (fHT) operators, which extends the notion of arbitrary phase-shifts from sinusoids to finite-energy signals (wavelets in particular). In particular, we characterize the shiftability of the DT-CWT in ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3383","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":"2026-05-18T03:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wUt81br4pnBVQihJ1hkQKu6F8foOWDnRdOvRI1f1LpBGnu50OU8mnnANxchvcMqDYwoYWNSg2KS7AQe9oYaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:52:33.813340Z"},"content_sha256":"323ae57d4b4a2a233e64e2551d515b076fc14a0459f3e9b01a87ccdc0e17b338","schema_version":"1.0","event_id":"sha256:323ae57d4b4a2a233e64e2551d515b076fc14a0459f3e9b01a87ccdc0e17b338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/bundle.json","state_url":"https://pith.science/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/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":"2026-06-06T06:52:33Z","links":{"resolver":"https://pith.science/pith/NYI4YM57NZT7LO7KTMZDYEBS5K","bundle":"https://pith.science/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/bundle.json","state":"https://pith.science/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYI4YM57NZT7LO7KTMZDYEBS5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NYI4YM57NZT7LO7KTMZDYEBS5K","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":"4f8deb843e4da59f7979fa2990a7d87f4ed7292167c54c928c5e6fbc3db0d10d","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-08-24T15:18:41Z","title_canon_sha256":"96f5b0d12718d46288602414c9018b1e4065ba262a93c94a6bb8385d17b73a3f"},"schema_version":"1.0","source":{"id":"0908.3383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3383","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3383v1","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3383","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"NYI4YM57NZT7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"NYI4YM57NZT7LO7K","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"NYI4YM57","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:323ae57d4b4a2a233e64e2551d515b076fc14a0459f3e9b01a87ccdc0e17b338","target":"graph","created_at":"2026-05-18T03:17:57Z","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":"The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a direct explanation for the improvement in the shift-invariance. The representation is based on the shifting action of the group of fractional Hilbert transform (fHT) operators, which extends the notion of arbitrary phase-shifts from sinusoids to finite-energy signals (wavelets in particular). In particular, we characterize the shiftability of the DT-CWT in ter","authors_text":"Kunal Narayan Chaudhury, Michael Unser","cross_cats":["cs.CV","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-08-24T15:18:41Z","title":"On the Shiftability of Dual-Tree Complex Wavelet Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3383","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:a1b54e596207ac907ec6c55b880445e3a90e1467abd161d08bc01fd1b84a2f7e","target":"record","created_at":"2026-05-18T03:17:57Z","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":"4f8deb843e4da59f7979fa2990a7d87f4ed7292167c54c928c5e6fbc3db0d10d","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-08-24T15:18:41Z","title_canon_sha256":"96f5b0d12718d46288602414c9018b1e4065ba262a93c94a6bb8385d17b73a3f"},"schema_version":"1.0","source":{"id":"0908.3383","kind":"arxiv","version":1}},"canonical_sha256":"6e11cc33bf6e67f5bbea9b323c1032ea8ee2b2c5d562a356155e50ccc4697240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e11cc33bf6e67f5bbea9b323c1032ea8ee2b2c5d562a356155e50ccc4697240","first_computed_at":"2026-05-18T03:17:57.775926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:57.775926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C97j+NMZAlk5FH+Cv4qagrmRqGvUC4KkpVhkkWGrV4Bk0XM5gqQn+8Fi9LpbGn+ckdb+3Cp5AkuiskLQN+mVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:57.776720Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1b54e596207ac907ec6c55b880445e3a90e1467abd161d08bc01fd1b84a2f7e","sha256:323ae57d4b4a2a233e64e2551d515b076fc14a0459f3e9b01a87ccdc0e17b338"],"state_sha256":"8827acb3ce411b8237a41600f634b8648177fd4adc42c1fd9bf464ae9bc87186"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jPkUuetafVMExKK5ToFdCxdEHndy7E2hRcF9oWNjyS54JoMHJe+ys1wAFFHTRYUqBbh5YVGVyBIsOmQYP/uCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:52:33.817535Z","bundle_sha256":"f1400d86d2465959b0e60eb814c5aac5eba97f27b63d262f37581ea8a01b268b"}}