{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VKMFAXCPGYEPKGNC4N4BOGT2TD","short_pith_number":"pith:VKMFAXCP","canonical_record":{"source":{"id":"1903.00790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-03-02T23:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"388f8a26982eccf1b37eaff8ce8d485105ff7dd12b33fd961fcfbcd20319c885","abstract_canon_sha256":"1ef289f00acdb71c568655ba012cf39efbc72e32dce6cdc8de15bb80d017b6fc"},"schema_version":"1.0"},"canonical_sha256":"aa98505c4f3608f519a2e378171a7a98c7596c211defbb4c6c6aede81cfeae87","source":{"kind":"arxiv","id":"1903.00790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00790","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00790v1","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00790","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"VKMFAXCPGYEP","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VKMFAXCPGYEPKGNC","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VKMFAXCP","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VKMFAXCPGYEPKGNC4N4BOGT2TD","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-03-02T23:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"388f8a26982eccf1b37eaff8ce8d485105ff7dd12b33fd961fcfbcd20319c885","abstract_canon_sha256":"1ef289f00acdb71c568655ba012cf39efbc72e32dce6cdc8de15bb80d017b6fc"},"schema_version":"1.0"},"canonical_sha256":"aa98505c4f3608f519a2e378171a7a98c7596c211defbb4c6c6aede81cfeae87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:13.256803Z","signature_b64":"E1cUx4tfc5qKb0t4Iy0xeMwDWSl4Xvy7S0iF7l3+9j3X7ehP+7GoXkWpi1FHBIDkKXdVuExQI7KT0AfC3avCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa98505c4f3608f519a2e378171a7a98c7596c211defbb4c6c6aede81cfeae87","last_reissued_at":"2026-05-17T23:52:13.255979Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:13.255979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00790","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":"2026-05-17T23:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+9FN1La61u8JM1EDwhxKqS4dWuIxgvFJ6Modu/fOdi6m/ewgQH42wazSLGM75cidF099Nvh7DI4NG4v78cqICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:41:51.806253Z"},"content_sha256":"d245fef7618d1beb900c19d173df8120ec762fc5c31bbe635ecf49be0ceadc8f","schema_version":"1.0","event_id":"sha256:d245fef7618d1beb900c19d173df8120ec762fc5c31bbe635ecf49be0ceadc8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VKMFAXCPGYEPKGNC4N4BOGT2TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-decimated Quaternion Wavelet Spectral Tools with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Brani Vidakovic, Taewoon Kong","submitted_at":"2019-03-02T23:31:38Z","abstract_excerpt":"Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for use in machine learning tasks. Since quaternionic algebra is an extension of complex algebra, quaternion wavelets bring redundancy in the components that proves beneficial in wavelet based tasks. Specifically, the wavelet coefficients in the decomposition are quaternion-valued numbers that define the modulus and three phases.\n  The novelty of this paper is de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00790","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":"2026-05-17T23:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYT9F+tnTDmiPFWCiZu47iTEzNb53+SGTLuF2PEi7rSEII9itilnjJJbK4i27Fwsh6NJzOMOB3ovuktxetRkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:41:51.806615Z"},"content_sha256":"a5659c9dea876423d6b36a0c98dabd46f716756b3a92e17144eaa9da24ba7ed2","schema_version":"1.0","event_id":"sha256:a5659c9dea876423d6b36a0c98dabd46f716756b3a92e17144eaa9da24ba7ed2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/bundle.json","state_url":"https://pith.science/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/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":"2026-07-03T08:41:51Z","links":{"resolver":"https://pith.science/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD","bundle":"https://pith.science/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/bundle.json","state":"https://pith.science/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKMFAXCPGYEPKGNC4N4BOGT2TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VKMFAXCPGYEPKGNC4N4BOGT2TD","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":"1ef289f00acdb71c568655ba012cf39efbc72e32dce6cdc8de15bb80d017b6fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-03-02T23:31:38Z","title_canon_sha256":"388f8a26982eccf1b37eaff8ce8d485105ff7dd12b33fd961fcfbcd20319c885"},"schema_version":"1.0","source":{"id":"1903.00790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00790","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00790v1","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00790","created_at":"2026-05-17T23:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"VKMFAXCPGYEP","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VKMFAXCPGYEPKGNC","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VKMFAXCP","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:a5659c9dea876423d6b36a0c98dabd46f716756b3a92e17144eaa9da24ba7ed2","target":"graph","created_at":"2026-05-17T23:52:13Z","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":"Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for use in machine learning tasks. Since quaternionic algebra is an extension of complex algebra, quaternion wavelets bring redundancy in the components that proves beneficial in wavelet based tasks. Specifically, the wavelet coefficients in the decomposition are quaternion-valued numbers that define the modulus and three phases.\n  The novelty of this paper is de","authors_text":"Brani Vidakovic, Taewoon Kong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-03-02T23:31:38Z","title":"Non-decimated Quaternion Wavelet Spectral Tools with Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00790","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:d245fef7618d1beb900c19d173df8120ec762fc5c31bbe635ecf49be0ceadc8f","target":"record","created_at":"2026-05-17T23:52:13Z","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":"1ef289f00acdb71c568655ba012cf39efbc72e32dce6cdc8de15bb80d017b6fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-03-02T23:31:38Z","title_canon_sha256":"388f8a26982eccf1b37eaff8ce8d485105ff7dd12b33fd961fcfbcd20319c885"},"schema_version":"1.0","source":{"id":"1903.00790","kind":"arxiv","version":1}},"canonical_sha256":"aa98505c4f3608f519a2e378171a7a98c7596c211defbb4c6c6aede81cfeae87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa98505c4f3608f519a2e378171a7a98c7596c211defbb4c6c6aede81cfeae87","first_computed_at":"2026-05-17T23:52:13.255979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:13.255979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E1cUx4tfc5qKb0t4Iy0xeMwDWSl4Xvy7S0iF7l3+9j3X7ehP+7GoXkWpi1FHBIDkKXdVuExQI7KT0AfC3avCCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:13.256803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d245fef7618d1beb900c19d173df8120ec762fc5c31bbe635ecf49be0ceadc8f","sha256:a5659c9dea876423d6b36a0c98dabd46f716756b3a92e17144eaa9da24ba7ed2"],"state_sha256":"ac872ae0e46d37665e4a1aadb41e5e8faa4021bcea8bdfb1c3d513be195607cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emuHkQnxCpHm94S71KXBH4lfDuTU/uGPikW1yuJbcWb/pwZiuIyj0GO97eqlW/bFMukeWrfS/o+KMfLS/BcCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T08:41:51.808527Z","bundle_sha256":"28b63ae2a9b27505d72e32af739deb1dbed8b54884e978134c8f4c9688a9a1be"}}