{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IWF2NHIOW3MVEU2ZU7XHQ6QC7O","short_pith_number":"pith:IWF2NHIO","canonical_record":{"source":{"id":"1402.3109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-13T12:32:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1b0bce67ee393b22b1862a6405297a335a24592e080e2970e8f889bad881fe25","abstract_canon_sha256":"92f2b1a179f433af2d81487ed2621e6588b8f92321852456e5028ab79b68fab5"},"schema_version":"1.0"},"canonical_sha256":"458ba69d0eb6d9525359a7ee787a02fba634294b4f88dc0f409fd420e3e73fd2","source":{"kind":"arxiv","id":"1402.3109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3109","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3109v1","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3109","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"IWF2NHIOW3MV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IWF2NHIOW3MVEU2Z","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IWF2NHIO","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IWF2NHIOW3MVEU2ZU7XHQ6QC7O","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-13T12:32:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1b0bce67ee393b22b1862a6405297a335a24592e080e2970e8f889bad881fe25","abstract_canon_sha256":"92f2b1a179f433af2d81487ed2621e6588b8f92321852456e5028ab79b68fab5"},"schema_version":"1.0"},"canonical_sha256":"458ba69d0eb6d9525359a7ee787a02fba634294b4f88dc0f409fd420e3e73fd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:37.201487Z","signature_b64":"g43u2CXHoy9tmi3vK0ACyijXk8123/TSt9vLPfIXFkcC3hGwydN6H/gABlWXvbeE/FoZhEs1WvasYN2md58qAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"458ba69d0eb6d9525359a7ee787a02fba634294b4f88dc0f409fd420e3e73fd2","last_reissued_at":"2026-05-18T02:42:37.200617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:37.200617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3109","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":"2026-05-18T02:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2dzQni0ylM2YchwwPb35JGppMv7pmGyjRNVUhw9sIuRMKNSbN91c+N7unwJppKgD6Mwpo/Po861xfDq1CaDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:49:13.009895Z"},"content_sha256":"4f15c46cb355554cb1e4d9df4324fe70226dc9924acf94a0e02a2424122f0968","schema_version":"1.0","event_id":"sha256:4f15c46cb355554cb1e4d9df4324fe70226dc9924acf94a0e02a2424122f0968"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IWF2NHIOW3MVEU2ZU7XHQ6QC7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Quaternionic Affine Group and Related Continuous Wavelet Transforms on Complex and Quaternionic Hilbert Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"K. Thirulogasanthar, S. Twareque Ali","submitted_at":"2014-02-13T12:32:26Z","abstract_excerpt":"By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its unitary irreducible representations. These representations are constructed both on a complex and a quaternionic Hilbert space. As in the real and complex cases, the representations for the quaternionic group also turn out to be square-integrable. Using these representations we constrct quaternionic wavelets and continuous wavelet transforms on both the complex and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3109","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":"2026-05-18T02:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bW/m8lQsFJefYsZ4r3mEn29RAj1E37EyccN0CjvyGd1r2NYlGzgo/c6gpciAdptEfKJCEEP49b+UnOu/L9MXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:49:13.010235Z"},"content_sha256":"94bbbf105a25f7285f872b6e982db1833619529d7f22c89cdbccda8287441fae","schema_version":"1.0","event_id":"sha256:94bbbf105a25f7285f872b6e982db1833619529d7f22c89cdbccda8287441fae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/bundle.json","state_url":"https://pith.science/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/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":"2026-06-28T09:49:13Z","links":{"resolver":"https://pith.science/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O","bundle":"https://pith.science/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/bundle.json","state":"https://pith.science/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWF2NHIOW3MVEU2ZU7XHQ6QC7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IWF2NHIOW3MVEU2ZU7XHQ6QC7O","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":"92f2b1a179f433af2d81487ed2621e6588b8f92321852456e5028ab79b68fab5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-13T12:32:26Z","title_canon_sha256":"1b0bce67ee393b22b1862a6405297a335a24592e080e2970e8f889bad881fe25"},"schema_version":"1.0","source":{"id":"1402.3109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3109","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3109v1","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3109","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"IWF2NHIOW3MV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IWF2NHIOW3MVEU2Z","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IWF2NHIO","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:94bbbf105a25f7285f872b6e982db1833619529d7f22c89cdbccda8287441fae","target":"graph","created_at":"2026-05-18T02:42:37Z","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":"By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its unitary irreducible representations. These representations are constructed both on a complex and a quaternionic Hilbert space. As in the real and complex cases, the representations for the quaternionic group also turn out to be square-integrable. Using these representations we constrct quaternionic wavelets and continuous wavelet transforms on both the complex and","authors_text":"K. Thirulogasanthar, S. Twareque Ali","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-13T12:32:26Z","title":"The Quaternionic Affine Group and Related Continuous Wavelet Transforms on Complex and Quaternionic Hilbert Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3109","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":"sha256:4f15c46cb355554cb1e4d9df4324fe70226dc9924acf94a0e02a2424122f0968","target":"record","created_at":"2026-05-18T02:42:37Z","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":"92f2b1a179f433af2d81487ed2621e6588b8f92321852456e5028ab79b68fab5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-13T12:32:26Z","title_canon_sha256":"1b0bce67ee393b22b1862a6405297a335a24592e080e2970e8f889bad881fe25"},"schema_version":"1.0","source":{"id":"1402.3109","kind":"arxiv","version":1}},"canonical_sha256":"458ba69d0eb6d9525359a7ee787a02fba634294b4f88dc0f409fd420e3e73fd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458ba69d0eb6d9525359a7ee787a02fba634294b4f88dc0f409fd420e3e73fd2","first_computed_at":"2026-05-18T02:42:37.200617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:37.200617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g43u2CXHoy9tmi3vK0ACyijXk8123/TSt9vLPfIXFkcC3hGwydN6H/gABlWXvbeE/FoZhEs1WvasYN2md58qAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:37.201487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f15c46cb355554cb1e4d9df4324fe70226dc9924acf94a0e02a2424122f0968","sha256:94bbbf105a25f7285f872b6e982db1833619529d7f22c89cdbccda8287441fae"],"state_sha256":"c3baf30d002ff7b3cf082539f27fa14cd4df222d57a8683410072965ec0a6e9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pPybTcGvYjas9T8Ch30N2EVT3qKkifknesf0tzOTZooxK7PNmEkYeIgMK3gDaiVBaNULIrPnMR98prbgvlklCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:49:13.012212Z","bundle_sha256":"634c2f76ce33b567005c83cd32a0803194c8c5ee117c2b6dd8d2f59df2119ccb"}}