{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GSOJYV4FYANMEMHSDMRRBAPXYR","short_pith_number":"pith:GSOJYV4F","canonical_record":{"source":{"id":"1404.4298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"02ab40414f94d3bd0688756416307cadf2a7b0d5855e683688965620edc4560f","abstract_canon_sha256":"e7288cbc0d08785fee16308082a7c9a9e43e9820e1ea886acbb8d97924daf3fc"},"schema_version":"1.0"},"canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","source":{"kind":"arxiv","id":"1404.4298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4298","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4298v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4298","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"GSOJYV4FYANM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSOJYV4FYANMEMHS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSOJYV4F","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GSOJYV4FYANMEMHSDMRRBAPXYR","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","cross_cats_sorted":[],"title_canon_sha256":"02ab40414f94d3bd0688756416307cadf2a7b0d5855e683688965620edc4560f","abstract_canon_sha256":"e7288cbc0d08785fee16308082a7c9a9e43e9820e1ea886acbb8d97924daf3fc"},"schema_version":"1.0"},"canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.730836Z","signature_b64":"4I+xMbpzLSguSmODIQ62M5iFX4YfWVF0UdCQS78S5SIJ490nGZCtRdUrgWixie+fZa302Tx4aJGL67IjlSlPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","last_reissued_at":"2026-05-18T02:54:05.730202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.730202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4298","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9j0oz2YD0wTfN9r+lb6Ue5mi556QGNTiypmFX/hmJ1LwZSSxjIytbJ7U7uGRHiYHukVxieNYP6Gr/yvrrg9LBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:22:35.293513Z"},"content_sha256":"b08491f38e29199d28e1e98ef22c4716df844e05d47a29c17c7d4740b12296b5","schema_version":"1.0","event_id":"sha256:b08491f38e29199d28e1e98ef22c4716df844e05d47a29c17c7d4740b12296b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GSOJYV4FYANMEMHSDMRRBAPXYR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wavelet Coorbit Spaces viewed as Decomposition Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Voigtlaender, Hartmut F\\\"uhr","submitted_at":"2014-04-16T16:09:14Z","abstract_excerpt":"In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\\\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation of a semi-direct product $\\mathbb{R}^{d}\\rtimes H$ with suitably chosen dilation group $H$, and certain decomposition spaces $\\mathcal{D}\\left(\\mathcal{Q},L^{p},\\ell_{u}^{q}\\right)$ (essentially as introduced by Feichtinger and Gr\\\"obner), where the localized ,,parts`` of a function are measured in the $\\mathcal{F}L^{p}$-norm.\n  This equivalence is useful in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4298","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsLo3/VFfQxYidsyFIZ9+NWgjAPgtAwhV4zGX7e7Et6/PFgjYxu3sRdsdX6ccGTKHZBnuENkl3F783MayTMGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:22:35.294163Z"},"content_sha256":"b801f169a9750a5dcff99d791cbdd35fd47eb48459f6566e8e6e992bad66fd1e","schema_version":"1.0","event_id":"sha256:b801f169a9750a5dcff99d791cbdd35fd47eb48459f6566e8e6e992bad66fd1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/bundle.json","state_url":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/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":"2026-05-26T01:22:35Z","links":{"resolver":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR","bundle":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/bundle.json","state":"https://pith.science/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSOJYV4FYANMEMHSDMRRBAPXYR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GSOJYV4FYANMEMHSDMRRBAPXYR","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":"e7288cbc0d08785fee16308082a7c9a9e43e9820e1ea886acbb8d97924daf3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","title_canon_sha256":"02ab40414f94d3bd0688756416307cadf2a7b0d5855e683688965620edc4560f"},"schema_version":"1.0","source":{"id":"1404.4298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4298","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4298v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4298","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"GSOJYV4FYANM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSOJYV4FYANMEMHS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSOJYV4F","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b801f169a9750a5dcff99d791cbdd35fd47eb48459f6566e8e6e992bad66fd1e","target":"graph","created_at":"2026-05-18T02:54:05Z","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":"In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\\\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation of a semi-direct product $\\mathbb{R}^{d}\\rtimes H$ with suitably chosen dilation group $H$, and certain decomposition spaces $\\mathcal{D}\\left(\\mathcal{Q},L^{p},\\ell_{u}^{q}\\right)$ (essentially as introduced by Feichtinger and Gr\\\"obner), where the localized ,,parts`` of a function are measured in the $\\mathcal{F}L^{p}$-norm.\n  This equivalence is useful in","authors_text":"Felix Voigtlaender, Hartmut F\\\"uhr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","title":"Wavelet Coorbit Spaces viewed as Decomposition Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4298","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:b08491f38e29199d28e1e98ef22c4716df844e05d47a29c17c7d4740b12296b5","target":"record","created_at":"2026-05-18T02:54:05Z","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":"e7288cbc0d08785fee16308082a7c9a9e43e9820e1ea886acbb8d97924daf3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-16T16:09:14Z","title_canon_sha256":"02ab40414f94d3bd0688756416307cadf2a7b0d5855e683688965620edc4560f"},"schema_version":"1.0","source":{"id":"1404.4298","kind":"arxiv","version":1}},"canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"349c9c5785c01ac230f21b231081f7c4691d57d3e8153e97166213111db67f61","first_computed_at":"2026-05-18T02:54:05.730202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.730202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4I+xMbpzLSguSmODIQ62M5iFX4YfWVF0UdCQS78S5SIJ490nGZCtRdUrgWixie+fZa302Tx4aJGL67IjlSlPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.730836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b08491f38e29199d28e1e98ef22c4716df844e05d47a29c17c7d4740b12296b5","sha256:b801f169a9750a5dcff99d791cbdd35fd47eb48459f6566e8e6e992bad66fd1e"],"state_sha256":"e48fee01060774be18b753e149a0d313f2ce130e74e772176ad72a5d61b8b1a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eBE+ZxM15PnG50WiYKF6c2k2NQ+NNV1C60R+uDNd/yjxqKNbx78BKpzEtf2ivwiic1GpbP7d63HJnuqZjZ1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:22:35.297604Z","bundle_sha256":"98672d758e2bf7c281e070d851e94c927afa7726b2581ae12d53c3e106061b30"}}