{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PMGDYEDCHPQNGA6IB65CTLKTMY","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":"68f2cc95ad147bc60540771c96c0b9995ba4b22736137bd1762ad772c696aa6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-10T05:36:31Z","title_canon_sha256":"78436ff39c94489896e7a02d4e2ba74a0c706afc51be61475ffc5a0e43a6c299"},"schema_version":"1.0","source":{"id":"1507.02782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02782","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02782v1","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02782","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"pith_short_12","alias_value":"PMGDYEDCHPQN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PMGDYEDCHPQNGA6I","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PMGDYEDC","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7c1e40ec3b4f192d18f6e143df49ba79e01d73d88a049984daed21728962ee25","target":"graph","created_at":"2026-05-18T01:37:03Z","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":"We consider a class of semidirect products $G = \\mathbb{R}^n \\rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under which conditions there exists a wavelet such that the associated reproducing kernel is integrable.\n  It is well-known that the existence of integrable wavelet coefficients is related to the question whether the unitary dual of $G$ contains open compact sets. Our main general result reduces the latter problem to that of identifying compact open sets in the quo","authors_text":"Bradley Currey, Hartmut F\\\"uhr, Keith Taylor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-10T05:36:31Z","title":"Integrable wavelet transforms with abelian dilation groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02782","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:b6c0a7be693de97b9add24f5c6af915862ee6ddb29a532614509cc9827f0066f","target":"record","created_at":"2026-05-18T01:37:03Z","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":"68f2cc95ad147bc60540771c96c0b9995ba4b22736137bd1762ad772c696aa6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-10T05:36:31Z","title_canon_sha256":"78436ff39c94489896e7a02d4e2ba74a0c706afc51be61475ffc5a0e43a6c299"},"schema_version":"1.0","source":{"id":"1507.02782","kind":"arxiv","version":1}},"canonical_sha256":"7b0c3c10623be0d303c80fba29ad5366191aaa05c7a288675e54fd8c8eb76f91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b0c3c10623be0d303c80fba29ad5366191aaa05c7a288675e54fd8c8eb76f91","first_computed_at":"2026-05-18T01:37:03.205058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:03.205058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/E1lzLI7Pn6vAEs+YEzALspGKgdyX7Ay4V/yGgj1S7wInYnvHMit48lzn2wVpy7+2nBzWfYaev0TSMrK4ZXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:03.205491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6c0a7be693de97b9add24f5c6af915862ee6ddb29a532614509cc9827f0066f","sha256:7c1e40ec3b4f192d18f6e143df49ba79e01d73d88a049984daed21728962ee25"],"state_sha256":"d76e7eca935adccae769dba8801fecdc1813b82c7cb7a31cec0a2ca38ea8ca84"}