{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EKO3EE4OFGSQWSXBSB3C677H53","short_pith_number":"pith:EKO3EE4O","schema_version":"1.0","canonical_sha256":"229db2138e29a50b4ae190762f7fe7eedaa3e51649728517dcaeaecfb0eb77b5","source":{"kind":"arxiv","id":"1011.0794","version":1},"attestation_state":"computed","paper":{"title":"Probability measures on solenoids corresponding to fractal wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Arlan B. Ramsay, Judith A. Packer, Kathy D. Merrill, Lawrence W. Baggett","submitted_at":"2010-11-03T02:55:16Z","abstract_excerpt":"The measure on generalized solenoids constructed using filters by Dutkay and Jorgensen is analyzed further by writing the solenoid as the product of a torus and a Cantor set. Using this decomposition, key differences are revealed between solenoid measures associated with classical filters in $\\mathbb R^d$ and those associated with filters on inflated fractal sets. In particular, it is shown that the classical case produces atomic fiber measures, and as a result supports both suitably defined solenoid MSF wavelets and systems of imprimitivity for the corresponding wavelet representation of the "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.0794","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-03T02:55:16Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2dae5b960a3beef0564342c795d678d8531f64a0cce42fc5ea11ec6f23c00893","abstract_canon_sha256":"19f6d2dee69105820d4b88a9984bc416ee9863046678d1f06fd4d0fc2d47a0e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:12.351212Z","signature_b64":"WwTUFh3aW8HJMfOl4ftZ8ytjnI+6OVEbHxG8WNXn8iIJ3PbhEufRYrsGHpKjN2bUdkVSiKSCR6Z0oTe71P4hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"229db2138e29a50b4ae190762f7fe7eedaa3e51649728517dcaeaecfb0eb77b5","last_reissued_at":"2026-05-18T04:37:12.350490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:12.350490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probability measures on solenoids corresponding to fractal wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Arlan B. Ramsay, Judith A. Packer, Kathy D. Merrill, Lawrence W. Baggett","submitted_at":"2010-11-03T02:55:16Z","abstract_excerpt":"The measure on generalized solenoids constructed using filters by Dutkay and Jorgensen is analyzed further by writing the solenoid as the product of a torus and a Cantor set. Using this decomposition, key differences are revealed between solenoid measures associated with classical filters in $\\mathbb R^d$ and those associated with filters on inflated fractal sets. In particular, it is shown that the classical case produces atomic fiber measures, and as a result supports both suitably defined solenoid MSF wavelets and systems of imprimitivity for the corresponding wavelet representation of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0794","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.0794","created_at":"2026-05-18T04:37:12.350601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.0794v1","created_at":"2026-05-18T04:37:12.350601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0794","created_at":"2026-05-18T04:37:12.350601+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKO3EE4OFGSQ","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKO3EE4OFGSQWSXB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKO3EE4O","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53","json":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53.json","graph_json":"https://pith.science/api/pith-number/EKO3EE4OFGSQWSXBSB3C677H53/graph.json","events_json":"https://pith.science/api/pith-number/EKO3EE4OFGSQWSXBSB3C677H53/events.json","paper":"https://pith.science/paper/EKO3EE4O"},"agent_actions":{"view_html":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53","download_json":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53.json","view_paper":"https://pith.science/paper/EKO3EE4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.0794&json=true","fetch_graph":"https://pith.science/api/pith-number/EKO3EE4OFGSQWSXBSB3C677H53/graph.json","fetch_events":"https://pith.science/api/pith-number/EKO3EE4OFGSQWSXBSB3C677H53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53/action/storage_attestation","attest_author":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53/action/author_attestation","sign_citation":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53/action/citation_signature","submit_replication":"https://pith.science/pith/EKO3EE4OFGSQWSXBSB3C677H53/action/replication_record"}},"created_at":"2026-05-18T04:37:12.350601+00:00","updated_at":"2026-05-18T04:37:12.350601+00:00"}