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The operator $U_5$ scales the elements of the canonical exponential spectrum for $L^2(\\mu_{\\frac14})$ by 5 --- that is, $Ue_{\\gamma} = e_{5\\gamma}$ where $e_{\\gamma}(t) = e^{2\\pi i \\gamma t}$. It is known that $U_5$ has a self-similar structure, which makes its spectrum, which is currently unknown, of particular interest. In order to better understand the spectrum of $U_5$, we demonstrate a decomposition of the projection valued measures and scalar spectral measures associated with $U"},"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":"1204.5116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-04-23T17:15:19Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"404f2fd691c124d9f28d94f8d8b760ca240f1658efd7ee0d12c51c18ea8069e1","abstract_canon_sha256":"82245bbe58064280dd14e16850984117b22a56fef2bd5120b32b78eb6c923759"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:14.740708Z","signature_b64":"cfrQNsPQS7G4CqgFvD2MQCalbTm6PYqDtv44sOoxPMK2/xsa/aXMUo/QblgFionhfIKiQTUROEvYZaXsDJj+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac88ead7a2671a13fd1ffcc5f2ae19016c2087398fad13718174e5123201712","last_reissued_at":"2026-05-18T03:57:14.740226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:14.740226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar spectral measures associated with an Operator-Fractal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.SP","authors_text":"Karen L. 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