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dx)$, and $f$ is supposed to satisfy [f \\in AC_{\\text{loc}}((a,b)), \\; p[f' + s f] \\in AC_{\\text{loc}}((a,b)).] In particular, thi"},"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":"1208.4677","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-08-23T06:21:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1ca473738d853c2a1ebb2903750997592535fd573e9bb3debb2df8fd5c5d5e54","abstract_canon_sha256":"929d0745cc0016b74368fe581ace47d02e6c9ba7b683a5f402b55f753b0661a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:01.513492Z","signature_b64":"oD/bHV5AIGQ5Vu+Z3ER82M2OZHa7fVPOpfUodimCJRFXZ7uKWgZSpc5JodGhFjjiaIp7BJyEm0oWANQoF64GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74f41ad5efe3df1c3f97ebf77ea310c6079a148a07dff299fbfd48cefdc06c64","last_reissued_at":"2026-05-18T03:27:01.513083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:01.513083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Gerald Teschl, Jonathan Eckhardt, Roger Nichols","submitted_at":"2012-08-23T06:21:15Z","abstract_excerpt":"We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \\subseteq \\mathbb{R}$ associated with rather general differential expressions of the type \\[\n  \\tau f = \\frac{1}{r} (- \\big(p[f' + s f]\\big)' + s p[f' + s f] + qf),] where the coefficients $p$, $q$, $r$, $s$ are real-valued and Lebesgue measurable on $(a,b)$, with $p\\neq 0$, $r>0$ a.e.\\ on $(a,b)$, and $p^{-1}$, $q$, $r$, $s \\in L^1_{\\text{loc}}((a,b); 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