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We find that the integrated intensity maps generally follow a log-normal distribution, with the cases that have $\\tau \\approx 1$ best matching the PDF of the column density. We fit a 2D variance-sonic Mach number relationship to our logarithmic PDFs of the form $\\sigma_{ln(\\Sigma/\\Sigma_0)}^2=A\\times ln(1+b^2{\\cal M}_s^2)$ and find that, for parameter $b=1/3$, parameter $A$ depends on the radiative transfer "},"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":"1304.3131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2013-04-10T20:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"bc919d2b546bef68d347823d632a87854c122b7a80dcaeb94421065b599270ba","abstract_canon_sha256":"298ade680087b6362c4623207d497de2b20427acb0e68e61bef83e8089de6a99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:40.167647Z","signature_b64":"lGJHrLvvbDlNSy2pgpjKOrUFbIyOJ9arkBXOETtpu39G+fax2BiNrdbZT76y9hPcFSJJ0J4HVPaI+RK8NujBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65198bedf152edc690102c31cf575881678f186411e64a8150f61a79f713496a","last_reissued_at":"2026-05-18T01:50:40.166937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:40.166937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Effects of Radiative Transfer on the PDFs of Molecular MHD Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"A. 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