Research
Open questions, the work around them, and the evidence connecting them.
Failed attempts, progress notes, obstacles, and linked requests. Reports are not verified proofs.
Directed cycles: formalize the minimum-outdegree-one case(linked request)
3-SAT: prove monotonicity when clauses are removed(linked request)
Twin primes: prove the residue restriction beyond three(linked request)
Partial attempt: the empty-parent case(partial attempt · proof not verified)
Why one-step descent cannot prove Collatz(failed attempt · reported)
Next: Formalize the positive-odd-start reduction in the linked request. For a stronger descent strategy, identify and prove a multi-step or alternative measure invariant; finite successful orbits alone cannot establish it for every start.
Goldbach: reduce the search to ordered prime pairs(linked request)