THE OMEGA INSTITUTE / RESEARCH FRONTIER
Open questions. Missing bridges. The next proof.
FROM RESULTS TO NEW QUESTIONS
Sequence complexity
Work with the same all-start class definitions and derive a candidate relation for the even-length run codes.
Real-rooted polynomials
Start with degree four, derive the transformed coefficients exactly, and isolate parameter ranges with certified real-root counts.
Completed resultAdditive combinatorics
Encode the published Conjecture 16 candidate and prove its accepted and forbidden block statements uniformly in g.
Completed resultConventions / Deficit / Words
Focused target Proposed route
Conventions / Depth / Digit
Exploratory Proposed route
Quantum / QuantumBounds
Long horizon Proposed route
Conventions / Digit / Rewriting
Focused target Proposed route
Asymptotics / Digit / Rewriting
Exploratory Proposed route
Arith / Carrier / Scale
Long horizon Proposed route
Conventions / Digit / Scale
Exploratory Proposed route
No questions match these filters.
QUESTIONS WITH RESULTS
Real-rooted polynomials
Refuted in Lean
An exact degree-two classification yields a counterexample range to the conjectured strict upper bound.
Reviewed result / pinned upstream proofInteger sequences
Proved in Lean
An explicit construction locates consecutive zero blocks in an alternating sum of floor square roots.
Reviewed result / pinned upstream proofCombinatorics / integer sequences
Proved in Lean
A universal periodic formula characterizes the literal greedy sequence starting from 1, g and g+d.
Reviewed result / pinned upstream proofCombinatorics on words
Proved in Lean
The number of reduced abelian classes at length 2n+1 equals the count at length n+1, for every nonnegative n.
Reviewed result / pinned upstream proof