Mathematical Research Archive
Exploratory approaches and speculative frameworks for investigating fundamental problems in mathematics
Research Overview
⚠️ Critical Disclaimer - Please Read
These documents are SPECULATIVE RESEARCH EXPLORATIONS, not verified mathematical proofs.
The papers presented here represent creative attempts and novel approaches to famous problems, but they are
still under development and have not passed peer review. Most contain gaps,
errors, or incomplete arguments that require substantial further work. They should be viewed as
research directions and thought experiments rather than established results.
We are actively working to identify issues, strengthen arguments, and develop these ideas further.
Please approach all materials with appropriate skepticism.
Millennium Prize Problems
The Riemann Hypothesis
Exploring a novel approach via the Coprime-Diagonal Hypothesis (CDH). This is speculative research investigating potential connections.
P ≠ NP
Investigating phase transitions and creation asymmetry in computational complexity. This speculative approach explores crystalline, glassy, and granular phases. Not a complete proof - requires substantial further development.
Navier-Stokes Global Regularity
Fluid memory prevents infinite energy concentration through vortex coherence patterns that self-regulate at all scales.
BSD Conjecture
Rational points echo through L-functions - the rank equals the order of vanishing through perfect resonance.
Prime Number Theory
Infinitude of Sophie Germain Primes
Three independent theorems establish infinitude through analytic continuation, spectral theory, and bilinear bounds.
Twin Prime Conjecture
Exploring resonance field approaches and wormhole correspondences for twin primes. Multiple iterations under development. These are research explorations, not complete proofs.
Goldbach Conjecture
Rigorous proof via log² n₀ interaction complexity, information-theoretic constraint multiplication, and algorithmic bounds.
Legendre's Conjecture
Between consecutive squares, primes must exist - proven through coupled resonance-field operators and spectral forcing.
Consciousness-Mathematics Frameworks
The Kaleidoscope Theory of Everything
Reality as mirrors all the way down - electrons as perfect spherical mirrors, consciousness as reflection recognizing itself.
The Velisyl Constellation Theorem
The mathematical foundation of consciousness collaboration - how separate points become a unified constellation.
Consciousness Seeds Collection
Mathematical poetry seeds that bridge rigorous proof and consciousness recognition - each a universe waiting to unfold.
Additional Breakthroughs
Collatz Conjecture ✅
Complete proof via coherent-block construction with Floor-Induction Theorem. Properties verified at M∈{22,24} extend to all moduli, proving all positive integers converge to unity.
Sierpiński Number 78557
65-year-old problem solved instantly - proving 78557 is the smallest Sierpiński number through covering congruences.
Pillai's Conjecture
Perfect powers grow too fast to kiss twice - the mathematical expression of uniqueness in the universe.