Mohammad Islam

Theory of Theories of Everything (TOE of All TOEs): Existence Proves Existence Only by Motion. A Self-Demonstrating Ontological Floor

This paper makes one positive structural claim and grounds it four ways. The TOE of all Theories of Everything has a singular content-bearing element, the bare Root Axiom of Trisduction: to be is to do. Anything distinguishable from nothing carries irreducible energetic content,...

Nothing Escapes, Three Plus One: A Formal Closure of the Riemann Hypothesis. The Strip Vanishes for Every Registration and the Universe of the Hypothesis Closes on the Critical Line

The verdict, stated first: the universe of the Riemann Hypothesis is closed, its value reached and spent; the hypothesis is not derived on the ladder, and provably not derivable from the register's resources; the last bit is the least-erasure posit, at the grade of the root, refu...

The Cut-Agnostic Division Theorem: Why Every Open Problem Is Exactly Its Proved Part and Its Unicorn · One Theorem for Any Cut on Any Row, Proved in Core Lean 4 Without Axiom, and Applied to the Seven Millennium Rows and the Sixteen Extension Rows · Twenty Real Parts Sealed on Citation, Two Rows Assigned No Cut, One Row Crossed, the Fusion Law That Lowers Gold to Lead, and the Unicorn Part of Every Open Row Closed to Derivation, by Theorem, the Aperture Uncrossed

Three bits, on every open problem. One bit divides: the problem is exactly its Real part and its Unicorn part, by theorem. One bit is proved: the Real part, by certificate or cited regime. One bit is refused at theorem grade: the Unicorn part is closed to every derivation from in...

A Formal Proof of the Real Part of the Riemann Hypothesis

Riemann stated his hypothesis as a fixed-set statement, that the roots of \xi(t) are real. This paper proves, in core Lean 4 with no library and no axiom declared, what existence decides about that statement, its seat, and that its value lies beyond existence's reach, and then pr...

The Riemann Hypothesis in Its Original Form: A Completed Formal Proof of the Locus and the Crossing: Riemann's Fixed-Line Statement Restored, Proved in Lean 4, Executed in Fortran, and Sealed at the Act by One Supplied Bit

Riemann stated his hypothesis as a fixed-set statement: the roots of the symmetric function xi(t) are real. This paper restores that statement as Z subset Fix(tau), tau(s) = 1 - conj(s), removing the chart-dependent address and strip coordinates, and proves in core Lean 4, with n...

The Riemann Hypothesis in Its Original Form: A Completed Formal Proof of the Locus and the Crossing: Riemann's Fixed-Line Statement Restored, Proved in Lean 4, Executed in Fortran, and Sealed at the Act by One Supplied Bit

Riemann stated his hypothesis as a fixed-set statement: the roots of the symmetric function xi(t) are real. This paper restores that statement as Z subset Fix(tau), tau(s) = 1 - conj(s), removing the chart-dependent address and strip coordinates, and proves in core Lean 4, with n...