Berkay Yüksel Sayim

Pairs of Consecutive and Near-Consecutive Powerful Numbers: Pell Families, Towers, and Localization

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We study the pairs n, n+1 of powerful numbers, the pairs n−1, n+1 at distance two, and how their numbers grow. For distance one we establish l...

Pairs of Consecutive and Near-Consecutive Powerful Numbers: Pell Families, Towers, and Localization

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We study the pairs n, n+1 of powerful numbers, the pairs n−1, n+1 at distance two, and how their numbers grow. For distance one we establish l...

Triples of Consecutive Powerful Numbers: Pell Addresses, a Height Inequality, and Witnesses

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We study the question of Erdős whether three consecutive integers can all be powerful. The middle n of such a triple is a Pell number T_k(m) a...

Consecutive Powerful Numbers and Pell Equations: Triples, Pairs, and Further Observations

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.A positive integer is powerful if every prime that divides it divides it at least twice. Pairs of consecutive powerful numbers exist in abunda...

Further Observations on Powerful Numbers: Gaps, Cyclotomic Values, and Independence Tests

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We collect observations on powerful numbers that arose in the study of triples and pairs of consecutive powerful numbers. Up to 10^14, only 0....

Further Observations on Powerful Numbers: Gaps, Cyclotomic Values, and Independence Tests

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We collect observations on powerful numbers that arose in the study of triples and pairs of consecutive powerful numbers. Up to 10^14, only 0....

Triples of Consecutive Powerful Numbers: Pell Addresses, a Height Inequality, and Witnesses

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.We study the question of Erdős whether three consecutive integers can all be powerful. The middle n of such a triple is a Pell number T_k(m) a...

Consecutive Powerful Numbers and Pell Equations: Triples, Pairs, and Further Observations

Note: the data deposit ZIP (deposit.zip) is temporarily withdrawn and will be provided again soon in a cleaned and usable English version.A positive integer is powerful if every prime that divides it divides it at least twice. Pairs of consecutive powerful numbers exist in abunda...

CHSH-Form Values Above 2 for Standard Fibonacci Anyons, and the Non-Topological Origin of Finite-Size Sector–CHSH Mutual Information in Z2 Lattice Gauge Theory

We quantify the mutual information I between topological sector labels T and CHSH values S in two-dimensional lattice models. Throughout, I denotes a classical Shannon mutual information between a global discrete label and a scalar measured value; it is not an entanglement entrop...

CHSH-Form Values Above 2 for Standard Fibonacci Anyons, and the Non-Topological Origin of Finite-Size Sector–CHSH Mutual Information in Z2 Lattice Gauge Theory

We quantify the mutual information I between topological sector labels T and CHSH values S in two-dimensional lattice models. Throughout, I denotes a classical Shannon mutual information between a global discrete label and a scalar measured value; it is not an entanglement entrop...

CHSH-Form Values Above 2 in Fibonacci Anyon Braiding: A Complete Landscape of Braid Words up to Length 12

We report a complete sequence-by-sequence landscape of CHSH-form values for six Fibonacci anyons in two encodings, covering all words of length L=3–12 with two generators and L=2–9 with three. In the two-generator d₁ᵦ encoding, braiding alone cannot exceed the classical value: th...

CHSH-Form Values Without Bell Nonlocality: Inapplicability of the Tsirelson Bound on a Non-Factorized Fibonacci Fusion Space

We construct a sequential measurement protocol on the n=8 Fibonacci-anyon fusion space of dimension D = F₇ = 13 whose CHSH-form expectation value attains |S| = 3.406, above the value 2√2≈ 2.828 that bounds CHSH correlations under the standard setting-locality precondition, which...

Leggett–Garg K₃ Values Above 1 in Fibonacci-Anyon Braiding: 99.998% of the Lüders Bound, and Exactly 1 for Ising Braiding

We numerically test the three-time Leggett–Garg inequality K₃ ≤ 1 for the standard B₃ Fibonacci-anyon braiding representation on the two-dimensional fusion space of three τ anyons. Exhaustive enumeration over all 4^L braid words up to length L=11 and random sampling to L=40 show...

A dichotomous Leggett–Garg witness for braid-representation density in SU(2)_k: exact at d=2, dimension-limited at d ≥ 3

Whether a temporal (Leggett–Garg) measurement can certify the computational power of an anyonic braid representation—its density in the unitary group, the property underlying universal topological quantum computation—has, to our knowledge, not been studied. We give a complete ope...

CHSH-Form Values Without Bell Nonlocality: Inapplicability of the Tsirelson Bound on a Non-Factorized Fibonacci Fusion Space

We construct a sequential measurement protocol on the n=8 Fibonacci-anyon fusion space of dimension D = F₇ = 13 whose CHSH-form expectation value attains |S| = 3.406, above the value 2√2≈ 2.828 that bounds CHSH correlations under the standard setting-locality precondition, which...

Leggett–Garg K₃ Values Above 1 in Fibonacci-Anyon Braiding: 99.998% of the Lüders Bound, and Exactly 1 for Ising Braiding

We numerically test the three-time Leggett–Garg inequality K₃ ≤ 1 for the standard B₃ Fibonacci-anyon braiding representation on the two-dimensional fusion space of three τ anyons. Exhaustive enumeration over all 4^L braid words up to length L=11 and random sampling to L=40 show...

Correlation Witnesses versus Magic: A k-Resolved Nonstabilizerness Map for SU(2)_k Anyon Fusion Spaces

Standard correlation witnesses — spatial Bell/CHSH inequalities, temporal Leggett–Garg K₃, and KCBS contextuality — are known to detect nonstabilizerness ("magic") in some settings. We report a worked example, a k-resolved nonstabilizerness map of the SU(2)_k anyon braid-represen...

Resolving the Full Modular Data of a Doubled-Fibonacci String-Net on a Finite Torus by Point-Group Rotation, and an Obstruction to Quasi-One-Dimensional Anyon Exchange

We report a real-space resolution of the full modular data of a doubled-Fibonacci Levin–Wen string-net, obtained by exact diagonalization on finite torus supercells (2×2, 2×3, 3×3), together with a sharply scoped negative result for the dynamical half of the same program — and we...

Bell Algebra without Bell Violation: CHSH Operators for Ising Anyons in the Kitaev Honeycomb Model

We construct four spatially separated Majorana zero modes (MZMs) per party on a finite Kitaev honeycomb lattice in its non-Abelian phase, bound to well-separated Ising vortices, and use them to realize a local, noncommuting CHSH measurement algebra. Two static fusion-parity obser...

Bell Algebra without Bell Violation: CHSH Operators for Ising Anyons in the Kitaev Honeycomb Model

We construct four spatially separated Majorana zero modes (MZMs) per party on a finite Kitaev honeycomb lattice in its non-Abelian phase, bound to well-separated Ising vortices, and use them to realize a local, noncommuting CHSH measurement algebra. Two static fusion-parity obser...