Blockchain Papers

Akim Setenta

Rigorous Construction of 4D Quantum Yang-Mills Theory and the Mass Gap via Nexus Spin-Network Regularization Akim C. Setenta1 Nexus Theory Research Group | @seventy.dev Manuscript v2.1 — June 2026. Prepared for submission to arXiv (math-ph; hep-th). Abstract We present a complete mathematical construction of non-abelian quantum Yang–Mills theory on ℝ⁴ for any compact simple gauge group G, with the strict positivity of the mass gap (Δ > 0) as the central object of study. Building on the Nexus OmniScientia program together with Loop Quantum Gravity (LQG) techniques, we define the physical Hilbert space ℋgauge through spin-network states over cylindrical functions, regularized by a gauge-invariant ultraviolet cutoff Amin = 4πγ√3 ℓP2 fixed by the minimal non-zero eigenvalue of the LQG area operator. The Hamiltonian constraint is regularized via Thiemann's trick, producing an operator that we argue is essentially self-adjoint on a dense domain of finite spin-networks. We then examine, axiom by axiom, whether the resulting Schwinger functions can satisfy the Osterwalder–Schrader (OS) requirements in the continuum limit ℓP → 0. Reflection positivity (OS3) is approached without any global gauge-fixing, via Markovian Dirichlet forms on the orbit space 𝒜/𝒞 — a route that, if it can be made fully rigorous, would sidestep the Gribov ambiguity entirely rather than resolve it head-on. Regularity and tightness (OS1) are addressed through a non-abelian polymeric cluster expansion; Euclidean covariance (OS2) is argued to be restored in the renormalization-group sense as anisotropic lattice artifacts become irrelevant. Finally, a candidate spectral-gap bound Δ ≥ (N/2)ΛQCD2 is proposed from a Bakry–Émery curvature argument on the gauge-orbit space. We present this construction in the spirit it deserves: as a coherent and, to our knowledge, novel research program that reorganizes the resolution of the Yang–Mills Millennium Problem around tools from constructive field theory and loop quantum gravity — not as a closed, peer-reviewed proof. Several steps that we label explicitly as ‘proof sketches’ still require the kind of analytic control (uniformity in the cutoff, explicit constants, rigorous Wick rotation on the orbifold) that the Clay Mathematics Institute's criteria demand. Section 13 catalogs these open points candidly, both for the benefit of readers and as a working roadmap for completing the proof. Keywords: Yang–Mills mass gap; Bakry–Émery curvature; constructive quantum field theory; Osterwalder–Schrader axioms; loop quantum gravity; Dirichlet forms; Gribov ambiguity. 1 Independent researcher. Correspondence and source materials: @seventy.dev.

Tomoya Hatanaka, Rikuto Fushio, Masataka Watanabe, William J. Munro · 6 authors

We propose a quantum hash function based on Gaussian boson sampling on a photonic quantum computer, aiming to provide quantum-resistant security. Extensive simulations demonstrate that this hash function exhibits strong properties of preimage, second preimage, and collision resistance, which are essential for cryptographic applications. Notably, the estimated number of attempts required for a successful collision attack increases exponentially with the mode counts of the photonic quantum computer, suggesting robust resistance against birthday attacks. We also analyze the sampling cost for physical implementation and discuss potential applications to blockchain technologies, where the inherent quantum nature of the hash computation could provide quantum-resistant security. The high dimensionality of the quantum state space involved in the hashing process poses significant challenges for quantum attacks, indicating a path towards quantum security. Our work lays the foundation for a new paradigm of quantum-resistant hashing with applications in emerging quantum-era information systems.

Zae Young Kim, Jeong-Hyuck Park

Modern technology has brought novel types of wealth. In contrast to hard cash, digital currency does not have a physical form. It exists in electronic forms only. To date, it has not been clear what impacts its ongoing growth will have, if any, on wealth distribution. Here, we propose to identify all forms of contemporary wealth into two classes: ‘distinguishable’ or ‘identical’. Traditional tangible moneys are all distinguishable. Financial assets and cryptocurrencies, such as bank deposits and Bitcoin, are boson-like, while non-fungible tokens are fermion - like. We derived their ownership-based distributions in a unified manner. Each class follows essentially the Poisson or the geometric distribution. We contrast their distinct features such as Gini coefficients. Furthermore, aggregating different kinds of wealth corresponds to a weighted convolution where the number of banks matters and Bitcoin follows Bose–Einstein distribution. Our proposal opens a new avenue to understand the deepened inequality in modern economy, which is based on the statistical physics property of wealth rather than the individual ability of owners. We call for verifications with real data.

Alexey Milekhin

It has been proposed in the literature that the volume of Einstein-Rosen bridge is equal to complexity of state preparation ("Complexity=Volume" conjecture). Taking this statement outside the horizon, one might be tempted to propose "Complexity=Time" correspondence. In this Essay we argue that in a blockchain protocol, which is the foundation of all modern cryptocurrencies, time is emergent and it is defined according to a version of "Complexity=Time".