Open research library
Papers you can read, cite and question
728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
Looking for an answer rather than a paper? Ask the whole corpus: answers cite the papers they come from.
Results for “topological” 14 papers
Ultrametric. Non-Archimedean geometry: tree metrics, strong triangle inequality, hierarchical distance Tagged papers: 115.
Ultrametric $p$‑adic Vacuum Energy Suppression and the Cosmological Constant
The observed dark‑energy density $\rho_{\Lambda}^{\rm obs}\approx10^{-47}\,\text{GeV}^4$ is smaller than the naïve quantum‑field‑theoretic vacuum estimate by roughly $10^{120}$, a discrepancy that dominates the cosmological‑constant problem. Existing proposals retain the Archimedean real number…
Cocycle Solving in Cognition: Ultrametric Reaction Times and Analogy Depth
Cognitive consistency and analogical difficulty are pervasive challenges for psychologists, educators, and artificial‑intelligence designers. Existing Euclidean models cannot capture the hierarchical constraints that appear in belief networks and analogy spaces. We therefore propose a formalism in…
Primality as a Non‑Archimedean Structure Projected onto the Real Line
Primes are defined as discrete divisibility objects in the integers, yet many analytic phenomena—Riemann zeros, cryptographic protocols, and quantum‑information patterns—depend on a continuous view of number theory. The gap lies in the lack of a real‑valued functional that captures $p$‑adic…
Majorana Zero‑Mode Parity, the Hexagon Equation, and the Necessity of Chiral Edge Modes in Two‑Dimensional Topological Superconductors
Topological quantum computation requires non‑Abelian anyons whose braiding implements fault‑tolerant logical gates. In two‑dimensional topological superconductors, vortices bind Majorana zero modes (MZMs) that furnish a projective braid‑group representation. A persistent open question is whether the…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection for Majorana Qubits
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Majorana Zitterbewegung Current Correlator: Vanishing ZBW Signal as a Z2 Topological Invariant
We compute the Zitterbewegung contribution to the current-current correlator $\langle j^\mu(x) j^\nu(0) \rangle$ for both Dirac and Majorana fermions in (2+1) dimensions. In the Dirac case, the ZBW term oscillates at frequency $2E$ with magnitude comparable to the static vacuum polarization term…
Computational Simulation Approach to Non-Archimedean Quantum Architectures
The prevailing quantum computing paradigm is fundamentally constrained by the continuous analog fragility inherent to Archimedean spaces, resulting in uncontrolled linear error accumulation that demands massive active correction overheads. To address this structural bottleneck, we propose a…
Non-Archimedean Syntactic Paradigm for Physics
The prevailing paradigm in modern physics assumes that the universe operates over continuous, Archimedean geometries, leading directly to the widespread belief that quantum information is intrinsically fragile. By projecting fundamentally discrete quantum states onto smooth vector spaces, standard…
Proof-of-Concept for Auditable Attention using Ultrametric Tree Distances
The dominance of high-dimensional Euclidean vector spaces in contemporary transformer architectures has precipitated an interpretability crisis, as continuous geometric embeddings can obscure the causal mechanisms of semantic attention. This paper presents a formal proof-of-concept for a…
Quantitative Simulation of the Brain's Cognitive Architecture
The human brain seamlessly integrates noisy local inputs into a globally consistent percept, a phenomenon that Euclidean models struggle to adequately explain. Theoretical physics suggests that frustrated complex systems settle into hierarchical equilibria characterized by ultrametric topologies.…
Spectral Analysis of Anomalous Diffusion on p-Adic Fractals
The reconcilement of continuous Riemannian geometry with the discrete arithmetic of the integers remains one of the most profound challenges in mathematical physics, particularly regarding the spectral interpretation of the Riemann zeros (Berry & Keating, 1999). While standard diffusion on…
Ultrametric Relaxation Dynamics in Topological Quantum Memory
The scalability of Topological Quantum Computing (TQC) is currently impeded by a “Thermodynamic Wall,” where the entropy generation from active error correction cycles scales exponentially with logical qubit count. This paper proposes a paradigm shift from active gate synthesis to passive…
Double Pendulum as a Topological Bridge
The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold…
Winding Number as Hidden Variable
This paper proposes that physical reality emerges from a pre-geometric substrate based on the circle \(S^1\), with its integer winding numbers providing a deterministic foundation for physics. A universal computation of pattern writing, evolution, and projection generates spacetime and particles,…
New papers by email
One short weekly digest: titles and links. No tracking; unsubscribe any time.