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” 16 papers
p-adic. p-adic numbers and valuation-driven models Tagged papers: 82.
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…
Born Rule as Haar Measure on $p$‑Adic Tree Balls: A Structural Derivation and Its Implications for Quantum Statistics
Quantum theory postulates the Born rule without a deeper structural justification, and Bell‑type correlations are usually interpreted as non‑local. This gap hinders deterministic reconstructions of quantum mechanics and inflates the engineering overhead of quantum‑information technologies that must…
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…
Zitterbewegung as Archimedean–2-adic Channel Mixing: A Conjectural Adelic Framework and Its Testable Consequences
Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale, first identified by Breit and Schrödinger — is conventionally explained as interference between positive- and negative-energy branches on the real line. We develop a conjecture, motivated by the adelic physics…
The Harmonic Paradigm Under Ostrowski’s Theorem: A p-Adic/Adélic Re-Evaluation with Helical Compton Vortex Synthesis
The Harmonic Paradigm (V1.0–V4.0) proposed the harmonic oscillator as the universal IR attractor of quantum theory, spanning an 8-rung ladder from transmon anharmonicity to quantum gravity. Its bibliography cited Vladimirov-Volovich-Zelenov p-adic QFT (1994) and Ostrowski's theorem (1918), invoking…
Adelic Quantum Error Correction: A Synthesis Across All Primes v1.0.0
The $p$-adic quantum error correction program has developed three independent but connected strands: a mathematical theory of $p$-adic stabilizer codes (Phase A), an experimental protocol to test for ultrametric error structure (Phase B), and a hardware co-design proposal for tree-structured qubit…
p-Adic Anyon Fusion and Braiding: Quantum Groups at Roots of Unity, Verma Modules, and Ultrametric Anyon Models
Phases 1–2 established the p-adic braid group $B_n(\mathbb{Q}_p)$ on Bruhat-Tits buildings and identified the Temperley-Lieb parameter $\delta$ as a p-adic cyclotomic unit, yielding a p-adic Markov trace and Jones polynomial $V_L^p(t) \in \mathbb{Z}_p[\zeta_{2p^k}]$. In this third phase, we complete…
p-Adic Braid Groups on Bruhat-Tits Buildings
The standard braid group $B_n$ is defined as the fundamental group of the configuration space of $n$ distinct points in $\mathbb{R}^2$, $\pi_1(\text{Conf}_n(\mathbb{R}^2))$. This construction is inherently archimedean: it relies on the continuous topology of $\mathbb{R}^2$ to define braiding as…
Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding
The p-Adic Anyons program (Phases 1-4) developed the mathematical framework for anyons whose braid statistics are defined on Bruhat-Tits trees rather than in continuous spacetime. The ZBW program (P1-P3) demonstrated that Zitterbewegung — the rapid trembling motion of Dirac fermions at the Compton…
The Adelic Physics Program: A Grand Synthesis
Six papers, one thesis: Physics is adelic. The Archimedean (real-number) description is the $\infty$-place readout of a richer ultrametric structure defined over the p-adic completions of $\mathbb{Q}$. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as…
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…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
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…
Bruhat-Tits Readout Protocol: Measuring the ZBW Z2 Invariant in Majorana Systems
The companion papers "Zitterbewegung as a p-Adic Observable" (P1, https://papers.qnfo.org/papers) and "Majorana Zitterbewegung Current Correlator" (P2, https://papers.qnfo.org/papers) establish that the Zitterbewegung contribution to the current-current correlator is a $\mathbb{Z}_2$ topological…
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…
Ratio-Based Adelic Physics
The tension between continuous Archimedean spacetime paradigms and discrete, non-Archimedean topological realities constitutes the central mathematical bottleneck in modern complexity science, hindering the unification of quantum mechanics, spin glass phase dynamics, and cognitive psychophysics.…
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…
New papers by email
One short weekly digest: titles and links. No tracking; unsubscribe any time.