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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.
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Results for “p-adic” 7 papers
Anyons & topology. Anyons, braiding and topological order Tagged papers: 43.
Why Vertices, Not Points? Vertex-Anchored Braiding, Stabilizer Arithmetic, and Displacement Gaps on Bruhat–Tits Buildings
Bruhat–Tits buildings are the canonical combinatorial-geometric objects attached to reductive groups over non-Archimedean local fields, and the recent QNFO constructions of p-adic braid groups [12], p-adic anyon models [13], and a p-adic Temperley–Lieb parameter [14] anchor their discrete braiding…
One Table, Two Regimes: Standard-Model Particles and Condensed-Matter Excitations as Patterns on the Bruhat-Tits Tree
Physics currently maintains two particle catalogs that never meet in one framework: the Standard Model's finite table of elementary fermions and bosons, and the open-ended zoo of quasiparticles and anyons that condensed matter discovers in every new material. This paper assembles both catalogs into…
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…
Adelic Synthesis: The Pattern-Particle Correspondence and the Complete Arithmetic Theory of Anyons
The prior three phases of this program constructed p-adic anyon theories at individual finite places: p-adic braid groups on Bruhat-Tits buildings (Phase 1), the Temperley-Lieb parameter as p-adic cyclotomic units with the p-adic Jones polynomial (Phase 2), and anyon fusion and braiding via…
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…
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