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Bruhat–Tits trees papers 43 papers
Bruhat–Tits trees. Bruhat-Tits trees used as the model space Tagged papers: 43.
Joint Bruhat–Tits Tree Product as a Testable Cross‑Domain Structure for Standard‑Model Mass Ratios, Quantum‑Error‑Correction Lattices, and Efimov Scaling
The Standard‑Model mass spectrum, Gottesman–Kitaev–Preskill (GKP) lattice spacings, and Efimov discrete‑scaling factor are each treated as empirical inputs, limiting predictive power. A conjectured universal geometry—the diagonal embedding of the product of Bruhat–Tits trees…
Joint Bruhat–Tits Tree Product as a Candidate Universal Structure for Standard Model Mass Ratios, Quantum Error-Correction Lattices, and Efimov Scaling: Formalization, Arithmetic Consequences, and a Partial Falsification
The Standard Model (SM) treats particle masses as free parameters, quantum-error-correction (QEC) lattice designs are chosen by heuristic optimization, and the Efimov discrete scaling factor lacks a structural explanation; a single mathematical object generating all three would change how each…
Time as Epistemic Emergence on a $p$-Adic Bruhat–Tits Tree: Static Constraint, Counting Laws, and the Observer-Generated Arrow
The problem of time in quantum gravity blocks any straightforward union of general relativity, in which the time coordinate is dynamical, with quantum mechanics, in which evolution requires an external background parameter; until it is resolved, a non-perturbative quantum theory of gravity cannot…
Time as Bruhat-Tits Tree Depth: Discrete $p$-Adic Temporal Ordering and Tree-Geodesic Causality
We develop a conjectural but internally precise model in which physical time is not a continuous real parameter but a discrete depth coordinate on a Bruhat-Tits tree: an event is a vertex of a rooted $(p+1)$-regular tree, and its time is the integer depth $d\in\mathbb{N}$, identified conjecturally…
Ultrametric Quantum Error Correction on Bruhat–Tits Trees: Energy Barriers, Classical Evidence, and the Quantization Question
We study a conjectured passive fault-tolerance scheme in which logical qubits are encoded on a Bruhat–Tits tree, the infinite homogeneous tree associated with a non-Archimedean local field, whose natural metric satisfies the strong (ultrametric) triangle inequality. The conjecture states that the…
Holographic Quantum Error Correction on Bruhat–Tits Trees: A Conditional Threshold and Resource Analysis at $10^{-4}$
We assess, quantitatively and conditionally, whether a quantum error correction (QEC) architecture in which the encoding map is realized as renormalization-group (RG) flow on a Bruhat–Tits tree $\mathcal{T}_p$ — the $p$-adic analogue of hyperbolic anti-de Sitter space — can achieve a QEC threshold…
Ultrametric Geometry as Passive Quantum Error Correction: Bruhat–Tits Qudit Codes and the Non-Archimedean Bound
We formalize a proposal for passive quantum error correction (QEC) in which logical qudits are encoded on the vertices of a ball of the Bruhat–Tits tree $T_{p+1}$, the incidence geometry of the $p$-adic numbers $\mathbb{Q}_p$, with Hecke-type operators acting as the natural gate set. The central…
Zitterbewegung as a $p$-Adic Ultrametric Observable: A $\mathbb{Z}_2$ Invariant on the Bruhat–Tits Tree, Its Readout, and Its Non-Additivity Signature
Zitterbewegung (ZBW) — the Compton-frequency trembling of Dirac wave packets — is conventionally modeled as an Archimedean interference oscillation between positive- and negative-energy branches. We develop a conjectural alternative in which the ZBW readout is ultrametric: the observable lives on a…
Spectral Decomposition of the Bruhat–Tits Tree as a Candidate Origin of Particle Mass Hierarchies: Exact Radial Spectrum, Finite Truncations, Semigroup Tests, and a Falsification Analysis
The Bruhat–Tits tree $\mathcal{T}_p$ of $\mathbb{Q}_p$ is the infinite $(p+1)$-regular tree that serves as the bulk of $p$-adic AdS/CFT. We test the conjecture that a natural Laplacian on $\mathcal{T}_p$ — or the prime-indexed arithmetic of the tree — encodes Standard Model mass ratios. We compute,…
Fidelity Budgets for Discrete Regularizations of Gauge Theories: Exact Single-Link Computations, Scaling Laws, and the Limits of Heuristic Bounds
Discrete regularizations of gauge theories — finite-dimensional link Hilbert spaces in quantum link models, truncated electric bases on quantum registers, and tensor networks on Bruhat–Tits trees — all face the same structural question: when does the discrete object faithfully encode its continuum…
Holographic Quantum Error Correction as AdS/CFT Renormalization-Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at 10⁻⁴
We analyze a proposal in which quantum error correction (QEC) is organized as renormalization-group (RG) flow on a Bruhat–Tits tree $\mathcal{T}_p$ — the $p$-adic analogue of hyperbolic anti-de Sitter (AdS) space — so that the encoding map of a holographic code is literally an RG trajectory from…
The q-Generalized α-Diameter: Scaling Exponents D_q^α for Arbitrary Ultrametric Ratios
In the QNFO ultrametric physics program, the fine-structure constant α has been reframed as a cross-ratio of two measurable electron length scales, and adelic extensions on Bruhat–Tits buildings have been proposed. A natural but unresolved question is how the characteristic "depth" associated with…
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 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 discovered in condensed matter. This paper assembles both catalogs into a single pattern table on the…
The Adelic Distinction: Physics as Automorphic Representation Theory on the Idele Class Group
Proposes that the adele ring and idele class group provide the single mathematical object whose automorphic representations generate all known particle physics, gauge interactions, and cosmological parameters. Covers gauge symmetry, spin, charge quantization, three generations, QFT as automorphic…
ODR Thesis: The Compton Count as the Only Primitive
ODR framework: Compton count as the only primitive physical invariant.
Quasiparticles as Rational Functions: Extending ODR to Condensed Matter
The Ontological Distribution of Reality (ODR) framework identifies a particle with its Compton count \(N_C = m/m_P \in \mathbb{Q}^+\), a dimensionless rational number whose prime factorization assigns it a fixed vertex on the Bruhat–Tits tree. This paper extends that framework to address a natural…
ODR Thesis: The Compton Count as the Only Primitive — A Five-Question Synthesis
The Ontological Distribution of Reality (ODR) framework identifies a particle with its Compton count \(N_C = m/m_P \in \mathbb{Q}^+\), a dimensionless rational number whose prime factorization assigns it a fixed vertex on the Bruhat–Tits tree. This paper synthesises five research questions into a…
The Compton-Counting Ontology and the Bruhat-Tits Tree
The Compton frequency of a particle, normalized by the Planck frequency, yields a dimensionless rational number --- the Compton count. We argue that this count subsumes every other physical quantity as a rational function, that the physical number system is therefore [\\(\\mathbb{Q}\\)]{.math…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees
v3.2 corrections (2026-07-25): arithmetic errors in mass ratio triplets corrected (5 of 9 verified independently); Efimov lambda derivation replaced with honest structural correspondence; constraining literature section added per KIF-18 symmetry; semigroup density epistemological risk acknowledged;…
Ultrametric Quantum Computation and the Langlands Program
A unified thesis establishing ultrametric quantum computation on Bruhat-Tits trees as the physical substrate for the Langlands program, with Hecke operators as quantum gates and the adele ring as the natural spacetime.
The Adelic ZBW Programme: ZBW-Majorana Hypothesis, Ostrowski-QEC Synthesis, and Cross-Programme Consilience
The structural underdetermination of the position operator in relativistic quantum mechanics -- manifested at the Archimedean place as zitterbewegung (the Newton-Wigner no-go) and at p-adic places as a discrete Bruhat-Tits observable -- arises from a single representation-theoretic origin: the…
Zitterbewegung: From Archimedean Puzzle to Adelic Observable
The structural underdetermination of the position operator in relativistic quantum mechanics arises from a single representation-theoretic origin: the Silent Parameter Principle. SU(2) and Z2^x share identical fusion rules at matching levels. The 2-adic ZBW frequency deviates from the Archimedean…
The Adelic Cross-Domain Program v5.0: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat–Tits Trees
The Adelic Cross-Domain Program maps the architecture of the Standard Model onto the geometry of Bruhat–Tits trees — the p-adic analogues of hyperbolic space. The fine-structure constant α, the renormalization group, quantum error correction, the Efimov effect, and the Standard Model mass spectrum…
Holographic QEC as AdS/CFT RG Flow on Bruhat–Tits Trees
Tasks X3.1 and X3.2 established bosonic QEC as RG fixed-point subspaces on Bruhat–Tits trees. Task X3.3 completes the trilogy by showing that this structure is holographic: the Bruhat–Tits tree $\mathcal{T}_p$ is the $p$-adic analog of anti-de Sitter space, tensor networks on $\mathcal{T}_p$ are…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees (Phase 3-4 Update)
Cross-Domain Phase 2 synthesis paper uniting six avenues (X1-X6). Key result: the Pythagorean semigroup P={2^a·3^b·5^c} is simultaneously the SM mass spectrum, GKP code lattice, Efimov discretuum, and diagonal embedding of T_{2,3,5}. Full calibration register with 15 entries.
Compton Frequency Cross-Ratios on Bruhat-Tits Trees: A Pre-Registered Search for Adelic Structure in the Standard Model Mass Spectrum (Version 2.3)
Version 1.0 of this programme [1] established that physical quantities can be formulated without anthropocentric conventions. Its extension into an "Adelic Theory of Everything" [2] attempted to match Standard Model particle masses to CM j-invariants via decimal PDG data — an approach we now…
Beyond the Qubit: Constructive Paradigms for Post-Particle Computation
Companion paper to "The Qubit Delusion" (v1.1, https://papers.qnfo.org/papers/paper-the-qubit-delusion/). If the qubit-gate-circuit model is an epistemic failure — a projection of particle ontology onto relational, field-theoretic reality — what comes next? We strip quantum mechanics to its minimal…
Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α
The fine-structure constant alpha is reframed as the cross-ratio of two measurable electron length scales (classical radius / Compton wavelength). Version 1.0 adds the adelically extended cross-ratio on Bruhat-Tits buildings, explicit falsifiability conditions, and synthesis with the QNFO adelic…
Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding
Shows that the ZBW-induced oscillatory trajectory of a Dirac fermion in a Bruhat-Tits building generates the braid group B_n, establishing ZBW as a physical mechanism for p-adic anyon braiding in topological quantum computation.
Bruhat-Tits Readout Protocol: Measuring the ZBW Z2 Invariant in Majorana Systems
Proposes three measurement protocols for the p-adic Z_2 invariant: Direct current-correlator measurement, Hensel-lifting amplification via the Bruhat-Tits building, and Gromov delta-hyperbolicity comparison of ZBW trajectories in Dirac/Majorana systems.
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
Formulates Zitterbewegung as a p-adic topological observable. Establishes that the ZBW current J_mu_ZBW carries a Z_2 invariant encoding the Dirac/Majorana distinction, and proposes ultrametric readout protocols via Bruhat-Tits buildings.
p-Adic Braid Groups on Bruhat-Tits Buildings
Constructs p-adic braid groups on Bruhat-Tits buildings, establishing the geometry of discrete braiding.
Bruhat-Tits Tree as a Unifying Geometric Object
Modern artificial intelligence, particularly in high-stakes domains, is hampered by a fundamental geometric mismatch: the reliance on continuous, “flat” Euclidean spaces to represent intrinsically hierarchical data. This incongruity leads to information loss and the proliferation of opaque “black…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
Formal Derivation of Emergent Spacetime to the Bruhat-Tits Tree
The fundamental incompatibility between the continuous spacetime of general relativity and the background-dependent time of quantum mechanics suggests that time is not a fundamental constituent of reality. This paper addresses the ontological crisis of time by formally deriving macroscopic spacetime…
Adelic Cross‑Ratio
Every quantitative description of the physical world relies on a choice of coordinate system—a language with its own scales, units, origin, and orientation. The same underlying reality can be expressed in infinitely many such languages, each assigning different numerical coordinates to the same…
KINETIC ISOMORPHISM
The schism between the time-reversible, unitary laws of quantum mechanics and the irreversible, adaptive nature of biological systems constitutes a central failure of modern ontology. We propose the kinetic isomorphism, a unified theoretical framework demonstrating that “static” matter and “active”…
Operationalizing Generalized Symmetries
The experimental realization of Fractional Chern Insulators (FCIs) in twisted moiré superlattices has opened a new frontier for topological physics, yet the classification of their underlying generalized symmetries remains theoretically abstract. This study operationalizes the framework of…
Nature of Zitterbewegung
Zitterbewegung, a profound and counterintuitive prediction of relativistic quantum mechanics, describes an intrinsic property of fundamental matter lacking a direct classical counterpart. This phenomenon challenges conventional notions of particle motion, revealing a deeper layer of reality governed…
Universe as Self-Proving Theorem
This document establishes a Geometric Unification Framework positing that the universe is a self-proving theorem, where physical laws and fundamental constants emerge as necessary consequences of its inherent logical and geometric consistency. The framework employs category theory as its…
The Bridge Theorem: A Rigorous Mathematical Framework Connecting p-adic and Bruhat-Tits Geometries
A rigorous mathematical framework establishing bridge connections between p-adic ultrametric spaces and Bruhat-Tits buildings.
Radix to Ultrametrics to Page-Wootters to Wheeler-DeWitt to Bruhat-Tits: A Convergent Synthesis
Convergent synthesis bridging discrete p-adic ultrametrics with continuous quantum geometry via Page-Wootters, Wheeler-DeWitt, and Bruhat-Tits buildings.
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