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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” 20 papers
Ultrametric. Non-Archimedean geometry: tree metrics, strong triangle inequality, hierarchical distance Tagged papers: 115.
Ultrametric p-Adic Arithmetic as Energy-Proportional Precision Computing: An Energy Model for Digit-Terminable Multiply-Accumulate
Fixed-width Archimedean floating-point arithmetic pays a constant energy cost per multiply-accumulate (MAC) regardless of the precision actually required by the computation. The gap this paper addresses is the absence of any explicit joules-per-operation model connecting non-Archimedean digit…
Geometric Ratios as Generators of Hierarchical Structure: An Arithmetic Audit of π, φ, and e
A recurring conjecture in the ultrametric-physics program holds that hierarchical—i.e., ultrametric—structure "emerges" when a scale ratio q is set equal to a fundamental geometric constant: π, the golden ratio φ = (1+√5)/2, or Euler's number e. This paper converts that conjecture into falsifiable…
Optimal Radix q under Resource Constraints: A Reconciled Derivation Framework for Ultrametric Hierarchies
Hierarchical (ultrametric) representations organize N items in a q-ary tree of depth n = ⌈ln N / ln q⌉, and the choice of branching factor q determines how storage, interconnection, and traversal resources scale. Prior ultrametric modeling has treated the radix as a fixed structural parameter…
The Distinction-Based Ultrametric: A Hierarchy Distance Without Primes, and the Statistical Test of Arithmetic Structure in Physical Spectra
Quantum mechanics is written in one completion of the rational numbers, the real line, though Ostrowski's theorem gives one completion for every prime. A line of work reads physical structure through those other places, but its empirical tests of prime-specific geometry in physical systems have…
The Consilience of the QNFO Keyword Taxonomy: Ultrametric Structure as a Testable Compression Prior
The QNFO research program spans seven domains — ultrametric physics, the laws of form, infomatics, paradigm engineering, consilience research, the QWAV platform, and interactive demos — and maintains a canonical keyword taxonomy of 335 terms used to scope external discovery. A recurring claim in the…
The Ultrametric Program: One Structural Object Across Seven Research Domains, and Its Falsifiable Tests
Seven research domains — ultrametric physics, the laws of form, infomatics, paradigm engineering, consilience research, a cloud-native platform, and interactive demos — are claimed to be seven vocabularies for one structural object: a nested, hierarchical partition logic. The object is defined by…
The Trapped-Ion Ultrametric Testbed: A Falsifiability Register for Testing p-Adic Structure in Quantum Dynamics
Twenty-one published records from a single research program, spanning December 2025 to August 2026, are here organized into one testable claim: trapped-ion quantum simulators are the first near-term platform on which ultrametric (p-adic) structure in quantum dynamics can be accepted or rejected by…
Non-Archimedean Projective Perspective: The Monna Map as a Visual Rendering Interface
Things farther away appear smaller, and two-point linear perspective is taken to approximate the eye. That entire phenomenology is Archimedean geometry. This paper asks what changes if the metric of physical space were instead non-Archimedean and ultrametric — would we perceive the same thing, and…
Radix-Agnostic Detection of Discrete Scale Invariance: A Certified Three-Stage Protocol and a Null Result from Planck 2018
Discrete scale invariance (DSI) — invariance under a discrete set of rescalings $x \to \lambda^n x$ — predicts log-periodic oscillations whose angular frequency in the logarithmic coordinate $u = \ln x$ is $\omega_0 = 2\pi/\ln\lambda$. When the scaling radix $\lambda$ is unknown, a radix-locked…
Boundary Ultrametricity: The Tree vs. ∂∞𝒯 Distinction, Applied to the ZBW Transition Graph
The QNFO corpus frequently conflates two distinct mathematical properties of trees: 0-hyperbolicity (of the vertex/graph metric) and ultrametricity (of the boundary metric). This note formalizes the distinction, proves the boundary Gromov-product metric on…
Searching for P-Adic Log-Periodic Signatures in the Cosmic Microwave Background Bispectrum: Upper Bounds from Planck 2018
Discrete scale invariance under integer rescalings of scale — the observable fingerprint of a p-adic (ultrametric) structure in the primordial fluctuation field — predicts log-periodic oscillations in the cosmic microwave background (CMB) statistics. The two-point angular power spectrum was already…
Passive Error Resilience Through Ultrametric Geometry: A Proposal for p-Adic Quantum Metrology
Active quantum error correction is the dominant paradigm for achieving fault-tolerant quantum computation, but its thermodynamic cost at utility scale remains unaddressed. Each round of syndrome extraction, decoding, and feedback erases information — and under Landauer's principle, that erasure…
Ultrametric Consilience Atlas: Cross-Domain Applications of p-Adic Mathematical Structure
A single mathematical structure — the p-adic ultrametric topology — appears in apparently unrelated domains: quantum error correction (stabilizer codes), protein folding (energy landscapes), neural coding (population activity clustering), financial markets (hierarchical correlation), climate…
P-adic Spin, Information, and Ultrametric Internal Quantum Numbers
Paper I established that the Archimedean continuum the real numbers_c suffices for all physical dynamics — depth without breadth. Here we complete the picture: what of the ultrametric completions of the rational numbers? We argue that the p-adic numbers the rational numbers_p are not "extra spatial…
Ultrametric Engine: Deploying a 20-Principle p-Adic Discovery Worker
The theoretical framework developed in P1-P5 requires computational infrastructure to make ultrametric (p-adic) analysis accessible to experimentalists. We specify and deploy an ultrametric discovery engine — a Cloudflare Worker implementing 20 principles from the proven Ask QWAV production system.…
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…
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.
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…
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…
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