Quick read · plain language
A New Way to Connect Discrete and Continuous Physics
A plain-language version of “Ratio-Based Adelic Physics”
The short version
This paper builds a new math framework that uses scaling ratios instead of whole numbers to connect tree-like discrete structures with smooth continuous space. It claims this explains error correction in quantum computing, language structure, and cosmic expansion, but admits it still needs real-world testing.
The problem with current physics
Physics today uses two different pictures of space that do not fit together. One picture treats space as smooth and continuous. The other picture treats complex systems as tree-like and step-by-step. This split causes trouble when physicists try to unite quantum mechanics with larger cosmic models. The paper says this tension is the main blockage in modern science.
The older Sherrington-Kirkpatrick model of magnetism assumes every part talks to every other part equally. This works for math but not for real three-dimensional objects. Real spin glasses in three dimensions do not show the tree-like behavior the model predicts. Some scientists say the tree behavior hides under noise. Others say the model simply fails in three dimensions. This fight has lasted for years without clear resolution.
The new ratio-based approach
The paper introduces a new way to build tree structures using any scaling ratio, not just whole number primes. This means ratios like pi or the golden ratio can serve as the base for building hierarchical spaces. The trees built this way have branches and edge weights tied to these ratios.
A special operator called the Vladimirov operator governs how things move across these trees. Its energy levels come in discrete steps set by the scaling ratio. The paper shows this operator smoothly connects to normal calculus when the ratio approaches one.
To bridge the tree world with normal space, the paper uses something called the Monna projection. This maps the infinite tree onto a simple line. The paper compares this to how a quantum wave function collapses to one state when observed.
What the paper claims to show
The paper reports several findings from computer simulations. Logical error suppression in quantum computing falls off exponentially with tree depth. Spatial dimensionality limits how symmetry breaking works in three dimensions. The Hubble constant for cosmic expansion comes out as a simple positive value from tree navigation depth.
The paper also says language parsing follows the same tree rules as magnetism. Sentence structure uses lowest common ancestor distance, not word order distance. This means human cognition and physical systems share one underlying geometry.
What remains unproven
The paper openly states several limits. The framework struggles to model pure continuous motion without using impossibly deep trees. Computing beyond certain scales exceeds what today's computers can handle. The paper relies on cut-off math proofs instead of full calculations in these cases.
The paper also admits it does not fit standard particle physics into this framework. It deliberately leaves out the standard model of particles and string theory landscapes. The cosmic predictions need checking against real cosmic background radiation data. The quantum error correction claims need testing with actual photonic spin glasses.
Words used here
- ultrametric
- a way to measure distance where the direct path is never longer than going through a middle point; like a family tree where two cousins are "close" because they share a recent grandparent, not because they live near each other
- replica symmetry breaking
- the way identical copies of a system freeze into different stable arrangements when cooled
- adelic
- a math approach that treats continuous and discrete number systems as equally valid partners
- Bruhat-Tits tree
- an infinite branching graph used to picture hierarchical number spaces
- Monna projection
- a rule that squashes an infinite tree structure down to a simple line
Learn more in plain language
- Quantum error correctionWikipedia (English, more technical)
- Spin glassWikipedia (English, more technical)
- Cosmic microwave background radiationSimple English Wikipedia
- Wave function collapseWikipedia (English, more technical)
- Ultrametric spaceWikipedia (English, more technical)
- Adele ringWikipedia (English, more technical)
This plain-language version was written by an AI model from the text of the paper and checked against plain-language rules: everyday words, no mathematics, no unexplained names. It leaves details out and can still be wrong; the paper is the source of record. To report a problem, open the paper, select the passage and choose Report.
For specialists: the technical digest, quoted from the paper
In the paper's words
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. This manuscript resolves these disparities by introducing a ratio-based adelic framework, utilizing generalized scaling ratios (q) and Bruhat-Tits tree topologies to replace traditional integer-prime models. By formulating the Vladimirov fractional derivative operator natively for arbitrary transcendental values and deriving the corresponding q-adic product formulas, this methodology actively maps discrete states onto continuous metrics using the Monna projection.
The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.
Numbers it reports
Continuous Topology and Ultrametric Complexity across Spin Glasses, Linguistics, and Cosmology Author: Rowan Brad Quni-Gudzinas Contact: rowan.quni@outlook.com ORCID: 0009-0002-4317-5604 ISNI: 0000000526456062 DOI: https://papers.qnfo.org/papers/ratio-based-adelic-physics/ Date: 2026-04-06 Version: 1.0.2 Abstract : 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.
from ReconcilingSection 3.0 provides the newly generalized ratio-based mathematical methods, including transcendental adelic products and the continuous Monna projection mechanism.
from 1.7 Structural PreviewIts eigenvalue spectrum fundamentally consists of discrete powers of the scaling ratio $q^{n\alpha}$, dictating that energy states are intrinsically quantized by the structural scale geometry itself (Dragovich et al., 2017).
from 3.3 The VladimirovWhile the resulting equations lack the simple arithmetic elegance of base-10 classical physics, their operational fidelity across multiple distinct scale regimes compensates entirely for the abstraction.
from 3.7 Methodological ValidationEmpirical 3D short-range Ising models fail to show this symmetry breaking simply because they are operating mathematically below the critical scaling threshold required to stabilize the hierarchy against thermal decay (Hed et al., 2004).
from 6.2 Resolving the
How it is done
By resolving the dimensionality dispute within 3D Ising models and formally deducing an emergent Lorentz symmetry directly from tree automorphisms, this generalized adelic ontology successfully projects discrete computational substrates onto continuous observables.
from ReconcilingThe study formally addresses how ultrametric topologies affect phase dynamics in disordered states, how scale ratios govern QEC thermodynamic limits, and how temporal dimensions emerge from static tree navigations.
from 1.6 Research Questions andValuations can be formally constructed using arbitrary scaling ratios $q \gt 1$, establishing absolute values derived purely from fundamental constants rather than base-10 numerical representations.
from 3.1 Ratio-Based ValuationConsequently, the Vladimirov operator acts as the master kinetic algorithm for ratio-based physics.
from 3.3 The Vladimirov
What would falsify it
Tension The fundamental architecture of physical reality exhibits a pervasive tension between the assumption of continuous Archimedean spacetime and the observable discrete, hierarchical nature of complex systems.
from 1.1 Context and FoundationalThis rigid constraint prevents the organic integration of $p$-adic mathematics into applied biophysics and observable cosmology.
from 2.4 P-Adic Mathematics inProduct Formulas for Transcendental Ratios Ensuring that these discrete $q$-adic calculations map safely to the observable macro-universe requires a unification equation bridging all mathematical completions.
from 3.4 Adelic
Where the claim stops
The framework natively struggles to model pure continuous dynamics without artificially executing infinite tree depths, inducing immense computational drag when approximating standard Newtonian physics.
from 6.7 Limitations of theEnding the discussion with responsible scientific skepticism does not weaken the core theorem, but rather maps the immediate territory for upcoming algorithmic refinement.
from 6.7 Limitations of theTension The fundamental architecture of physical reality exhibits a pervasive tension between the assumption of continuous Archimedean spacetime and the observable discrete, hierarchical nature of complex systems.
from 1.1 Context and Foundational
Where to read
- Reconciling244 words · 1 min
- 1.0 Introduction997 words · 4 min
- 2.0 Literature1,029 words · 4 min
- 3.0 Methodological Framework1,006 words · 4 min
- 4.0 Results I: Physical1,105 words · 5 min
- 5.0 Results1,128 words · 5 min
- 6.0 Discussion1,078 words · 5 min
- 7.0 Conclusion and Future709 words · 3 min
- Appendices730 words · 3 min
Read from the paper itself: 68 sections, 8,331 words. Nothing in this digest is written by a model; a line that is not a sentence of the paper is not shown. Have a specific question? Ask this paper.