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609 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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Teaching papers 33 papers
Teaching. Course and seminar material Tagged papers: 33.
Flag Structures and the Flagging Act: A Cross-Domain Survey with Explicit Counting Derivations and a Posed Re-Entry Problem
The word "flag" names a family of mathematically precise objects — chains of nested subspaces (flag varieties), nested set systems with exchange axioms (flag matroids), asymptotic-inequality certificates (flag algebras), and directional curvature invariants of Finsler spaces — and, in ordinary…
Emergent Universality from Symmetric Rules: Rule-110 Emulation by Alternating Trivial Cellular Automaton Rules
Elementary cellular automaton (ECA) rule 110 is Turing complete, yet its local rule is chiral: it treats its left and right neighbours differently, and this handedness underlies the glider dynamics that carry its computation. A recent construction shows that rule 110 can nevertheless be emulated by…
One Metalogic, Many Logics: A Quantitative Pedagogical Framework for Proof-Assistant-Based Logic Teaching with LogiKEy
Teaching logic to mixed cohorts of computer science, mathematics, and philosophy students is difficult because each cohort brings different expectations and because the standard curriculum fragments into isolated courses on propositional, modal, epistemic, and deontic logic. The LogiKEy methodology…
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…
From Statements to Questions: AI as Epistemic Repair Infrastructure
Human conflict often begins not with a lack of speech, but with speech that has hardened into statements. Statements can conceal the assumptions that make them possible: what one side takes as perception, the other experiences as accusation. This poster proposes a practical framework for using large…
Visual Graphs vs Matrices: Epistemic Limits, Cognitive Preference, and the Design of Understandable Computation
The ZX calculus and the matrices of linear algebra denote exactly the same maps. A field that knows this has, nonetheless, converged on the pictures. This paper argues that the convergence is not a matter of taste and not a matter of mathematics: it is a fact about bounded cognition. Where…
ZX Diagrams at the Seam: Spiders, Pauli Webs, Gadgets, and the Cafeteria Problem of Cross-Disciplinary Imports
Diagrammatic languages are the most successful interface between quantum computing and the human mind. The ZX calculus — with its spiders, Pauli webs, and gadgets — is taught as the intuitive picture of quantum processes, and its completeness theorems are among the finest results in the field. Yet…
The Universal Ignorance Audit: A Fifteen-Question Method for Systematic Inquiry into the Structure of Not-Knowing
The Universal Ignorance Audit is a fifteen-question, five-phase method for systematically interrogating the structure of not-knowing in any domain. Where conventional epistemic tools treat ignorance as an absence to be filled, the audit treats it as an active, structured state with architecture:…
Frequency as Valuation Theory: The Rational Ratio at the Heart of Physical Law
Frequency in dimensionless Planck units is a rational ratio a/b in Q. The Compton frequency of a fundamental particle is its invariant identity — its prime spectrum.
Autaxys Ontological Closure: When Is a Physical Quantity Computationally Real?
We propose an operational criterion for physical reality: a quantity is physically real only if there exists a finite Turing-machine protocol that approximates it with a computable modulus of convergence, yielding measurement-distinguishable predictions. This criterion is not a metaphysical claim…
Pillar 3: PBO/Autaxys — Pattern-Based Ontology as Intrinsic Self-Ordering
PBO/Autaxys: Pattern-Based Ontology as Intrinsic Self-Ordering
The RG-Harmonic Isomorphism: Synthesis of Eight Research Question Deliverables
Synthesis paper unifying 8 research question deliverables from the RG-Harmonic Isomorphism spinoff program. Confirms the harmonic oscillator as the universal grammar of quantum theory across all 5 pillars.
The Revolutionary Beginner's Guide to Quantum Computing: Why We Don't Have Quantum Computers Yet — and What the Geometric Alternative Offers
A 20-chapter beginner's guide to quantum computing that starts with an honest question — why don't we have quantum computers yet? — rather than the usual "here's what a qubit is." The guide teaches the standard curriculum (qubits, entanglement, algorithms, error correction) accurately, explains why…
Embodied Mathematics After Lakoff & Nunez: A QNFO Perspective
This review examines Where Mathematics Comes From (Lakoff & Núñez, 2000) from the QNFO perspective, identifying convergence on anti-Platonism, the symbol-concept distinction, and critique of formalism. Extensions include ultrametric formalization of the four grounding metaphors and a cognitive…
A Skeptical Journey Through Conventional Reality
Journey Through Conventional Reality Questioning the Foundations Beneath Our Scientific Stories Rowan Brad Quni We live immersed in narratives woven by science–tales of fundamental particles, computational minds, and infinite cosmic possibilities. These stories are powerful, shaping our…
Knowing Patterns: An Epistemology for People Tired of Being Fixed
No steps. No habits to install. No “mindset shifts” to practice until they stick. No journaling prompts. Descriptions of how patterns work. In physics. In biology. In the daily motion of attention, mood, action, and thought. Descriptions of what a “thing” actually is (a temporary knot of relations)…
Syntactic Generation
Traditional models of physical reality rely on the assumption of foundational substances. These base materials are typically conceptualized as particles, fields, or continuous spatial manifolds. Such approaches inevitably generate persistent philosophical dualisms and questions regarding ultimate…
Care Is Stronger
Disagreement functions as an inevitable component of human relationships. Political ideology, moral values, and personal life choices frequently create divisions between individuals. This document examines the psychological processes that transform simple disagreement into relational rupture. It…
Mechanistic-Ethics
URL: https://papers.qnfo.org/papers/mechanistic-ethics-and-the-biology-of-meaning/ Date: 2026-03-04 Version: 1.0 1.1 The Clockwork Universe Superdeterminism posits that every event, including the firing of human neurons, occupies a fixed coordinate sequence established at the universe’s singularity.…
Static Architecture of Reality
URL: https://papers.qnfo.org/papers/static-architecture-of-reality/ Date: 2026-03-21 Version: 1.0.1 Human consciousness presents a world in constant flux. From the rotation of planets to the decay of particles, every measurement confirms a dynamic universe. This experience of temporal flow is so…
The Threshold of Meaning
Chapter 1: Defining the Undefinable–Language, Semantics, and the Limits of Words - 1.1 The Problem of Contested Terms: “Life,” “Death,” and “Afterlife”–Historical, legal, biological, and spiritual definitions. - 1.2 Linguistic Registers: Propositional, Performative, Narrative, Poetic–How context…
WINDING NUMBERS AND STRANGE LOOPS
The historical preference for linear mathematical frameworks in physics represents a profound ontological oversight. This paper establishes that physical reality emerges not from linear foundations with circular corrections, but from circular/topological primitives with linear projections. The…
Double Pendulum as a Topological Bridge
The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold…
New School of Athens
Raphael’s School of Athens is more than a masterpiece of the High Renaissance; it is a near-perfect visual schema of the central tension in Western thought. At its focal point, Plato’s finger directs our gaze upward, to a transcendent realm of Forms, of pure pattern and a priori truth. Beside him,…
Topology of Quanta
The historical development of quantum mechanics was marked by a profound bifurcation between physical intuition and mathematical formalism, a divergence often characterized as a category error that delayed the integration of topology into physics by nearly a century. This paper argues that the…
An Epistemic Mirror
This paper reframes the “hard problem” of consciousness from an intractable ontological mystery to a tractable problem of epistemology. It argues that the explanatory gap is a structurally necessary epistemic boundary condition of any cognitive architecture that employs dimensionality reduction for…
Math is NOT the Universe
This report re-evaluates our Euclidean understanding of reality, showing its inadequacy for modern physics. It traces the shift from Newtonian absolute spacetime to Einstein’s curved spacetime and the scale-dependent complexities of fractal geometry and quantum theory. This analysis argues for a…
Quantum Mechanics as Applied Wave Harmonics
This textbook introduces a deterministic derivation and reinterpretation of quantum mechanics from the first principles of classical wave mechanics. It argues that all phenomena conventionally attributed to quantum mechanics are emergent properties of a fundamentally classical reality composed of…
Standard Model
The Standard Model (SM) of particle physics represents the most precise and empirically successful framework devised for describing fundamental particles and their interactions. This rigorous empirical success is intrinsically coupled with severe, formally demonstrable theoretical deficiencies that…
The Simplicity of Reality: Deconstructing the Mathematical Epicycles of Modern Physics
Simplicity of Reality: Deconstructing the Mathematical Epicycles of Modern Physics Abstract: This paper argues that the impenetrable mathematical abstraction of modern theoretical physics is not a necessary feature of reality, but a direct symptom of a flawed ontological foundation initiated by…
Part I: Observing Ignorance
Our journey into the information spectrum begins with a fundamental question: How aware are we of what we know and, more importantly, what we don’t know? This isn’t a simple yes-or-no answer. Information awareness isn’t a light switch, flipped on or off; it’s a dimmer, capable of expressing a wide…
(Imperfectly) Defining Reality: Our Human Quest to Construct Reality from Science
This inherent drive within the scientific method, particularly as it solidified during the Enlightenment and the subsequent rise of positivism, prioritizes the operationalization and quantification of phenomena. The need for repeatable experiments, shared understanding among researchers, and the…
Continuum is Real
For over a century, physics has been defined by an ontological schism. The continuous, deterministic, and local reality described by classical mechanics and general relativity stands in direct opposition to the discrete, probabilistic, and non-local phenomena of quantum mechanics. This division has…
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