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  • Today, 5-6 May 2026
    • Key Pages of this Model
    • • New Foundations: An introduction
    • • Notations 0-10: The Geometric Foundation
    • • Notations 0-24: From Planck Scale to Grand Unification
    • • Geometric Emergence of Gauge Symmetries
    • • The 7.356° Gap: Natural Path From Geometry to Physics
    • • The Breaking Cascade: Notations 24-67
    • • E8 and Maximum Symmetry at Notation-32
    • • A Base-2 Map from the Planck Scale to the Observable Universe in 202.34 Steps
    • • Hubble Constant
    • • Langlands Correspondences as Physical Mechanism
    • •Testable-Predictions
    • • PPC: Analysis
    • • 202 Notations-Groups of 10
    • • Other pages:
      • • 2025: December 11 Anniversary
      • • DeepSeek – Pre-space-time
      • • RI-MOM (Regularization Independent-Momentum)
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    • March 4: Six AIs Concur
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    • Feb. 18: State of Universe
    • Feb.1: SOU First Draft
    • February – SOU
    • Jan. 22: Geometry-Physics
    • Jan. 18: Pure perfection
    • Jan. 3: 0-10 Notations
    • Jan. 3: Doradus
    • Jan. 2: Sagittarius B2
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    • Nov 10: Again-π-e-φ-√2
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    • March 13: Breakthrough
    • Feb. 28: Consciousness
    • Feb. 14: What Is Love?
    • February 10: Essences
    • Jan. 30: Absurdities
    • 2025: January 11 – AI Intro
    • 2024
    • 2024: Dec. 30: – Grokked!
    • Dec. 14: Structures
    • December 3: Paradigms
    • November 15: Thought
    • October 16: First Instant
    • October 2: Infinitesimals
    • 9-11: Interdependencies
    • Sept. 3: Too Simple
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    • July 14: Enigmatic Univ.
    • July 5: Mistaken
    • July 1: First Page
    • June 8: You, you, you
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    • May 21: Nobel Laureates
    • May 8: big bang on ice
    • April 22: Frank Wilczek
    • April 8: Study Mistakes
    • March 21: Number Theory
    • Mar. 13-14: Pi Day
    • March 10: Qualitative
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    • Jan. 9: 12 Key Concepts
    • Jan.8: What’s infinite?
    • Jan.5: What’s time?
    • Jan. 4: Grasp it all
    • 2024: Jan. 2 – New year
    • 2023
    • 2023: Dec. 12, End-Of-Year
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    • Oct. 27: New Science
    • Oct. 20: Standard Model
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    • Sept. 28: UniverseView
    • Sept 23: Exquisite Grid
    • Sept.15: Eight-Minutes
    • Aug. 30: Third Way
    • Aug. 23: No Big Bang
    • August 17: Perfect Start
    • July 31: Start/Grow
    • July 20: Planck Scale
    • July 1: Revolutions
    • June 18: AI Ethics
    • May 31: Be creative
    • May 30: Jinping / Marx
    • May 20: The Firsts
    • May 3: Most Simple
    • Apr 20: The basics
    • April 4: Resolution
    • Mar. 21: Beyond pi (π)
    • March 4: Pi Day 2023
    • Feb. 3: New Inflaton
    • Jan 27: Pi, finite-infinite
    • 2023 Jan. 21: de facto de jure
    • 2022 Dec. 23: All Time Is Now
    • 19 December 2022
    • Dec. 6: All-Natural View
    • Dec 1: Paradigm Shifts
    • Nov 23: BB Versus QE
    • Nov. 6: Big Bang Silent
    • Oct. 8: Reason to believe
    • Sept. 25: JWST Smooth
    • Sep 9: Universe/Math
    • August 31: Conundrums
    • August 4: Simple Model
    • July 28: Eight Concepts
    • July 12: Starting Point
    • July 10: Basic Gaps
    • June 29: The Knowns
    • Apr 15: Questions
    • June 9: Editors
    • June 3: 202 Notations
    • May 30: New Way
    • May 17: Perfection-Gaps
    • May 14: Agreements
    • Apr 30: Hypostatics
    • Apr 8: Point Particle
    • Apr 5: Fourier Gravity
    • April 2: Checklist
    • April 2: Re-envision
    • April 2: Begin Here
    • March 17: STEM Tool
    • March 14: Pi Day
    • Mar 2: My Universe View
    • Feb.26: Vladimir Putin
    • Feb 16: Known Unknowns
    • Feb 1: Prove It To Me
    • Jan 8: The First Particle
    • Jan 2: Tredecillions
    • 2022 Jan. 2: Primordial
    • 2022
    • 2021 Nov. 18: Almost there
    • Nov. 10: Questions
    • Oct. 19: Extremes
    • October 6: Key Concepts
    • Sept. 10: Virtual Reality
    • June 10: Empower
    • June 5: Re-envision It All
    • June 1: Envision A Start
    • May 12: Universe Starts
    • April 12: Questions
    • Mar. 23: James Peebles
    • March 14: Pi Day
    • Jan. 25: Essentials
    • 2021 January 18: Precis
    • 2021
    • 2020 Dec. 26: Conscious
    • Dec. 14: The First Instant
    • November 16: Expansion
    • Oct. 29: Our history
    • October 16: Countdown
    • Sept. 23: Kinder, Gentler
    • Sept 18: Continuity
    • Sept. 15: Our Goals
    • Aug. 16: Just A Second!
    • Aug. 2: First Minutes
    • July 20: Concepts & Ideas
    • June 25: Integrate All
    • June 9: The Now
    • May 24: Biased
    • May 23: Infinite-Finite
    • April 23: Warm & Fuzzy
    • April 2: Indeterminancy
    • Mar. 24: Space-time
    • Mar. 8: Imperfections
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    • Feb 23: Perfection
    • Feb. 9: 12 Keys
    • Jan 24: Alternatives
    • Jan 10: Departures
    • 2020 January 1, 2020: The “I”
    • Dec. 20: Model Review
    • Dec. 18: Newton’s Curse
    • Dec. 10: Access it all
    • Nov. 28: Compilation
    • Nov. 11: Finite-Infinite
    • Oct. 12: Map the Universe
    • October 1: Simple Model
    • Sept 14: Bottom-up
    • Aug.14: Nobel Laureates
    • Aug. 1: Transformation
    • July 14: More questions
    • July 2: Nature of Time
    • June 17: Gell-Mann
    • June 11: From Lemaître
    • June 9: Hattie is right
    • May 2019: Structure II
    • April 28: Finite-Infinite
    • April 22: Structure I
    • April 20: New STEM
    • April 3: Pi-to-E8
    • Mar. 30: Maybe
    • Mar. 25: Key Pages/Chart
    • Mar. 24: Start-Begin
    • Mar. 23: The Sphere
    • Mar. 22: Looking Back
    • Mar. 11: Five Constructs
    • Mar. 10: Pi Day 2019
    • Mar. 6: Steps Redefine
    • Mar. 5: Foundations
    • Mar. 4: Universe Clock
    • March 1: Assumptions
    • Feb 28: Calculations
    • Feb 24: Open Questions
    • Jan. 31: Key Question
    • 2019 (January): Model
    • 2019
    • Dec 16: Buzz Lightyear
    • Dec. 11: Planck Scale
    • Dec 7: Reformulating
    • Nov. 12: “To Infinity”
    • November 6: No Elitism
    • Oct. 26: Overview
    • Oct. 23: Points
    • Oct. 22: Quantum Gravity
    • Oct: Weinberg-Wheeler
    • Oct. 20: Five Stories
    • Oct. 16: Dark Stuff
    • Oct. 12: What now?
    • Oct. 1: 64 Notations
    • October: Everything…
    • Sept. 28: Open Letter II
    • Sept. 20: Gravity
    • Sept. 19: A Simple Way
    • Sept. 17: Open Letter
    • Sept. 14: Your Review
    • Sept. 12: Questions
    • Sept 5: Commonsense
    • Aug. 26: Problems
    • August 3: Functions
    • July 27: Attitudes
    • July 23: Options
    • July 16: Standard Models
    • July 8: Compilations
    • July 4: Revolutions
    • June 21: Emergence
    • June 10: Measurements
    • May 18: Alternative
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    • April 16: Einstein
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    • March 15: Redefine
    • March 14: Pi Day
    • March 5: Our Goals
    • March 1: Cosmology III
    • Feb. 17: Finite-infinte
    • Feb. 10: Cosmology II
    • Feb. 3: Cosmology I
    • Jan. 27: What if
    • 2018
    • 2018, Jan. 24: Team
    • Dec 22, 2017: Lucasians
    • Dec 19: Anniversary
    • Dec 3: Little Index
    • Nov 15: Simple First
    • Nov 27: Fabric d’Universe
    • Nov 18: Pi to Forms
    • Nov 12: Seven Reasons
    • Nov 11: Veterans’ Day
    • Nov 9: Overview
    • Nov 6: Exascale
    • Nov 8: Expo-Universe
    • Nov 5: The Infinite
    • Nov 4: Dusty roads
    • Nov 3: Open Dialogue
    • Oct 28: Who What When
    • Oct 20: Simple Concepts
    • Oct 7: In Search Of
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    • Sept 27: Belief Systems
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    • Sept: Big Bang Is Wrong
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    • Dec 18: Kings & Queens
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"One Sphere to the Standard Model to the universe: How Base-2 Geometry Generates Gauge Symmetries"

Genesis: Quaternions – Gauge Symmetry

An illustration depicting various geometric shapes: four spheres, a tetrahedron icon with four vertices, and mathematical symbols related to quaternions, labeled as part of 'The Inescapable Geometric-to-Algebraic Pipeline'.
A diagram illustrating the multiplication table of quaternions, showing relationships between the elements i, j, k, and their negatives, with arrows indicating multiplication direction.

https://upload.wikimedia.org/wikipedia/commons/a/a5/Cayley_Q8_multiplication_graph.svg

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