A complete guide to understanding GIFT, explained for humans
Each concept has:
Whether you’re a curious student, a science enthusiast, or just someone who wondered “why is the universe the way it is?”, this guide is for you.
GIFT (Geometric Information Field Theory) proposes that the fundamental constants of physics — numbers like 1/137, the masses of particles, the strengths of forces — are not arbitrary. They emerge from the shape of hidden dimensions in the universe.
The core idea in one sentence: The universe has 7 hidden dimensions curled up in a specific shape called K₇, and the properties of this shape mathematically determine everything we measure.
Why should you care?
The Standard Model of physics has 19 free parameters — numbers we measure but can’t explain. Why is the electron 1836 times lighter than the proton? Why are there exactly 3 families of particles? Why is the fine structure constant 1/137?
GIFT proposes answers: zero free parameters. Everything comes from geometry.
The fancy word: Field of real numbers, dimension 1.
The kitchen table version: A ruler. The numbers we use every day: 1, 2, 3.14159…, -7, √2. You can place them on an infinite line.
In GIFT: The basic brick. Everything else is built on top.
The fancy word: Extension of reals with imaginary unit i² = -1, dimension 2.
The kitchen table version: A treasure map. With real numbers, you can only go left or right on a line. With complex numbers, you have a 2D map: left/right AND up/down. The number “i” is simply “one step up.” And i × i = -1 means “two steps up = turn around.”
Everyday use: The electricity in your home uses complex numbers! Alternating current “rotates” like a needle on the map.
In GIFT: Complex numbers describe the phases of quantum waves.
The fancy word: 4-dimensional division algebra with three imaginary units i, j, k.
The kitchen table version: The video game controller. Want to rotate a 3D character in a game? Quaternions have 4 components (1 real + 3 imaginary: i, j, k) that can describe any 3D rotation without “gimbal lock” (the bug where sometimes two axes merge).
Fun fact: Discovered in 1843 by Hamilton, who carved the formula i² = j² = k² = ijk = -1 on a bridge in Dublin!
In GIFT: Intermediate step toward octonions. Shows that number systems “grow” by powers of 2.
The fancy word: 8-dimensional division algebra, non-associative.
The kitchen table version: The ULTIMATE Lego kit.
| System | Dimension | What you can do |
|---|---|---|
| Reals | 1 | Measure a length |
| Complex | 2 | 2D rotations, electricity |
| Quaternions | 4 | 3D rotations, video games |
| Octonions | 8 | Everything possible |
After octonions, there’s nothing more. Mathematically proven (Hurwitz theorem, 1898). It’s the richest number system that exists.
The weirdness: Octonions are not “associative.” (a × b) × c ≠ a × (b × c). It’s as if the order you assembled your Legos changed the final result!
In GIFT: The universe uses the most complete kit available. The 7 imaginary units of octonions give the 7 dimensions of K₇.
The fancy word: 16-dimensional algebra, but no longer a division algebra.
The kitchen table version: The defective Lego kit. You can keep doubling: 16, 32, 64… But starting at 16, the “Legos” no longer fit together properly. You can have pieces that, multiplied together, give zero even if neither is zero. It’s broken.
In GIFT: This explains why nature stops at octonions. No choice — it’s the last “proper” algebra.
The fancy word: The smallest finite projective plane, PG(2,2).
The kitchen table version: The perfect social network.
7 people, 7 WhatsApp groups:
It’s the most “efficient” configuration possible. No redundancy, no gaps.
1
/|\
/ | \
/ | \
2---7---3
\ | /
\ | /
\|/
4---5---6
The magic trick: This network has 168 ways to rearrange itself while keeping the same structure (like a Rubik’s cube). And 168 ÷ 56 = 3. Three particle families!
In GIFT: The Fano plane encodes octonion multiplication. It’s the “times table” of the universe.
The fancy word: Set equipped with an associative operation, with identity element and inverses.
The kitchen table version: A club with rules.
A mathematical group is like a club where:
Simple example: The rotations of a square form a group. You can rotate by 0°, 90°, 180°, 270°. Two rotations combined = another rotation. The 0° rotation changes nothing. Each rotation has its inverse.
The fancy word: Unitary group of dimension 1, isomorphic to the circle.
The kitchen table version: The clock hand. U(1) is all the ways to point in a direction on a circle. The hand can be at noon, at 3 o’clock, at 7:42… it’s a continuum of positions.
In physics: It’s the symmetry group of electromagnetism. Changing the “phase” of a charged particle (like rotating the hand) doesn’t change observable physics.
In GIFT: U(1) naturally emerges from larger structures like E₈.
The fancy word: Special unitary group of dimension 2, double cover of SO(3).
The kitchen table version: The Möbius strip of rotations.
Imagine you spin around 360°. Normally, you’re back where you started, right?
Not in quantum mechanics! You need to spin 720° (two full turns) to truly return to the initial state. It’s as if the universe counts half-turns.
SU(2) captures this weirdness: it has “twice as many” elements as ordinary rotations.
In physics: It’s the group of the weak force (the one that causes radioactivity). It also describes electron spin.
In GIFT: SU(2) is contained in G₂ and E₈.
The fancy word: Special unitary group of dimension 3, dimension 8.
The kitchen table version: The RGB paint mixer.
Quarks have a property called “color” (nothing to do with real colors, it’s just a name). There are 3 colors: red, green, blue.
SU(3) describes all the ways to mix these colors together, like a sophisticated paint mixer that can turn red into green, green into blue, etc.
In physics: It’s the group of the strong force (the one that glues quarks together). The 8 “gluons” correspond to the 8 dimensions of SU(3).
In GIFT: dim(SU(3)) = 8 = dim(𝕆). Coincidence? GIFT says no.
The fancy word: Smallest exceptional Lie group, dimension 14, automorphisms of octonions.
The kitchen table version: The guardian of the octonions.
Imagine a crystal ball with patterns inside. G₂ is the set of all transformations that preserve the structure of octonions. It’s like the set of ways to rearrange a Rubik’s cube while keeping the rules of the game intact.
Why 14? Octonions have 7 imaginary units. The transformations preserving them form a 14-dimensional space. It’s a mathematical fact, not a choice.
The 5 exceptional groups: G₂, F₄, E₆, E₇, E₈ — these are the “outsiders” in the classification of Lie groups. They don’t belong to any infinite family.
In GIFT: G₂ is EVERYWHERE. dim(G₂) = 14 appears in Koide (14/21 = 2/3), in δ_CP (7×14+99), etc.
The fancy word: Exceptional Lie group of dimension 52.
The kitchen table version: The architect of the halfway house. F₄ is related to the “octonion plane” (the octonionic projective plane).
In GIFT: dim(F₄) = 52 appears in scale bridge calculations.
The fancy word: Exceptional Lie group of dimension 78.
The kitchen table version: The grandparent of symmetries.
E₆ contains SO(10) which contains SU(5) which contains U(1)×SU(2)×SU(3). It’s like the great-grandparent of all Standard Model symmetries.
Bonus: E₆ has a 27-dimensional representation linked to the exceptional Jordan algebra.
In GIFT: The Jordan algebra (dim 27) appears in m_μ/m_e = 27^φ.
The fancy word: Exceptional Lie group of dimension 133.
The kitchen table version: The mysterious older brother. E₇ has a fundamental representation of dimension 56. And 168/56 = 3!
| In GIFT: N_gen = | PSL(2,7) | / dim(fund(E₇)) = 168/56 = 3. |
The fancy word: Largest exceptional Lie group, dimension 248.
The kitchen table version: The Versailles Palace of math.
E₈ is the most complex and beautiful symmetry group that exists. Its structure is so rich that:
Fun fact: In 2007, a team of 18 mathematicians took 4 years to completely calculate E₈’s structure. The result is 60 gigabytes!
In GIFT: E₈ × E₈ (248 + 248 = 496 dimensions) is the fundamental symmetry group. 248 appears in m_τ/m_e = 7 + 10×248 + 10×99.
The fancy word: Reflection group associated with a root system.
The kitchen table version: The symmetries of a kaleidoscope.
Imagine a kaleidoscope. The mirrors create multiple reflections, and certain mirror configurations create patterns that repeat regularly. The Weyl group is the set of these “reflections” for a given Lie group.
For E₈: The Weyl group has an astronomical order: 696,729,600.
In GIFT: The “Weyl number” Weyl = 5 appears in various formulas.
The fancy word: Locally Euclidean topological space.
The kitchen table version: The surface of the Earth.
The Earth is round (a sphere), but when you walk around your neighborhood, it looks like a flat plane.
A manifold is the same: globally it can have a complicated shape, but locally (when you zoom in) it always looks like “normal” space.
The fancy word: Number of independent coordinates needed to specify a point.
The kitchen table version: How many questions to find you?
In GIFT: The universe = 4D visible + 7D hidden = 11D total.
The fancy word: Closed and bounded manifold.
The kitchen table version: An island vs the infinite ocean.
The surface of the Earth is compact: you can walk a long time, but you’ll eventually return to your starting point.
In GIFT: K₇ is compact — the 7 dimensions are “folded” on themselves, not infinite.
The fancy word: Compactified spatial dimensions beyond the observable 3+1.
The kitchen table version: The garden hose.
From far away, a garden hose looks like a line (1 dimension).
Up close, you see it’s a tube — each point on the “line” is actually a little circle (1 + 1 = 2 dimensions).
The universe might be the same:
The 7 curled-up dimensions have the shape of K₇.
In GIFT: We don’t “see” K₇, but its properties dictate the constants we measure.
The fancy word: Compact Kähler manifold with vanishing first Chern class (Calabi-Yau) vs compact manifold with G₂ holonomy.
The kitchen table version: K₇’s cousins.
Calabi-Yau spaces are the “hidden shapes” used in traditional string theory. They have 6 dimensions (to make 10 total with 4 of spacetime).
Problem: There are BILLIONS of different ones (the famous 10^500 solution “landscape”). Which one to choose?
In GIFT: K₇ (G₂ holonomy, 7 dimensions) is more constrained than Calabi-Yau (SU(3) holonomy, 6 dimensions). G₂ achieves 13× better precision than Calabi-Yau approaches.
The fancy word: Compact 7-dimensional manifold with G₂ holonomy, constructed by “twisted connected sum.”
The kitchen table version: The cosmic diabolo.
Imagine a diabolo (the juggling toy):
K₇ is a “7-dimensional diabolo” whose shape is dictated by octonions (via G₂).
Its characteristics:
In GIFT: Everything flows from K₇. It’s THE shape of the hidden universe.
The fancy word: Total space projecting onto a base space with fibers.
The kitchen table version: The hairbrush.
Imagine a hairbrush:
At each point of the base, there’s a “fiber” attached. The whole thing forms the bundle.
In physics: Spacetime is the base, and at each point are attached “fibers” containing information about fields.
In GIFT: K₇ is “fibered” over spacetime in a specific way.
The fancy word: Study of properties invariant under continuous deformation.
The kitchen table version: Play-Doh vs ice sculpture.
The classic: Coffee mug = donut. Both have exactly 1 hole (the mug handle = the donut hole). You can deform one into the other without cutting or gluing.
In GIFT: Physical constants are topological — they come from the “number of holes,” not distances. That’s why they’re stable and universal.
The fancy word: Quantities unchanged by continuous deformation.
The kitchen table version: A shape’s DNA.
You can change your hairstyle, clothes, gain or lose weight… but your DNA stays the same.
Topological invariants are shapes’ DNA. You can deform K₇ in a thousand ways, b₂ will stay 21 and b₃ will stay 77.
In GIFT: Physical constants = the universe’s DNA. They can’t be different.
The fancy word: Ranks of homology groups, counting independent cycles.
The kitchen table version: Counting holes in Swiss cheese.
| Betti | Counts what | Example |
|---|---|---|
| b₀ | Separate pieces | 1 block of cheese = 1 |
| b₁ | Through-tunnels | Hole you can poke through |
| b₂ | Enclosed bubbles | Trapped cavity |
| b₃ | 3D “hyper-bubbles” | (hard to visualize!) |
For K₇:
Why these specific numbers?
In GIFT: These two numbers are enough to calculate almost all physical constants! For example, sin²θ_W = 21/(77+14) = 3/13.
The fancy word: Dual theory of homology, with cochains.
The kitchen table version: The cosmic land registry.
If homology counts holes, cohomology classifies and labels them.
It’s like the difference between:
In GIFT: H² and H³ of K₇ give the spaces where different physical fields “live.”
The fancy word: Group of transformations obtained by parallel transport around loops.
The kitchen table version: Santa Claus’s test.
Santa Claus leaves the North Pole with his compass pointing South. He goes to the equator, turns right, goes around the Earth, returns to the North Pole.
Result: His compass has rotated 90°! Nobody touched it — it’s the curvature of the Earth that did it.
Holonomy measures “how much things rotate when you make a loop.”
G₂-holonomy = K₇’s curvature rotates things exactly according to G₂ rules (the 14 allowed directions).
In GIFT: G₂ holonomy is what links K₇’s shape to the octonions.
The fancy word: Alternating sum of Betti numbers: χ = Σ(-1)ⁿbₙ.
The kitchen table version: Euler’s magic formula.
For any polyhedron: Vertices - Edges + Faces = 2
A cube: 8 - 12 + 6 = 2 ✓ A tetrahedron: 4 - 6 + 4 = 2 ✓
This formula generalizes to all dimensions!
In GIFT: χ(K₇) is linked to the number of generations via the Atiyah-Singer index.
The fancy word: Measure of a connection’s deviation from being torsion-free.
The kitchen table version: The corkscrew.
Imagine you walk straight ahead, but space itself “twists” like a corkscrew. You end up having rotated without wanting to.
Torsion measures this “twisting” of space.
In K₇: Torsion must be very small (κ_T = 1/61) for physics to be consistent.
In GIFT: Joyce’s theorem guarantees we can have a torsion-free metric on K₇.
The fancy word: Section of an exterior bundle, generalizations of functions and vector fields.
The kitchen table version: The flux detector.
Imagine different types of “detectors”:
Differential forms generalize this to any dimension.
In GIFT: The 3-form φ (G₂’s associative form) defines K₇’s structure.
The fancy word: Half-integer spin particles obeying Fermi-Dirac statistics.
The kitchen table version: The individualists.
Fermions are “antisocial” particles: two fermions can never be in the same place in the same state.
That’s why matter is solid! Electrons (fermions) repel each other and don’t compress infinitely.
The family: Electrons, quarks, neutrinos, muons, taus…
The spin thing: You need to rotate a fermion 720° (two turns) to return to the initial state!
In GIFT: Fermions are associated with H³(K₇), hence b₃ = 77.
The fancy word: Integer spin particles obeying Bose-Einstein statistics.
The kitchen table version: The social butterflies.
Bosons love being together: they can all pile up in the same place in the same state.
That’s what enables lasers (lots of identical photons) and Bose-Einstein condensates (ultra-cold matter).
The family: Photons, gluons, W, Z, Higgs, graviton (hypothetical)…
In GIFT: Bosons are associated with H²(K₇), hence b₂ = 21.
The fancy word: First-generation charged lepton, mass 0.511 MeV.
The kitchen table version: The little sister.
The electron is the lightest charged lepton. It’s the one that orbits atoms and makes electricity.
It has two heavier siblings: the muon (×207) and the tau (×3477).
In GIFT: The electron defines the fundamental scale λ_e = h/m_e c.
The fancy word: 2nd and 3rd generation charged leptons.
The kitchen table version: The overweight siblings.
Exactly like the electron, but heavier:
Nobody knew why these precise ratios. GIFT says:
In GIFT: The three sisters (Koide) = dim(G₂)/b₂ = 14/21 = 2/3.
The fancy word: Neutral leptons, very light, weakly interacting.
The kitchen table version: The ghosts.
Neutrinos pass through matter as if it didn’t exist. Billions pass through you every second without you knowing.
They “oscillate” between three types (electron, muon, tau) while traveling — it’s like they change costumes in flight.
In GIFT: Neutrino mixing angles (θ₁₂, θ₁₃, θ₂₃) and CP phase (δ = 197°) are derived from topology.
The fancy word: Fermions carrying color charge, confined in hadrons.
The kitchen table version: The prisoners.
Quarks are always locked up in groups of 2 or 3. You can never see one alone — that’s “confinement.”
The 6 types:
In GIFT: Quark mass ratios like m_s/m_d = 20 are derived from topology.
The fancy word: Scalar boson of the electroweak symmetry breaking mechanism.
The kitchen table version: The cosmic molasses.
The Higgs field fills the entire universe like invisible molasses. Particles that interact with it “get stuck” and acquire mass. Those that don’t interact (photons) remain massless.
Discovery: 2012 at the LHC, 2013 Nobel Prize.
In GIFT: λ_H (Higgs coupling) = √17/32 = √(dim(G₂) + N_gen) / 2^Weyl.
The fancy word: Gauge boson of electromagnetism, zero mass, spin 1.
The kitchen table version: The messenger of light.
The photon IS light. It carries the electromagnetic force between charged particles. It always travels at the speed of light and has no mass.
In GIFT: Vacuum impedance (377 ohms) is linked to α via E₈ structures.
The fancy word: Gauge bosons of quantum chromodynamics, numbering 8.
The kitchen table version: The nuclear superglue.
Gluons “glue” quarks together. But unlike photons, gluons carry the charge themselves (color) — so they interact with each other!
Why 8? That’s the dimension of SU(3). And 8 = dim(𝕆), the dimension of octonions!
In GIFT: α_s = √2/12 (strong coupling) comes from dim(G₂) - 2 = 12.
The fancy word: Gauge bosons of the weak interaction, massive.
The kitchen table version: The heavy messengers.
W⁺, W⁻ and Z⁰ carry the weak force (the one behind radioactivity). Unlike the photon, they’re very heavy (~80-90 GeV), which is why the weak force has short range.
In GIFT: M_Z/M_W = √(13/10) comes from sin²θ_W = 3/13.
The fancy word: U(1) interaction between electric charges.
The kitchen table version: Magnets and electricity are the same thing.
Maxwell showed in 1865 that electricity and magnetism are two faces of the same force. Light is an electromagnetic wave.
In GIFT: α = 1/137.033 determines the strength.
The fancy word: SU(2) interaction responsible for β decays.
The kitchen table version: The particle transformer.
The weak force can transform one type of particle into another (e.g., a down quark into an up quark). It causes β radioactivity.
In GIFT: sin²θ_W = 3/13 describes weak/EM mixing.
The fancy word: SU(3) interaction between quarks via gluons.
The kitchen table version: The universe’s superglue.
It’s the strongest force (hence the name). It glues quarks in protons/neutrons, and protons/neutrons in atomic nuclei.
Weirdness: The more you try to separate two quarks, the stronger the force gets! That’s confinement.
In GIFT: α_s = √2/12 ≈ 0.1179 at the M_Z scale.
The fancy word: Spacetime curvature according to general relativity.
The kitchen table version: The cosmic trampoline.
Imagine spacetime as a trampoline. Masses “push down” on the trampoline, creating dips. Other objects roll toward these dips — that’s gravity!
In GIFT: Gravity potentially emerges from E₈ × E₈ structures at the Planck scale.
The fancy word: U(1) × SU(2) unifying EM and weak above ~100 GeV.
The kitchen table version: The cocktail before mixing.
At very high energy, electromagnetism and the weak force are indistinguishable — like vodka and orange juice in the glass before mixing.
As it cools, the “cocktail” separates: you get EM (photon) and weak (W, Z).
The mixing angle: sin²θ_W ≈ 0.231 says “how much” of each.
In GIFT: sin²θ_W = 21/91 = 3/13 = b₂/(b₃ + dim(G₂)).
The fancy word: Local symmetry group defining fundamental interactions.
The kitchen table version: The rules of the card game.
In a card game, certain rules define what’s “allowed”:
A gauge group is the set of rules that define a force.
In GIFT: E₈ × E₈ is the “original card game” from which all others are simplifications.
The fancy word: α = e²/4πε₀ℏc ≈ 1/137.036
The kitchen table version: The cosmic radio volume knob.
α measures “how strong” electromagnetism is. It’s the “volume” of interactions between light and matter.
If α were different:
Before GIFT: “That’s just how it is, we measure it, we don’t know why.”
GIFT: α⁻¹ = 128 + 9 + correction = 137.033
Where 128 = 2⁷ (linked to the 7 dimensions of K₇) and 9 = 99/11 (ratio of topological numbers).
In GIFT: Feynman said every physicist should have this number posted in their office to remind them of their ignorance. GIFT proposes an explanation.
The fancy word: Electroweak model parameter relating couplings.
The kitchen table version: The electroweak cocktail recipe.
At very high energy, electromagnetism and the weak force are the same force — like orange juice and vodka before being mixed.
sin²θ_W ≈ 0.231 means “about 23% weak force, 77% electromagnetism” in the final mix.
GIFT: sin²θ_W = 21/91 = 3/13
It’s the number of “2D bubbles” (21) divided by the total (77 + 14 = 91).
In GIFT: The cocktail recipe isn’t arbitrary — it’s dictated by the shape of the cosmic shaker (K₇).
The fancy word: (√m_e + √m_μ + √m_τ)² / (m_e + m_μ + m_τ) = 2/3
The kitchen table version: The three sisters.
Imagine three sisters: Electronette (very small), Muonica (medium), and Taulina (tall).
In 1982, a Japanese physicist (Koide) noticed something weird: if you take their “heights” in a certain way and do a calculation, you get exactly 2/3.
For 40 years, nobody knew why.
GIFT says: 2/3 = 14/21 = dimension of G₂ / number of 2D bubbles
The “heights” of the three sisters are dictated by the geometry of K₇.
In GIFT: This troubling coincidence becomes a logical consequence.
The fancy word: Why 3 fermion families in the Standard Model.
The kitchen table version: Why 3 Musketeers?
All particles come in 3 increasingly heavy “copies”:
Why not 2? Or 47?
Before GIFT: “We observe 3, we don’t know why.”
GIFT: The Fano plane has 168 symmetries. 168 ÷ 56 = 3.
It’s like asking “Why does a cube have 6 faces?” The answer isn’t “just because,” it’s “because it’s a cube.” The shape imposes the number.
In GIFT: The number of families isn’t an accident — it’s a geometric consequence.
The fancy word: φ = (1 + √5)/2 ≈ 1.618
The kitchen table version: The number of beauty.
φ appears in sunflower spirals, nautilus shells, the Parthenon facade…
In math: It’s the only number such that φ² = φ + 1.
In GIFT: m_μ/m_e = 27^φ. The golden ratio encodes mass ratios!
The fancy word: M_Pl = √(ℏc/G) ≈ 2.18 × 10⁻⁸ kg
The kitchen table version: The scale where gravity goes quantum.
At the Planck scale (~10⁻³⁵ m), gravity and quantum mechanics become equally strong. That’s where our current physics breaks down.
In GIFT: The “scale bridge” connects M_Pl to m_e via topological invariants.
The fancy word: Theory without adjustable constants.
The kitchen table version: IKEA vs Custom-made.
The Standard Model = Custom furniture. The carpenter takes 19 measurements at your place and builds furniture that fits perfectly. But he can’t explain why your living room has those dimensions.
GIFT = Universal IKEA furniture. The instructions say: “Take a 7-dimensional diabolo with G₂ holonomy.” There’s only one way to assemble it. The dimensions come out automatically.
In GIFT: 19 mysterious numbers → 0 mysterious numbers. Everything comes from the shape.
The fancy word: A theory’s ability to be refuted by experiment.
The kitchen table version: The real difference between science and horoscopes.
A horoscope says: “You will meet someone interesting.” Impossible to disprove.
GIFT says: “The neutrino CP phase δ_CP = 197°, no more, no less.”
The DUNE experiment will measure this in 2034-2039.
That’s science: predictions that can die.
In GIFT: GIFT plays the game honestly. It makes testable predictions.
The fancy word: Absence of fine-tuning, order-1 parameters.
The kitchen table version: No miraculous adjustments.
A theory is “natural” if it doesn’t need parameters tuned to 0.0000001% precision to work.
In GIFT: Zero adjustable parameters = maximum naturalness.
The fancy word: Properties appearing at one level that don’t exist at lower levels.
The kitchen table version: Water isn’t “wet” at the atomic level.
Individual atoms aren’t wet. “Wetness” emerges when billions of atoms are together.
In GIFT: 4D physical constants “emerge” from 7D topology.
The fancy word: Machine-checked mathematical proofs using proof assistants.
The kitchen table version: The ultra-strict math teacher.
Lean 4 is a computer program that checks every step of every proof. You can’t cheat, can’t make calculation errors, can’t “skip” a step. If Lean accepts your proof, it’s mathematically certain.
In GIFT: ~330 relations verified in Lean 4 with 0 “sorry” (holes). Zero domain-specific axioms.
The fancy word: International collaboration compiling particle physics data.
The kitchen table version: The official particle encyclopedia.
The PDG publishes the best values for all masses, lifetimes, etc. every year. It’s THE reference.
In GIFT: All comparisons use PDG 2024.
The fancy word: Hadron collider at CERN, 27 km circumference.
The kitchen table version: The world’s biggest microscope.
The LHC accelerates protons to nearly the speed of light and smashes them together. The collision energy creates new particles (E = mc²).
Major discovery: Higgs boson (2012).
In GIFT: The LHC measured W, Z, Higgs masses that GIFT predicts.
The fancy word: Deep Underground Neutrino Experiment, detector in the USA.
The kitchen table version: The ghost hunter.
DUNE will send neutrinos 1300 km and study their oscillations with unprecedented precision.
GIFT prediction: δ_CP = 197° ± 5° (measurable 2034-2039)
In GIFT: If DUNE finds δ_CP very different from 197°, GIFT is falsified. This is the key test.
The fancy word: ESA mission measuring the cosmic microwave background.
The kitchen table version: The universe’s baby photo.
The Planck satellite took the most detailed “photo” of the Big Bang’s fossil radiation — the oldest light in the universe.
In GIFT: Planck measured Ω_DE, n_s, etc. that GIFT predicts.
British mathematician, proved in 1996 the existence of compact manifolds with G₂ holonomy. For GIFT: His theorem guarantees K₇ can exist.
Japanese physicist, discovered in 1982 the Q = 2/3 relation for lepton masses. For GIFT: GIFT explains Koide via 14/21 = dim(G₂)/b₂.
Mathematicians, index theorem (1963), Fields Medals and Abel Prize. For GIFT: Their theorem gives N_gen = 3.
Physicist and mathematician, M-theory, only physicist with a Fields Medal (1990). For GIFT: M-theory (11D) is the natural framework where GIFT lives.
| Concept | Express Analogy |
|---|---|
| Octonions | Ultimate Lego kit |
| Fano Plane | Perfect social network (7 people) |
| G₂ | Guardian of octonions (14 directions) |
| E₈ | Versailles Palace of symmetries (248 rooms) |
| K₇ | Cosmic diabolo (7D) |
| b₂ = 21 | 21 bubbles in Swiss cheese |
| b₃ = 77 | 77 hyper-bubbles |
| Holonomy | Santa’s compass test |
| Topology | Play-Doh (vs ice sculpture) |
| Invariants | The universe’s fingerprints |
| U(1) | Clock hand |
| SU(2) | Möbius strip of rotations |
| SU(3) | RGB mixer |
| Fermions | Individualists (won’t pile up) |
| Bosons | Social butterflies (love piling up) |
| Higgs | Cosmic molasses |
| α = 1/137 | Radio volume knob |
| sin²θ_W | Cocktail recipe |
| Koide = 2/3 | Three sisters’ proportions |
| N_gen = 3 | Why 3 Musketeers |
| 0 parameters | IKEA vs custom furniture |
| Falsifiability | Science vs horoscopes |
| Lean 4 | Ultra-strict teacher |
| DUNE | Ghost hunter |
| Term | Section |
|---|---|
| α (fine structure constant) | Part V |
| Atiyah-Singer | Key Figures |
| Betti numbers | Part II |
| Bosons | Part III |
| Calabi-Yau | Part II |
| Cohomology | Part II |
| Complex numbers | Part I |
| Dimension | Part II |
| DUNE | Part VII |
| E₆ | Part I |
| E₇ | Part I |
| E₈ | Part I |
| Electromagnetism | Part IV |
| Electron | Part III |
| Euler characteristic | Part II |
| F₄ | Part I |
| Falsifiability | Part VI |
| Fano plane | Part I |
| Fermions | Part III |
| Fiber bundle | Part II |
| G₂ | Part I |
| Gauge groups | Part IV |
| Gluons | Part III |
| Golden ratio | Part V |
| Gravitation | Part IV |
| Group | Part I |
| Higgs boson | Part III |
| Holonomy | Part II |
| Joyce | Key Figures |
| K₇ | Part II |
| Koide | Part V |
| LHC | Part VII |
| Manifold | Part II |
| Muon/Tau | Part III |
| N_gen | Part V |
| Neutrinos | Part III |
| Octonions | Part I |
| PDG | Part VII |
| Photon | Part III |
| Planck mass | Part V |
| Planck satellite | Part VII |
| Quaternions | Part I |
| Quarks | Part III |
| Real numbers | Part I |
| sin²θ_W | Part V |
| Strong force | Part IV |
| SU(2) | Part I |
| SU(3) | Part I |
| Topology | Part II |
| Torsion | Part II |
| U(1) | Part I |
| W/Z bosons | Part III |
| Weak force | Part IV |
| Weyl group | Part I |
| Witten | Key Figures |
GIFT Framework v3.3 — For Everyone
“If you understood this, you’ve understood more than 99% of people!”