The Shape of Things

A project of GotChoices.org

About this project

What started as a hobby — an engineer's "what if" exploration of a 1997 paper proposing the electron is a confined photon — has yielded some remarkable results: percent-level particle mass predictions from geometry alone, an emergent neutron that nobody put in by hand, and a neutrino mass ratio that falls out of integer winding numbers.

I don't claim the model is correct. It may be coincidence, numerology, or something deeper. But it is interesting — and it may offer fresh angles on some of physics' unsolved problems, from the origin of mass to the nature of dark matter.

This project does not compete with the Standard Model. The Standard Model works — its predictions are confirmed to extraordinary precision. But it requires ~25 free parameters (particle masses, coupling constants, mixing angles) that are measured, not explained. MaSt/GRID attempt to derive those parameters from a simpler starting point: the geometry of a compact six-dimensional space.

Model-E uses 7 measured inputs to derive the rest:

Input	What it sets
α = 1/137	Ma ↔ ℵ ↔ t coupling strength (value is input)
m_e	electron ring scale
m_p	proton ring scale
Δm²₂₁	neutrino ring scale
m_μ / m_e	e-sheet aspect ratio and shear (R53 Solution D)
m_τ / m_e	(same — two ratios fix two parameters)
Δm²₃₁ / Δm²₂₁	neutrino shear

Of these, 3 are dimensional scales (every theory needs units) and 4 are dimensionless (α plus the mass/splitting ratios). The Standard Model has ~19 dimensionless parameters. Model-F does not reduce this count further than model-E, but it derives the structure of α coupling geometrically (see below).

From these inputs, model-F derives: 14 of 16 compound particle masses within ~1.12%, nuclear masses from deuterium to iron with α_Coulomb = Z² × α exactly, three lepton generations via shear resonance (inherited from model-E), neutrino oscillation via shear, charge quantization via GRID, and — new in model-F — structural α universality (the tube↔ℵ↔t chain makes α the same for every charged particle and exactly Z²α for nuclei), Z₃ confinement on the p-sheet (the proton as three (1, 2) "quark" constituents bound at 120° phase offsets, derived from density-fluctuation cancellation), and per-sheet Dirac–Kähler spin giving the Standard Model taxonomy (lepton/meson/baryon = 1/2/3-sheet object) structurally.

For background on who built this, how AI was used, and how to judge what you're reading, see DISCLAIMERS.

Please clone this repo and encourage your friends to do the same. If you have the scientific background to review some of the studies contained here, please help out!

New here? The papers/ folder offers three entry paths — scientific, intuitive, and reflective — depending on how you like to learn. Start with What If? for the core idea in plain language, or Matter from Light for the full technical story.

The big picture

This project attempts a unified geometric account of fundamental physics — including gravity — from two free parameters and a discrete lattice.

The work is organized in two layers:

GRID (Geometric Relational Interaction Domain) is the substrate: a minimal 4D causal lattice whose phase dynamics produce Maxwell's equations and whose information density produces Einstein's field equations and the gravitational constant G. GRID derives both long-range forces from six axioms without importing either one. Beyond the theoretical derivations, GRID provides a functional mechanical model of the spacetime fabric: a hexagonal lattice where edges carry standing-wave modes, junctions scatter energy by impedance matching, and curvature arises from pentagonal defects. Simulations confirm that this lattice propagates directional waves (no Maxwell input), superposes them exactly, and accommodates Schwarzschild geometry — the event horizon is not a lattice failure, but the physical singularity is. See grid/synthesis.md for what has been established.

MaSt (Material – Space – time) is the architecture built on that substrate: six compact dimensions where particles are standing electromagnetic waves. MaSt takes Maxwell's equations (now derived by GRID) and the coupling constant α as inputs, then produces the particle spectrum, masses, charges, nuclear structure, and plausible mechanisms for the strong force (Q95) and matter–antimatter asymmetry (Q97). Quantum behavior in MaSt is not postulated — it emerges from wave mechanics on compact geometry: quantized energy levels are standing-wave modes, uncertainty is the Fourier bandwidth limit, and spin is winding topology.

Together, GRID + MaSt attempt to unify general relativity with quantum field theory through a common geometric substrate.

The MaSt Continuum

MaSt = Material – Space – time.

The framework proposes that spacetime has six additional compact ("material") dimensions — three pairs forming material sheets — where particles are standing waves of confined electromagnetic energy. The full arena is Ma × S × t (6 + 3 + 1 = 10 dimensions).

See studies/Taxonomy.md for the full framework reference.

Symbol	Name	Dimensions	What it is
Ma	Material space	6	The compact dimensions; three periodic sheets
Ma_e	Electron sheet	2	Modes: electron, muon, tau
Ma_ν	Neutrino sheet	2	Modes: neutrino mass eigenstates
Ma_p	Proton sheet	2	Modes: proton, hadrons, nuclei
S	Space	3	The three large spatial dimensions
t	Time	1	Time

The three sheets (3Ma) have vastly different scales:

Sheet	Size	Mode energy	Particle family
Ma_p	~fm	~GeV	Proton, hadrons
Ma_e	~pm	~MeV	Electron, muon, tau
Ma_ν	~μm–mm	~meV (THz)	Neutrinos

Guiding principle

Energy and geometry are the only fundamentals.

Mass, charge, spin, and magnetic moment are all emergent:

Property	Emerges from
Mass	Energy confined in periodic geometry
Charge	Shear of the material sheet lattice
Spin	Winding ratio of geodesic (p:q)
Mag. mom.	Axial projection of compact B field

Conservation laws are emergent too — but exact. Mass conservation is energy conservation. Charge conservation is topological winding-number conservation (you can't smoothly unwrap a path on a material sheet). Spin conservation is geodesic topology. These are exact because topology is exact.

The only true inputs are: (1) the existence of energy (photons), (2) the existence and shape of material dimensions (Ma), and (3) the rules of propagation (Maxwell's equations — now derived by GRID from a discrete lattice). Everything else — the particle zoo, their properties, their interactions — should follow.

GRID's six axioms (grid/foundations.md) now derive both Maxwell's equations and gravity from this principle. See studies/Taxonomy.md §6 for the full mechanism catalog.

Models

The MaSt model has evolved through six generations. The current model is model-F — an 11D architecture that derives the α-coupling mechanism geometrically (value still input), Z₃ confinement on the proton sheet (making the proton a three- quark composite), and the Standard Model particle taxonomy from per-sheet Dirac–Kähler spin + SU(2) composition.

Model	Era	Key idea	Status
model-A	S1–R25	WvM / single-sheet electron	Superseded
model-B	R26–R38	Three tori / ma.py — first particle predictions	Superseded
model-C	R39–R44	Generalized model / ma_model.py — dynamic torus, dark matter, electroweak	Superseded
model-D	R45–R52	Filtered model / ma_model_d.py — waveguide cutoff, (1,3) proton, GRID integration	Superseded
model-E	R53–R56	Full T⁶ with generation structure — 18/20 spin-correct, shear resonance, 9×9 metric	Superseded
model-F	R59–R62	11D architecture — geometric α coupling, Z₃ confinement on p-sheet, per-sheet Dirac–Kähler spin, Standard Model taxonomy from sheet-count	Active

Headline results — for the full architecture, inventory, and references, see models/model-F.md.

• Geometric α coupling — the tube↔ℵ↔t chain makes α structurally universal across sheets, modes, compounds, and nuclei. α_Coulomb = Z² × α exactly for any Z-nucleus. Value of α still input.
• Z₃ confinement on the p-sheet — (3, 6) proton as a three- quark bound state of (1, 2) constituents; derived from 2ω density-fluctuation cancellation (N = 3 is minimum cancelling copy count). Selection rule: free p-sheet modes require n_pt ≡ 0 (mod 3). Nuclear scaling n_pt = 3A, n_pr = 6A.
• e-sheet geometric exemption — localization ratio R_loc = m·L/ℏc < 1 on the e-sheet makes the electron delocalized, so Z₃ binding can't form; electron propagates as a free single mode. Derived, not postulated.
• Per-sheet Dirac–Kähler spin (R62 derivation 7d) — each flat 2-torus sheet hosts a spin-½ fermion tower; compound modes compose via SU(2) angular-momentum addition. Standard Model taxonomy falls out: 1-sheet ↔ lepton, 2-sheet ↔ meson, 3-sheet ↔ baryon.
• ν charge = 0 derived — real-field KK modes are tube- conjugate-symmetric; without a symmetry-breaker the tube charge averages to zero. e-sheet (extreme shear) and p-sheet (Z₃ quark structure) break this symmetry; ν-sheet doesn't.
• 14 of 16 compound particles matched within 1.12% under Z₃-compliant + composite-α search. Several beating model-E. Pion desert halved (23% → 10–13%) but not closed.
• Three charged lepton generations from R53 Solution D; mass ratios algebraically exact.
• Nuclear masses d → ⁵⁶Fe within 1.4% with α_Coulomb = Z² α exact.
• Single-k symmetry — k = 1.1803/(8π) same for all sheets; structural fixed point (R60 Track 14), closed form open.

Foundation

This project builds on a line of thought running through a century of physics:

de Broglie (1924) proposed that particles are waves, with wavelength λ = h/p. This was the first suggestion that matter and waves are the same thing, not merely analogous. MaSt takes this literally: particles are standing electromagnetic waves on material geometry.

Schrödinger (1926) originally conceived his wave equation as describing a real physical wave — not a probability amplitude. He was deeply uncomfortable with Born's statistical interpretation and spent decades defending the reality of the wave. His discovery of zitterbewegung (trembling motion at the Compton scale in the Dirac equation) hinted at real circular motion underlying particle structure. MaSt vindicates Schrödinger's intuition: the wavefunction on Ma is a real electromagnetic standing wave, and the zitterbewegung is the photon circulating on the (1,2) geodesic.

Kaluza (1921) and Klein (1926) showed that a single compact extra dimension, appended to Einstein's four-dimensional spacetime, produces electromagnetism from pure geometry — the electromagnetic potential is the off-diagonal component of the 5D metric. MaSt extends KK from one compact dimension to six (Ma = 3 × material sheets), producing not just electromagnetism but the full particle spectrum: masses, charges, spins, and decay patterns. R36 showed that the KK gauge field is not an assumption imposed on the model — it emerges from solving the wave equation on compact × non-compact space.

Williamson and van der Mark (1997) (PDF, video overview) proposed the specific mechanism: an electron is a single photon confined to a (1,2) torus knot. The model reproduces spin ½ (exact, topological) and charge ≈ 0.91e (approximate, geometric). This project extends WvM into the MaSt framework: the photon lives on a flat material sheet (a periodic 2-dimensional surface), and the electron's properties emerge from the geometry of that surface. The neutrino crisis — uncharged spin-½ particles are impossible on a single sheet (R25) — forced the architecture from one sheet to three (3Ma = Ma_e × Ma_ν × Ma_p), yielding Ma (R26).

Structure

• models/ — Model documentation: versioned writeups of each MaSt model generation (A through D). See models/README.md.
• grid/ — GRID (Geometric Relational Interaction Domain): the substrate layer. Derives Maxwell + Einstein from a discrete lattice. See grid/README.md.
• studies/ — Questions that require a computational model to answer. See studies/STATUS.md for the registry.
• qa/ — Physics questions answered by logic and existing theory (no computation). See qa/README.md.
• papers/ — Authored documents presenting theories, results, and proofs. See papers/README.md.
• primers/ — Self-contained tutorials on topics needed to follow the studies. See primers/README.md.
• labs/ — Proposed physical experiments to test predictions of the model. See labs/README.md.
• viz/ — Interactive browser-based visualizations. See viz/index.html.
• reference/ — Source material by others and recorded conversations.
• lib/ — Shared Python code (Ma solver, mode search, metrics).

Navigation

File	Purpose
models/model-F.md	Current model (active) — 11D architecture, geometric α coupling, Z₃ p-sheet confinement, per-sheet Dirac–Kähler spin + SU(2) compound composition, Standard Model taxonomy from sheet-count
models/model-E.md	Previous model — full T⁶ with generation structure, 18/20 spin-correct, 9×9 metric
models/model-D.md	Filtered model with waveguide cutoff and (1,3) proton
models/model-C.md	Historical — particle tables, parameter census, dynamic torus
models/README.md	Model index: all six generations (A–F)
STATUS.md	Project-level status: mission, active front, open problems
studies/Taxonomy.md	MaSt framework reference: dimensions, geometry, particle catalog, mechanisms
grid/README.md	GRID — substrate layer: derives Maxwell + G from a discrete lattice
studies/STATUS.md	Study-by-study registry: active, backlog, done
qa/Q84-mast-terminology.md	MaSt naming conventions and migration guide
qa/README.md	Index of answered and open physics questions
qa/INBOX.md	Capture queue for new questions
papers/README.md	Papers: matter-from-light, sub-quantum memory, atoms-from-geometry, universe-as-mode
primers/README.md	Tutorials: matrix notation, Maxwell, KK theory, charge-from-energy
labs/README.md	Proposed physical experiments to test model predictions
reference/WvM-summary.md	Living summary of the foundational WvM paper
viz/index.html	Browser launcher for all interactive visualizations

License

This work is licensed under Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0). You are free to share and adapt this material for any purpose, including commercial, provided you give appropriate credit to GotChoices.org and distribute any derivative works under the same license. See LICENSE for details.