A relational ontology and a geometric system for fundamental physics.
Welcome to the Omnisyndetic Framework! The work presented here is best read as a relational ontology exploration of fundamental physics - an approach to see if matter can be derived from relation and geometry itself, rather than from assumed base constituency or space. Rather than chase a smallest block, we ask a different question, what if the fundamental act is building instead? Or more directly: “the drawing of a difference?” We call this contrast, and how this contrast is resolved by structural coherence.
Think of it as Spencer-Brown’s Laws of Form meets symmetry theory, with a coherence theory of truth and a little of Simondon and Whitehead, with deep rooting in a structural reading of the Tao de ching. It’s written to be direct and checkable - a hub for learning, exploring, and trying the calculators yourself - all are welcome.
This framework is developed and published independently, with all derivations, proofs, and outputs fully open access and auditable through the Open Science Framework. While not peer reviewed in the traditional journal sense, it maintains full structural rigour and invites public audit and critique. Every step, from logic to geometry, is open to inspection and verification.
Live link to the calculator - browse, apply, and audit each state line by line.
Pick a baryon, set the inputs, press Apply. The table talks to the calculator above, everything recalculates locally in your browser… no background calls. Every symbol is live, you can audit values line by line as you scroll, clean and visible.
Filter jumps to a family, Search finds a name or charge, Precision sets the decimals, Recompute syncs the catalogue with your current constants.
Roots and ground states, then the spin 3/2 resonance lifts, all from one geometry. You get the λ-pair, κ, coherence C = e−κ, energies, and the arc class. Built to be checked, compared, taught.
The sequence stays the same - Inputs, Radial Deviation, Charge Law, Coherence, Energies, Classification - values update as you change an input.
| Name | Group | PDG | Z | m* (MeV) | Lower λ | Upper λ Apply | Vec | Status |
|---|
A live calculation from the two radii. Start at Inputs, follow the sequence, land at Classification.
We list the geometric and physical constants for both radii. This sets the baseline.
| Symbol | Meaning | Value | Unit |
|---|---|---|---|
| λL | Lower coherence radius | — | fm |
| λU | Upper coherence radius | — | fm |
| λ0 | Euclidean crossover | — | fm |
| ħc | Physical constant | — | MeV·fm |
| NARP | Arc return pressure | 27.61879 | MeV·fm |
Deviation shows how far each radius sits from λ₀.
| Case | Value |
|---|---|
| Lower | — |
| Upper | — |
The contrast law links ε, κ, and the charge integer n.
| Case | ε value |
|---|---|
| Lower | — |
| Upper | — |
With κ set, compute \(C=e^{-\kappa}\), δ=1−C, ‖D‖=√δ, projection α, and Δdiv.
| C | δ | ‖D‖ | |
|---|---|---|---|
| Lower | — | — | — |
| Upper | — | — | — |
| α₀ | α [MeV⁻¹] | |
|---|---|---|
| Lower | — | — |
| Upper | — | — |
| Δdiv | |
|---|---|
| Lower | — |
| Upper | — |
\(M_0\) as the second-order closure measure, fixed for this system.
Validation and echo energies describe the two halves of return. Their sum defines the apparent mass on each side.
| Case | Eval [MeV] | Eecho [MeV] | m [MeV] |
|---|---|---|---|
| Lower | — | — | — |
| Upper | — | — | — |
Each curvature arc ⌒n is analytic in NARP and gives discrete coherence bands.
| n | κ(arc n) | Form |
|---|---|---|
| 1 | 0.036207232 | 1 / NARP |
| 2 | 0.054709899 | √(2π − 2π/(π/2)) / NARP |
| 3 | 0.064175648 | √(2π − 2π/2) / NARP |
| 4 | 0.074103656 | √(2π − 2π/3) / NARP |
| 5 | 0.081176488 | √(2π − 2π/5) / NARP |
| 6 | 0.090758072 | √(2π) / NARP |
| 7 | 0.106147354 | √(2π + 2π/e) / NARP |
The upper arc index U sets the triad classification, channel, and sector.
| SU Channel | Flavour Sector | Spin Rule | Result |
|---|---|---|---|
| SU(2)/SU(3) | — | spin-½: S1/2 = 3 − U | — |
| spin-3/2: S3/2 = 4 − U | — | ||
parsimony parameter economy reasoning before fit
We begin from relation. One measured input on the proton’s expressed arc, the radius \( \lambda_U \). Place it near the muonic scale, run the live sequence, recover the proton mass… clean. The detailed discussion sits here:
Below are the commonly cited proton charge radii with their published uncertainties, followed by the structural radius used in this framework. The muonic value is the most precise. Electronic spectroscopy and low-\(Q^2\) scattering now agree with the smaller radius band.
| Method | rp (fm) | Uncertainty | Source |
|---|---|---|---|
| Muonic H Lamb shift | 0.84087 | ± 0.00039 | Pohl 2010, Antognini 2013, PDG 2024 |
| H spectroscopy | 0.8335 | ± 0.0095 | Beyer 2017 |
| H Lamb shift | 0.833 | ± 0.010 | Bezginov 2019 |
| e–p scattering (PRad) | 0.831 | ± 0.014 stat, ± 0.012 sys | Xiong 2019, PDG 2024 |
| Framework radius on upper arc | 0.842228852595 | placed | this page |
Our placed \( \lambda_U \) sits slightly above the muonic value by 0.00129 fm, about 0.2%. The muon samples nearer the proton and will co-distinguish fine structure… even if small, it shows. Uncertainties above are the stated experimental errors of each method.
Method and scope
Geometry first. Constants are relational. Data verify rather than calibrate. NARP is held fixed across the catalogue. This page demonstrates the complete live derivation with one structural input. No curve fitting, no Monte Carlo. Parsimony in action.
Why it matters
If a small geometry can recover established structure at refresh speed, parameter economy holds. The framework extends to ladders, decays, and spin-1/2 ground states with the same rules… predictive from first principles, structurally, without assuming extra measurement relations.
Begin with the two radii, trace each relation through coherence and charge, and watch a baryon resolve in real time.
For anything to be, it must differ from what is not. Being is not non-being. What can be confirmed is what you can tell apart. You cannot distinguish yourself from yourself. Distinction needs relation. That is the mantra here.
You are probably asking the question: two radii. Think Plato’s world of forms. They are one convergence of identity about a symmetry centre. At the Euclidean crossover \( \lambda_0 = 1/\sqrt2 \) symmetry holds and the figure goes featureless; step either side and the span splits into a compressed \( \lambda_{\mathrm L} \) and an expressed \( \lambda_{\mathrm U} \). Drag the slider - watch the figure vanish at the centre, then reappear - the two mass points move in tandem as the solution closes across a quantised arc. One structure read on two sides of a tiny centre, returning a single mass and a single charge, and setting the order parameter for classification and prediction.
The centre is the Euclidean crossover. At full symmetry \( \kappa = 0 \) and \( C = 1 \). All orientations are equivalent; selection waits for a break about the centre. Step off and the span splits: \( \lambda_{\mathrm L} \) on one side, \( \lambda_{\mathrm U} \) on the other. Closure across an arc \( \smile n \) returns one resolution.
In symmetry terms the pair \( (\lambda_{\mathrm L}, \lambda_{\mathrm U}) \) is the order parameter. The sign fixes which side carries compression; the magnitude sets how far the break runs. Residual symmetry classes appear as discrete arcs, each a stable curvature threshold.
Working variables follow Volume I. Set the radial offset \( \Delta = (\lambda-\lambda_0)/\lambda_0 \) and the angular deviation \( \epsilon \). Then \[ \kappa = \epsilon^2 + \Delta^2,\qquad C = e^{-\kappa}. \] Each arc holds a coherence window set by \( C \). Inside the window the configuration resolves; the class fixes; the sequence proceeds.
On the calculator: hold at the centre and the readout fades; nudge the slider and the twin radii separate, the arc label appears, both branch masses meet as closure forms and the returned charge locks. That convergence is the symmetry selection that drives classification and prediction. Energy reads on one global scale (NARP) as \( E_{\mathrm{val}} + E_{\mathrm{echo}} = mc^2 \).
Each configuration carries curvature \( \kappa \). Small \( \kappa \) reads calm and coherent; larger \( \kappa \) works harder. Coherence reads \( C=e^{-\kappa} \) on 0 to 1. The slider sets \( \lambda \). The crossover \( \lambda_0 \) mirrors positions that land the same mass. The map shows arcs that mark curvature thresholds. NARP sets the global energy scale and the energy splits into \( E_{\mathrm{val}} \) and \( E_{\mathrm{echo}} \). Together they give \( m^* \)
First observation samples the asymmetry directly and returns \(E_{\mathrm{val}}\). Second observation reads the structural echo of that asymmetry and returns \(E_{\mathrm{echo}}\). The closed circuit is \(E_{\mathrm{val}} = 6(\mathrm{NARP}/\lambda)e^{-\kappa}\) and \(E_{\mathrm{echo}}=\Delta_{\mathrm{div}}\alpha(1+\lVert D\rVert)M_0\). Their sum closes the form into \(mc^2\). At \( \lambda_0 \) the echo term vanishes… step away and closure energy ramps on smoothly.
Individuation is contrast resolving into form. Distinctions settle, closure holds, one returned identity now carries the set. Inside one closure uniqueness holds, \(i\ne j \Rightarrow \chi_i\ne\chi_j\) for \(\chi=(U,L,\epsilon,\kappa)\). The relation moves as one… validation feeds echo, echo fixes mass, the individuated figure persists.
We use coherence in the older epistemic sense from the coherence theory of truth. It is not phase relations in field theory and not prose fluency. It asks how well a configuration fits within a system of relations. Has the structure resolved; has the relation returned. What stabilises under contrast individuates; what does not resolve does not individuate.
Coherence measures contrast alignment: \( C=e^{-\kappa} \). In the working model \( \kappa=\epsilon^2 \). At the Euclidean crossover \( C=1 \). Every identity is equal and none can be distinguished, so individuation halts. Step off the centre and individuation begins. Low coherence needs more echo and curvature; high coherence needs less.
No field theory background required. Curiosity is enough.
Choose a tile to open a short, visual guide. You can roam freely or follow the suggested order inside each page.
See the centre snap to a perfect triangle, then watch symmetry break into the sixfold circuit.
Read allowed bands, learn centres and thresholds, and why two radii can land one mass.
Turn placement into pressure. Walk the validation–echo split and see how the total forms.
Hold vs close: \(E_{\mathrm{val}}\) and \(E_{\mathrm{echo}}\). Watch how changing \( \lambda \) tilts the balance.
How charge gates which arcs are admissible and shifts the window you can occupy.
See how degeneracy lifts across the crossover and how thresholds make structure discrete.
Geometry-only spectrum with zero parameters. Then add one radius per baryon for exactness.
An entire subject on its own: how first- and second-order observation generate the mass sum.
Gentle mappings to familiar physics using the arc lattice as the guide.