THE FIVE PLATONIC SOLIDS
Tetrahedron, cube, octahedron, dodecahedron and icosahedron. These are the five regular convex polyhedra—not a complete list of the shapes in nature.
ROBERT ASHWORTH · FOUNDER PORTFOLIO
Wonder.
Structure.
Something to test.
Trading research, engineering, funding workflows and visual worlds—connected to the records behind the work.
FULL ESTATE REVIEW / OPEN
The archive is larger
than one demonstration.
Trading studies, source breadth, Grant Factory, submitted applications, identity architecture, immersive systems, LumaJet, LumaSkin, energy and constraint research are being reconciled into one record. The geometry demonstration below is one part of this wider estate.
Browse the expanded evidence catalogueHistorical implementations and results retain their dates and original denominators. Private device roots, unreviewed screenshots and incomplete source packages remain open items.
64overlapping evidence records
15configured engines mapped
26geometry families catalogued
19cinematic visual studies
01 / ONE PORTFOLIO, A TRACEABLE RECORD
The full body of work.
One evidence catalogue.
ProofLock supplies the shared evidence layer. The current commercial entry point is a buyer-owned baseline validation sprint: one authorized source, an agreed comparator, and a reviewable decision.
This working catalogue includes newly recovered source records and historical reports. It remains open while the private archive is reconciled. Download the public evidence catalogue
Read the canonical portfolio map ↗ Open the evidence index ↗
02 / THE GEOMETRY REGISTRY
Every form gets
a fair question.
Preserving the 18 championship families and adding eight. Separate historical transform registries are indexed in the wider portfolio. Catalogued, illustrated and tested are different stages. None is promoted as a universal winner.
The June 2026 championship receipt remains unchanged: 18 families, 0 performance-ready implementations. This expanded catalogue does not overwrite that historical result or summarize the entire research estate. Download registry JSON · Evaluation protocol ↗
03 / A REPRODUCIBLE FIRST COMPARISON
More paths.
Better trade-offs?
Explore ideal DC resistor networks with 64 nodes and equal total conductor material. Six layouts share identical terminals; honeycomb and sunflower use different positions and are shown separately.
| Network | Mean conductance ↑ | Mean path stretch ↓ | Breaks preserving all nodes connected |
|---|
In this model, adding connections has a cost: the same amount of material must be spread across more wire.
Assumptions, units and limitations
For each graph, cross-section A = V / total wire length and edge conductance g = A / (ρℓ). Diameter D, material volume V and resistivity ρ are normalized to 1. Mean effective conductance averages all 2,016 terminal pairs equally, in normalized units V/(ρD²). Higher conductance describes this declared resistor model only.
Download complete results and graph coordinates · Methods and reproduction ↗
THE NEXT ENGINEERING QUESTION
Can a signal travel
with less loss?
That requires a defined medium, frequency band, source, load and noise environment. The present DC model screens geometry trade-offs; it does not yet predict signal attenuation.
| Application | Freeze before testing | Measure against the baseline |
|---|---|---|
| Electrical / RF paths | Material, length or footprint, conductor volume, dielectric, frequency band and matched loads | Transmission / insertion loss (S21), reflection (S11), group delay, energy and temperature |
| Digital communication | Same channel, modulation, data rate, transmit power and noise conditions | Bit error rate, received signal-to-noise, latency, energy per delivered bit |
| Fluid / thermal channels | Same fluid, viscosity, footprint, material and inlet / outlet conditions | Flow rate, pressure drop, pumping power, temperature uniformity and fouling sensitivity |
Use untouched validation cases and retain failures. An independent rerun and representative physical measurement are required before an operational claim. Measurement reference ↗
04 / FROM A NAME TO AN EQUATION
Familiar patterns.
Precisely defined.
Five regular convex solids. A cycloid for an ideal descent. A spiral placement rule. A branching relation with explicit physical assumptions.
BRACHISTOCHRONE
Uniform gravity, frictionless point mass, released from rest. A fastest-descent curve is not a universal fastest signal path.
SUNFLOWER / PHYLLOTAXIS
rₙ = c√n · θₙ = nπ(3 − √5)A useful placement rule to test for packing, sampling and array design. The arrangement alone establishes no communications advantage.
TREE-INSPIRED TRANSPORT
r₀³ = r₁³ + r₂³Murray’s classical relation balances ideal laminar-flow pumping and maintenance costs. Real materials, pulsation and asymmetric networks can change the optimum.
“Tree of Life” is a symbolic motif, not a single equation that unlocks a universal physical effect.
Your four Echo geometry families
Your founder paper groups the work into Echo Field Dynamics; Echo Sequence Geometry; Echo Lattice Geometries; and Echo Waveforms & Gradient Structures. This is a conceptual taxonomy, distinct from the five Platonic solids and from the task-specific testing registry.
05 / THE VISUAL LANGUAGE
Art opens
the conversation.
Nineteen distinct cinematic studies, mathematical forms you can explore, and a studio for making your own visual frames.
01—10
Wonder Studio
Ten visual worlds and the frame editor ↗
11—16Bounded Light Speed
Six cosmic studies and light / wave models ↗
17—19Geometry Observatory
Hopf, trefoil, gyroid and superformula explorer ↗
AI-assisted cinematic imagery is artistic interpretation. Source image detail and export dimensions are disclosed in the collections. An enlarged 20K file does not contain 20K of native captured detail.
06 / WORKING REVIEW PACKET
Lead with the work.
Leave with a decision.
A route through the expanding portfolio for the 5 October meeting. Choose a relevant research or grant record from the catalogue before the technical demonstration. The meeting date is founder-reported; this page does not announce an institutional event or endorsement.
- Frame the purpose · 2 minutes
Show the visual collection, then identify one reviewer-relevant engineering problem.
- Demonstrate · 5 minutes
Choose a relevant dashboard, research receipt or grant packet. Use the mathematical explorer when geometry is the question.
- Inspect the evidence · 5 minutes
Open the registry, frozen results, source, limitations and retained negative outcomes.
- Agree a bounded next step · 3 minutes
Name the owner, dataset, comparator, acceptance criteria and independent reproduction plan.
Institutional activity
Correspondence is classified by what occurred. Prepared packets, submitted applications, agency tracking, review decisions and awards are recorded as separate stages. Private messages and contact details remain in the founder’s review packet.
Value and readiness
Engineering depth and organized evidence can improve reviewability. Commercial value still depends on independent reproduction, ownership documentation, buyer acceptance and contracted revenue.
The latest located valuation update is dated 25 September 2026. Its historical financing range remains an internal negotiation hypothesis; the expanded asset and submission inventory is being reconciled before any reassessment. No new appraisal is asserted.
Inspect readiness and remaining gates ↗Follow a claim
to its source.
Source code shows an implementation. A run receipt supports the named run. Independent reproduction and a buyer’s acceptance are separate milestones.