J.Konstapel, Leiden,9-10-2026.
What the Vacuum.Net Theory Says About Making, RatherThan Recycling, Critical Raw Materials
© 2026 J. Konstapel. Quotation with attribution is permitted. Reproduction of the whole requires written permission.
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Aanleiding: FD van vandaag Vier Nederlandse projecten bestempeld als ‘strategisch’ in EU-plan voor cruciale grondstoffen
1. Introduction
On 9 October 2026 the European Commission designated 46 new strategic projects under the Critical Raw Materials Act. Four are Dutch. All four recycle: copper (3ECYCLE, Mitsubishi Metals); bauxite, aluminium and copper (Myne, Harderwijk); batteries (Back to Battery, The Hague); and printed circuit boards (CRITICAL, Rotterdam).
The 2030 targets are 10% domestic extraction, 40% domestic processing and 25% recycling. They cover seventeen materials. The 46 projects need €21.1 billion. An earlier round of 47 projects has raised €2 billion so far. No mine has opened in the Union for ten years.
All three targets rest on the same assumption. An element is a stock. It sits in the ground, in a factory or in a discarded phone. It can be dug up, refined or recovered. It cannot be made.
This essay questions that last claim. It states the question with the Vacuum.Net theory. It then sets the measured record beside it.
2. The theory in brief
Picture a fishnet stretched in water. Strands run everywhere under tension. Where strands wind around each other, knots appear. Between them lie meshes: openings with a shape and a size.
Four words carry the theory:
- Strand — the net itself.
- Winding — a strand closed on itself. Physics calls this energy.
- Knot — windings that hold each other in three directions. Physics calls this mass.
- Mesh — the opening between strands.
Dewey Larson wrote the same ladder in 1959 as powers of one ratio, space over time. Speed is S/T. Energy is T/S. Mass is T³/S³.
On this ground, an element is a knot. To ask whether we can make an element is to ask what fixes which knot closes.
3. An element has two numbers
Larson gives the mass of an element as two parts. The first is rotational: two units for each unit of atomic number Z. The second is vibrational. It depends on the state of the surroundings, which Larson calls the magnetic ionization level, I.
$$A = 2Z + I \cdot Z^2 / 156.444$$
The number 156.444 is Larson’s inter-regional ratio. On Earth, I = 1.
So an element carries two numbers. Z is its address. I is the state of the net around it. The address belongs to the knot. The state does not.
The rule can be checked by hand against the European list. Take copper, Z = 29. The rotational part is 2 × 29 = 58. The vibrational part is 29² / 156.444 = 841 / 156.444 = 5.38. The sum is 63.38. The measured value is 63.55.
| Element | Z | 2Z | Z²/156.444 | Computed | Measured | Difference |
|---|---|---|---|---|---|---|
| Lithium | 3 | 6 | 0.06 | 6.06 | 6.94 | −12.7% |
| Aluminium | 13 | 26 | 1.08 | 27.08 | 26.98 | +0.4% |
| Silicon | 14 | 28 | 1.25 | 29.25 | 28.09 | +4.1% |
| Cobalt | 27 | 54 | 4.66 | 58.66 | 58.93 | −0.5% |
| Nickel | 28 | 56 | 5.01 | 61.01 | 58.69 | +4.0% |
| Copper | 29 | 58 | 5.38 | 63.38 | 63.55 | −0.3% |
| Germanium | 32 | 64 | 6.55 | 70.55 | 72.63 | −2.9% |
| Neodymium | 60 | 120 | 23.01 | 143.01 | 144.24 | −0.9% |
| Dysprosium | 66 | 132 | 27.84 | 159.84 | 162.50 | −1.6% |
| Tungsten | 74 | 148 | 35.00 | 183.00 | 183.84 | −0.5% |
| Lead | 82 | 164 | 42.98 | 206.98 | 207.20 | −0.1% |
Seven of eleven land within 1%, or close to it. Lithium, silicon, nickel and germanium do not. The rule is a first-order description. It is not a table of isotopes.
4. Three operations on a knot
The net allows three things to happen to a knot.
Rearranging. The knots stay closed. Only their places change. This is chemistry and metallurgy. It is what the four Dutch projects do. A typical step costs of the order of 10⁵ joule per mole.
Opening. A knot loses one closure and steps down the ladder, from T³/S³ to T/S. The factor between the rungs is T²/S², which is c². One full mass unit is 1.6605 × 10⁻²⁷ kg × (2.998 × 10⁸ m/s)² = 1.49 × 10⁻¹⁹ J. Per mole, that is 9.0 × 10¹³ J.
Raising. A knot takes on one closure and moves one address up.
The second and third operations change the element. Both depend on the second number: the state.
5. The state moves the limit
Larson sets a limit at 236 mass units. A knot above it must shed mass. The limit follows from the rule in Section 3.
At I = 1, element 91 gives 182 + 8281/156.444 = 234.9. Element 92 gives 184 + 8464/156.444 = 238.1. Uranium is the first knot above the line. It opens, slowly.
At I = 2 the vibrational part doubles. Element 78 gives 156 + 77.8 = 233.8. Element 79 gives 158 + 79.8 = 237.8. Gold is the first knot above the line.
At I = 3, element 70 gives 140 + 94.0 = 234.0. Element 71 gives 142 + 96.7 = 238.7. Lutetium is the first knot above the line.
| State I | Last knot under 236 | First knot above |
|---|---|---|
| 1 | 91, protactinium | 92, uranium |
| 2 | 78, platinum | 79, gold |
| 3 | 70, ytterbium | 71, lutetium |
One reading follows. It is a reading, not a derivation. At I = 3, every knot above 70 opens. What remains sits just under the line. Elements 57 to 70 are the rare earths. Lead, at 82, would open into the region Europe is short of.
The theory therefore makes a plain statement. Which elements exist in a place is a function of the state of that place. Change the state, and the list of stable knots changes.
6. The measured record
The statement in Section 5 can be set against five bodies of measurement. They differ in standing. This essay keeps them apart.
6.1 Established: the state sets which knot is stable
The storage ring ESR at GSI in Darmstadt has measured three cases.
- Dysprosium-163. The neutral atom is stable. With all 66 electrons removed, it becomes holmium-163 — address 66 to 67. The half-life is 47 days. Jung and colleagues reported this in 1992. The step carries 50.3 keV per knot: 50.3 × 10³ × 1.602 × 10⁻¹⁹ = 8.06 × 10⁻¹⁵ J, or 4.85 × 10⁹ J per mole.
- Rhenium-187. The neutral atom has a half-life of 43 billion years. Fully ionized, it has a half-life of 32.9 years. That is nine orders of magnitude.
- Thallium-205. The neutral atom is stable. Fully ionized, it becomes lead-205 — address 81 to 82 — with a half-life of 291 days. Leckenby and colleagues published this in Nature in November 2024.
In all three cases, nothing touched the knot. Only the surroundings changed. The knot then moved one address up.
The rates follow from the half-lives. The fraction moved after time t is 1 − 2^(−t/T). For dysprosium, that is 1.46% per day. For thallium, 0.24% per day. For rhenium, 2.1% per year.
Dysprosium is itself on the European list. It is used in permanent magnets.
6.2 Established: a cage sets the state
Beryllium-7 becomes lithium-7. Its half-life as a metal is 53.12 days. Ohtsuki and colleagues placed single beryllium-7 atoms inside cages of sixty carbon atoms. The half-life became 52.68 days. The difference is (53.12 − 52.68) / 53.12 = 0.83%.
Different chemical surroundings give shifts of about 0.2%. High pressure gives shifts of the same order.
The effect is small. Its form matters more than its size. A cage is a mesh. The mesh was set, and the rate at which one element became another followed.
6.3 Reported and disputed: rare earths from a layered film
Iwamura and colleagues at Mitsubishi Heavy Industries let deuterium gas pass through a thin film of palladium and calcium oxide layers at 70 °C. They reported three changes on the surface.
| From | To | Change in Z | Change in mass |
|---|---|---|---|
| Caesium-133 | Praseodymium-141 | 4 | 8 |
| Barium-138 | Samarium-150 | 6 | 12 |
| Tungsten (74) | Platinum (78) | 4 | — |
The amount of praseodymium grew in proportion to the deuterium that passed. Toyota Central R&D Labs reported a nearly complete replication in 2013. Measurements at the SPring-8 synchrotron followed the change in place.
Two things stand out. Praseodymium and samarium are rare earths. And the reported steps obey the rotational rule of Section 3: the mass rises by exactly two for each unit of address. Eight for four. Twelve for six.
The quantities are of the order of nanograms. The field at large has not accepted the result. It stands as reported, replicated once, and unexplained.
6.4 Tested and not confirmed: the neutrino lever
Larson ties I to the concentration of neutrinos held in matter. Jenkins, Fischbach and colleagues reported from 2008 that decay rates follow the distance between Earth and Sun. They proposed solar neutrinos as the link.
Kossert and Nähle at the Physikalisch-Technische Bundesanstalt repeated the measurement with counters that track their own efficiency. They found stable activities and no oscillation. Norman and colleagues found none in six further isotopes.
This line does not carry. The state that moves a knot has been found in the electrons around it, not in a neutrino flux.
6.5 Reported, not independently repeated: living cultures
Vysotskii and Kornilova report that growing microbial cultures in heavy water turn manganese-55 into iron-57. The stated rate is 1.7 × 10⁻⁹ per nucleus per second. No independent replication was found for this essay.
6.6 Designed, not built: tonnes
Marathon Fusion published a design in 2025. Fast neutrons from a fusion plasma turn mercury-198 into mercury-197, which becomes gold-197 in about 64 hours. The computed yield is about 2 tonnes per gigawatt of thermal power per year. The design has not been built and has not passed review.
It is the long road: fire, neutrons, a plant. It is listed here for one reason. It shows that quantity as such is not excluded.
7. What the record adds up to
Three statements can now be kept apart.
- The state fixes which knot is stable. Measured three times at GSI. Not disputed.
- A mesh can set that state. Measured once, in the carbon cage, at under 1%.
- A layered structure yields rare earths. Reported by one industrial laboratory, replicated by a second. Not accepted.
The theory joins the three. Its fourth axiom says that constants are functions of the local state of the net. Its design work says that a mesh sets that state. If I is such a state function, the mesh is the lever for the knot.
That identity is open. The complete derivation of the theory lists it as open: its two descriptions of the state of the net have not been shown to be one quantity.
One further link has not been made by anyone. The Mitsubishi film is a stack of layers a few nanometres thick, with a flow through it. In the terms of the net, it is a stack of meshes with one open passage. Nobody has read it that way. Nobody has varied the layer thickness against the natural unit of the theory.
8. The open number
The distance between the record and a kilogram is one number: the rate.
At GSI the state is set completely. The rate is 1.46% per day for dysprosium. But the state is held in a ring that stores millions of ions, not grams. In the carbon cage the quantity is free. But the state shifts by less than 1%. In the Mitsubishi film both are small.
The price of the step is known for one case. The dysprosium step carries 4.85 × 10⁹ J per mole. That is roughly ten thousand times a chemical step. It is also twenty thousand times less than a full mass unit. The knot does not have to be opened. It has to be moved one address.
What decides the matter is therefore a curve, not a principle. One axis: how far a structure shifts the state. The other: how fast the knot follows. Three points on that curve exist. They were measured for other reasons.
Two existing kinds of group can add points. A storage-ring group can repeat the dysprosium measurement at partial ionization, charge state by charge state. A thin-film laboratory can repeat the Mitsubishi film at a series of layer thicknesses, with a sham stack beside it.
9. What changes for people
The European plan rests on places. A tungsten mine in Spain. A germanium plant in Belgium. A recycling hall in Harderwijk. Behind them lie the places that are not in the plan: the cobalt diggings of Katanga, the rare-earth ponds of Inner Mongolia.
A raw material is scarce because it is somewhere else. Recycling shortens the journey. It does not end it. The copper in a Rotterdam circuit board still came from a hole in the ground.
If the state fixes the element, scarcity is no longer a matter of place. That would remove the reason for the mine, the export ban and the strategic list alike. It would also remove the work of the people who dig, ship and sort.
None of that is at hand. What is at hand is smaller. The seventeen materials on the list are not seventeen fixed stocks. At least three knots on or near that list have been seen to change address when their surroundings changed.
10. Status of this essay
- From sources. The European figures. Larson’s mass rule and limit. The GSI half-lives. The beryllium shift. The Mitsubishi and Toyota reports. The PTB result.
- Computed here. The mass table. The limits at I = 1, 2 and 3. The conversion rates. The price of the dysprosium step.
- Read. The rare earths as the knots just under the line at I = 3. The Mitsubishi steps as the rotational rule. The layered film as a stack of meshes.
- Open. Whether I is a state function that a mesh sets. The curve of state shift against rate.
- Not carried. The neutrino lever.
Annotated references
The occasion
Lalkens, P., and Schram, E. (2026). “Vier Nederlandse projecten bestempeld als ‘strategisch’ in EU-plan voor cruciale grondstoffen.” Het Financieele Dagblad, 9 October 2026.
Why read it: the four Dutch projects, the three targets and the €21.1 billion, in one page. Reading advice: note the official’s remark that no mine has opened in ten years.
European Parliament and Council (2024). Regulation (EU) 2024/1252, the Critical Raw Materials Act.
Why read it: the legal form of the idea that an element is a stock. Reading advice: Article 5 for the benchmarks, Annex I for the list.
The net
Konstapel, J. (2026). The Vacuum.Net Theory: Foundational Paper, sixth edition. Constable Research, Leiden.
Why read it: the five axioms, including the fourth, on which Section 7 rests. Reading advice: the ternary ground first.
Konstapel, J. (2026). Applied Vacuum Theory, Part Four: Energy as Passage, third edition. Constable Research, Leiden, 27 September 2026.
Why read it: the two roads — mesh and knot — and Larson’s limit in numbers. Reading advice: Section 7.
Konstapel, J. (2026). Three Roads to a Dynamic Vacuum. Constable Research, Leiden, 6 October 2026.
Why read it: the measured record for the mesh, and the Dutch groups that hold the equipment. Reading advice: Sections 6 and 9.
Larson, D. B. (1988). Basic Properties of Matter. Salt Lake City: ISUS. Chapters 24, “Isotopes”, and 25, “Radioactivity”.
Why read it: Equation 24-1, the limit of 236, and the level I. Everything in Sections 3 and 5 comes from these two chapters. Reading advice: Chapter 24 in full — an engineer writing, not a professor.
The established measurements
Jung, M., et al. (1992). “First observation of bound-state β⁻ decay.” Physical Review Letters 69, 2164.
Why read it: stable dysprosium-163 becomes holmium when its electrons are removed. The founding measurement of Section 6.1. Reading advice: four pages; read all.
Bosch, F., et al. (1996). “Observation of bound-state β⁻ decay of fully ionized ¹⁸⁷Re.” Physical Review Letters 77, 5190.
Why read it: nine orders of magnitude in a half-life, from the surroundings alone.
Leckenby, G., et al. (2024). “High-temperature ²⁰⁵Tl decay clarifies ²⁰⁵Pb dating in early Solar System.” Nature 635, 321.
Why read it: the third case, thirty-two years after the first, and twice as slow as predicted. Reading advice: the methods section shows what holding a state costs.
Litvinov, Yu. A., and Bosch, F. (2011). “Beta decay of highly charged ions.” Reports on Progress in Physics 74, 016301.
Why read it: the overview of every decay that changes with charge state. The place to look for further candidates on the European list.
Ohtsuki, T., et al. (2004). “Enhanced electron-capture decay rate of ⁷Be encapsulated in C₆₀ cages.” Physical Review Letters 93, 112501.
Why read it: a cage changes a rate. Small, clean and undisputed. Reading advice: the comparison table of half