G7 — The Physical Inventory

The Expedition: G7 · G6 · G5 · G4 · G3 · G2 · G1 · G1 Analysis

Status: O / M / T / Q

G1 gave us the geometry.

G2 gave us the factor of 2.

G3 turned that factor into a coordinate.

G4 brought Planck length and Planck time into the same indexed sequence.

G5 asked the uncomfortable question:

What, if anything, is special about 67?

G6 defined how we might find out.

G7 begins the experiment.

Not an experiment in a laboratory.

An experiment in mapping.

For the first time in this expedition, independently established physical scales are allowed to populate the 81018 coordinate system.

We do not choose where they belong.

We calculate it.

The conversion center

The working coordinate is [L_n=l_P,2^n].

Given a physical length (L), its coordinate is [n=\log_2\left(\frac{L}{l_P}\right)].

The mathematics is straightforward. The interpretation is not.

The choice to use the Planck length as the reference and powers of two as the coordinate intervals belongs to the model.

It does not establish that nature itself is discretized in powers of two.

That distinction remains in force.

The first rule

The physical quantity comes first.

The coordinate comes second.

Never the other way around.

If an independently established length is (L), we calculate its coordinate.

We do not search for a physical quantity that will land at 67.

This is the central methodological rule of G7:

Physics populates the map. The map does not manufacture the physics.

The first anchor

The 2022 CODATA recommended Planck length provides the reference scale:

[l_P\approx1.616255\times10^{-35}\ {\rm m}]. Within this model, that reference is assigned [n=0].

This is an A — modeling choice. The Planck length itself is a physical quantity.

The decision to make it the zero point of this particular coordinate system is ours.

That distinction must remain visible.

The physical inventory begins

The first entries should not be selected because they are interesting.

They should be selected because they are defensible.

Proton charge radius

The proton charge radius is approximately [r_p\approx8.4\times10^{-16}\ {\rm m}.]

Its coordinate is approximately [n_p\approx65.5.] This is a measured characteristic scale.

It is not a hard spherical boundary around a proton.

Its coordinate therefore tells us where a recognized physical length falls on the 81018 scale.

Nothing more.

Neutron scale

A neutron reduced Compton wavelength is approximately

[1.32\times10^{-15}\ {\rm m}], placing it at approximately [n\approx66.2].

This is a different kind of physical entry. It is a characteristic quantum-mechanical length, not a measured neutron radius.

That distinction matters.

Muon scale

The reduced Compton wavelength associated with the muon is approximately

[1.87\times10^{-15}\ {\rm m}], placing it near [n\approx66.6].

Again: different physical quantity, different meaning, same coordinate system.

Classical electron radius

The classical electron radius is approximately [2.82\times10^{-15}\ {\rm m}], which places it near

[n\approx67.2]. Now let’s pause for a moment. Not because we have found an explanation, but

because the map has become interesting.

What we have—and what we do not have

The present inventory contains several entries in the neighborhood of 67.

Approximately: [65.5,\quad66.2,\quad66.6,\quad67.2].

That is an observation about the mapping. It is not yet an observation about nature.

These quantities are not interchangeable. One is a measured proton property.

Others are characteristic quantum lengths.

The classical electron radius is a derived electromagnetic scale.

A numerical neighborhood among unlike quantities may be suggestive.

It may also be coincidental.

At this stage we do not know.

And that is exactly why it belongs here.

The atomic scale

The Bohr radius is approximately [5.29\times10^{-11}\ {\rm m}], which maps to approximately [n\approx81.4]. This gives us an important outward control.

The 81018 coordinate does not collapse all familiar physics into the neighborhood of 67.

The atomic scale lies much farther outward.

That matters.

The short-distance frontier

At the other end of the inventory, particle physics gives us a different kind of information.

Experiments do not simply provide a succession of measured particle radii.

They also establish limits on possible internal structure.

For example, searches for quark compositeness probe distances of order [10^{-20}\ {\rm m}].

That corresponds to approximately [n\approx49.1].

But it would be incorrect to write: “The quark is (10^{-20}) meters in size.”

That is not what the experiment establishes. It establishes a constraint on possible substructure at that scale within the model tested.

This gives G7 another essential rule:

A measured size, a defined characteristic scale, and an experimental upper limit are three different kinds of evidence.

They may share a coordinate.

They do not share an epistemic status.

The initial inventory on 21 September 2026

Physical entry	Approximate length	81018 coordinate	Classification
Planck length	(1.616\times10^{-35}) m	0	Reference / model anchor
Quark compositeness scale	(10^{-20}) m	49.1	Experimental constraint
Proton charge radius	(8.4\times10^{-16}) m	65.5	Measured characteristic scale
Neutron reduced Compton wavelength	(1.32\times10^{-15}) m	66.2	Defined quantum scale
Muon reduced Compton wavelength	(1.87\times10^{-15}) m	66.6	Defined quantum scale
Classical electron radius	(2.82\times10^{-15}) m	67.2	Defined characteristic scale
Bohr radius	(5.29\times10^{-11}) m	81.4	Atomic characteristic scale

This table is deliberately incomplete.

That is important.

G7 is not presenting a finished physical map.

It is opening the inventory.

Additions, changes, and updates will be recorded within this supplemental chart.

The question has changed

At the beginning of the expedition, 67 was a number in a chart.

Then it became a question.

Now physical scales are beginning to appear around it.

But the correct question is still not:

“What is 67?”

The correct question is:

Does the physical description of reality undergo any independently identifiable transition near this coordinate?

That is much harder.

And much more interesting.

The controls

Before assigning significance to 67, we need controls.

We must examine neighboring coordinates:

[65,\ 66,\ 67,\ 68,\ 69].

But we must also examine a wider neighborhood.

If dozens of coordinates show comparable concentrations of interesting quantities, the apparent significance of 67 weakens.

If the concentration disappears when a different legitimate reference or coordinate convention is used, that matters.

If a mathematical or physical transition can be identified independently at 67, that would be different.

If no such transition exists, we record that too.

The test must be capable of producing either answer.

The most important sentence in G7

The physical inventory is not here to prove the 81018 model.

It is here to challenge it.

That changes the relationship between the model and the data.

We are no longer asking:

Can the model accommodate this observation?

We are asking:

What would the model have to survive before we allowed ourselves to believe that the coordinate means something physically?

That is the standard.

G7 — where the map meets the world

Something new has happened.

The geometric coordinate has acquired occupants.

Not theoretical occupants chosen by the model.

Physical quantities drawn from established physics.

Some are measurements.

Some are defined characteristic scales.

Some are experimental constraints.

Their meanings differ.

Their coordinates can nevertheless be compared.

And now, unexpectedly, several independent entries occupy the neighborhood around 67.

We will not explain that today.

We will not name it.

We will not protect it.

We will populate the map farther.

Then we will test the neighborhood.

And only after that will we ask whether the apparent structure is:

a coordinate artifact,

a numerical coincidence,

a mathematical feature,

a physical transition,

or something we have not yet learned how to describe.

That is the work of G7.

The map is open.

Next: G8 — The Boundary

###