Our Expedition: G7 · G6 · G5 · G4 · G3 · G2 · G1 · G1 Analysis · G7 inventory

What if the structure of reality is simpler than we think?

What if the apparent complexity of the universe emerges from a small number of simple relationships — scale, geometry, constraint, symmetry, and continuity?

81018 is an open investigation of that possibility. It began in a classroom in December 2011. It is not a finished cosmology.

The long working map of this site is The Seven Doors. This page is the short front door.

Status to have in mind

Established. A regular tetrahedron, six edge midpoints, a central octahedron and four smaller tetrahedra. Every new edge is exactly half the old one. That is G1.

Consequence of the construction. Repeat the act and you get a factor of two. That is G2.

Model choice. Treat that factor as a discrete scale coordinate from the Planck length. That is G3–G4. Nature is not thereby proved to be discretized in powers of two.

Hypothesis. That coordinate corresponds to physically meaningful structure. That hypothesis is what G5–G7 are built to test, not to protect.

The method: Observation → Mathematics → Model → Hypothesis → Test → Evaluation.

Seven doors

I. Scale architecture

Can a simple geometric operation become a scale coordinate?

G1 certifies the construction. G2 certifies the factor of two. G3 writes the numerical map. About two hundred doublings separate the Planck length from a cosmological length. That count is a logarithm, not a census of physical floors.

II. Discrete geometry

What can geometry do before physics is imposed?

Tetrahedra, octahedra, sphere packing, the 7.356° angular gap, the four hexagonal plates of the Planck Polyhedral Core, π, e, √2, and φ. Geometry first. Identification with energy budgets later, and only as a labeled conjecture.

III. Dynamics

How does a static hierarchy become a history?

Doubling, Quiet Expansion, Planck-scale generation. Toy models until a measurement says otherwise.

IV. Physical and cosmological consequences

What might follow if the geometry is physically meaningful?

Dark matter, dark energy, Hubble tension, structure, CMB. These are hypotheses to test. They are not the front door.

Current conjecture, one click away: Why is the universe 68.7% dark energy? — a postulated combination of the tet–oct volume fraction and the tetrahedral gap. Combination rule not derived. \(w = -1\) is the rigid prediction.

V. Mathematical formalization

Can the intuition become mathematics?

Constraint classes, recurrence, invariance, operators, symmetry. Langlands and E8 stay here until they earn a lower door.

VI. Finite ↔ infinite

What changes when we ask what “finite” means?

Continuity, symmetry, harmony — as qualitative structure, not as experimental physics.

VII. Value · integrity · ethics

If structure matters, does value follow?

A philosophical extension. Not a scientific consequence.

What is live this month

G7 — The physical inventory. Independently established lengths placed on the coordinate. Physics populates the map. The map does not manufacture the physics.
G7 inventory supplemental. Widened table, five G5 controls. Null on notation 67 is not eliminated. First measured composite size in the list is the proton charge radius near \(n \approx 65.5\), not 67.
Working long form: The Seven Doors. Classroom origin: first homepage. Scale chart: 202 notations.

Where to start

If you have…	Go here
Five minutes	G1 — First certified coordinate
The map	G3 and the chart
The test	G7 and the inventory
The seven-door map	7-29
A conjecture, not a result	Dark energy z