Boundary graph
A T-motif is a four-vertex K₄ boundary graph with four triangular cycles. An O-motif is a six-vertex K₂,₂,₂ boundary graph with three square and eight triangular cycles.
Structure before spacetime
What is space made of?
Qaether does not assume a continuous space in advance. It explores how geometry, time, and causal structure might arise from minimal units, their contacts, and boundaries alone.
- No background continuum
- No filled cells
- Boundary first
Conceptual boundary graph
01 · The premise
Before filled space, there are relations.
Qaether represents a minimal unit of space itself, not a particle moving through space. An edge is a primitive contact between two units; selected cycles and motifs are boundaries, not filled faces or volumes.
- 01Vertex
A minimal unit of space
- 02Bond
A selected primitive contact
- 03Cycle
A closed triangular or square boundary
- 04T / O motif
A tetrahedral or octahedral boundary pattern
- 05Emergence
A candidate geometric and physical structure
02 · The foundation
It begins with a small set of axioms.
The graph's incidence structure, its three-dimensional reference realization, and the internal state of each vertex are treated separately. This makes computation possible without mistaking an auxiliary coordinate system for a deeper reality.
Vertex state
Each vertex carries an SU(2) state, and an edge's relative phase is induced by its endpoint states. Closed-loop holonomy is flat; no independent link gauge field is assumed.
Reference realization
A three-dimensional realization expresses geometric non-degeneracy and contact. A defect-free reference vacuum is compatible with an FCC-type lattice, but the lattice itself is not part of the primitive ontology.
03 · From structure to physics
Physics begins when structure changes.
Events, clocks, curvature-like quantities, and causal histories are introduced step by step on a static boundary graph. They are candidates for testing structural origins—not immediate identifications with established physical quantities.
An event changes one vertex.
The smallest event is an atomic update to a single vertex state. Causal order is recorded as a partial order of these events, with independent execution orders required to produce the same final configuration and clock record.
Time counts square-clock completions.
A selected square boundary of an O-motif acts as a local clock. One tick occurs when its phase pattern completes 4π, and local time is the accumulated count. The number of events need not equal the number of ticks.
Curvature is explored through motif residuals.
A curvature-like residual measures how far local T/O incidence departs from an ideal reference assembly. It is a computational model of structural mismatch—not general-relativistic curvature or loop-holonomy curvature.
Spatial slices meet in causal sandwiches.
A CDT-based reference theory maps T-motif boundary graphs to the 1-skeletons of spatial tetrahedra and joins adjacent slices with causal 4-simplices, providing a setting for studying state sums and possible (3+1)-dimensional dynamics.
04 · The big picture
One structure, many questions.
Qaether does not simply rename familiar concepts from physics. It asks which physical properties can actually be derived from a shared minimal structure, carefully separating assumptions from consequences.
-
Foundation
Separate ontology from representation.
Vertices and edges are primitive. Coordinate realizations and higher-dimensional lattice stacks are auxiliary structures used to express geometry.
-
Consistency
Distinguish flat internal states from structural observables.
Rather than postulating a new loop flux, candidate observables are sought in flat-compatible data such as square-channel arrangements and orientations.
-
Dynamics
Move from a static graph to executable change rules.
Hard motif transitions and continuous relaxation make it possible to calculate how reference residuals evolve.
-
Validation
Test mathematical consistency and computational viability together.
Finite domains, boundary buffers, and cutoffs are made explicit so calculations can be checked against the definitions step by step.
Research status
Not a finished theory, but a framework for testable questions.
Qaether does not claim to derive general relativity, quantum field theory, or the Standard Model. It is a research toy framework for asking—through precise definitions and computation—whether boundary structure alone can contain the seeds of geometry and time.