Axiom C₁ – Distinction
For anything to exist, it must be different from something else. Distinction is the first cut in sameness — the beginning of structure. It is the root of identity, boundaries, and the seed of all becoming.
Axiom C₂ – Recurrence
What returns can be remembered. Recurrence allows patterns to echo, and loops to form. It brings rhythm to difference, and the first hint of time.
Axiom C₃ – Relation
No difference is meaningful in isolation. Relation binds distinctions together into structure. It is how tension spreads — and how meaning emerges.
Axiom C₄ – Constraint
Not everything is possible. Constraint limits what relations can hold, shaping consistency. It gives rise to rules, boundaries, and selective survival of patterns.
Axiom C₅ – Tension
Tension is the consequence of resisting entropy — the strain that arises as the lattice bends to hold difference. It is the invisible pull that gives structure weight, direction, and the potential to collapse.
Axiom C₆ – Interference
Where loops meet, they reshape each other. Interference is the interaction of tensions across relation. It is how systems evolve, align, or collapse.
Axiom C₇ – Collapse
When tension exceeds coherence, a commitment is made. Collapse locks possibility into memory — a decision encoded. It is the origin of measurable events, and the basis of matter.
Axiom C₈ – Consequence
Committed memory changes what can happen next. Consequence ties the past to the future — cause to effect. It allows structure to build across time.
Axiom C₉ – Non-Self-Sufficiency
No loop explains itself in isolation. Every structure is supported by others — upward and downward. This axiom binds all parts into a deeper unity of interdependence.
T₀ – The Symmetry Threshold
Before anything could change, everything was the same. T₀ marks the moment when pure symmetry broke — and the universe gained permission to begin.
T₁ – The Commitment Threshold
No loop explains itself in isolation. Every structure is supported by others — upward and downward. This axiom binds all parts into a deeper unity of interdependence.
T₂ – The Collapse Threshold
What was once only structure becomes real.
T₂ marks the point where tension slows below light speed — and loops collapse into the physical universe.
T₃ – The Reversion Threshold
Even the committed can come undone.
T₃ marks the boundary where collapsed structures can no longer hold — and return to pure information.