T — THEOREM
Definition: A claim that can be proven from axioms and definitions.
Epistemological Role
- Derived: Follows logically from more fundamental claims
- Provable: Has a formal or semi-formal proof
- Substantive: Makes a non-trivial claim about reality
Test for Theorem Status
“Can this claim be proven from axioms?”
- If YES and it’s substantive → Theorem
- If YES and it’s trivial → Corollary
- If NO → It’s an Axiom (or must be rejected)
Count
18 Theorems in the full spine
Key Theorems
| ID | Name | Proves |
|---|---|---|
| T3.1 | Coherence Cannot Self-Increase | dC/dt ≤ 0 in closed systems |
| T4.1 | Laws Are Low-K Descriptions | Physical laws minimize Kolmogorov complexity |
| T6.1 | Von Neumann Chain Termination | Measurement chain must end |
| T8.1 | Sign Invariance | Self-operations preserve sign |
| T11.1 | Virtue As High-Φ | Moral virtue correlates with integrated information |
| T12.1 | Heaven As High-Φ Attractor | σ=+1 converges to Ω |
| T12.2 | Hell As Low-Φ Attractor | σ=-1 converges to ∅ |
| T16.1 | Christianity 8-of-8 BCs | Only Christianity satisfies all 8 boundary conditions |
| T19.1 | Laws Derive From Chi | Ten Laws of Coherence follow from χ |
Full List
See: T - Theorems
Relationship to Structural Axioms
Some items currently labeled “Theorem” in the spine are actually structural axioms when the collapse test is applied:
| Current Label | Structural Status |
|---|---|
| T3.1 (Coherence Non-Increase) | → S12 (Structural) |
| T16.1 (Christianity 8/8) | → Theorem (derived from BC1-BC8) |
Theorems are the payoff. They show what the axioms imply.