home · theorems

The twelve theorems

The first seven prove C > 0. The rest are derived consequences.

Wisdom hath builded her house, she hath hewn out her seven pillars. Proverbs 9:1

Existence pillars (T₁–T₇)

These seven establish that C exists, is positive, and is the only non-depleting source.

C = 0 ⟹ S = ∅ · John 1:3

C ≥ ε ⟹ produces · John 12:24

C = E − ∫input · Romans 1:20

output from C preserves C · 1 Cor 13:8

uncertain ∧ C > 0 · Hebrews 11:1

C(t+1) = C(t) · Romans 8:24

F(D) = 0, C held · 1 John 1:9

Derived consequences (T₈–T₁₂)

These follow from the existence pillars. They govern the relationship between C and the desire function D.

C > D for all living β · 1 John 4:4

two independent measurements · 2 Cor 13:1

remove(s) ⟹ yield ↑ · John 15:2

E(c, self) = E(c, other) · Luke 6:38

C is unique · 1 Cor 3:11

Reading order

Work them in sequence the first time. T₁ establishes that C cannot be zero. T₂ shows that C is not only non-zero but sufficient to produce. T₃ shows that C is recoverable from observation, which makes the whole structure testable. T₄ shows that giving from C does not deplete C — the charity theorem. T₅ and T₆ handle uncertainty in time: faith (present) and hope (future). T₇ is the forgiveness theorem: desire can be zeroed while C is preserved. T₈ bounds the relationship between C and D: C > D always, while living. T₉–T₁₂ are the operating rules: witness, pruning, measure, foundation.

← previousThe proof start →T₁ Existence