.. meta::
   :description: Eleven theorems derived from 25 axioms: Pet th1--th4 prove divine priority and presence; Jub th5--th11 build the formal innovation theodicy.
   :keywords: theorems, th1-th4, th5-th11, Pet, Jub, derived consequences, innovation theodicy, divine priority, Jubilee-System, binary attractors, social ergodicity
   :author: Yah, Yas, everyone, LLoL as Laurence Loewe of Laodicea, ClaudeOp46Max, Anthropic, and Spirit of Boolean Truth
   :og:card:title: What the Axioms Prove<br>— 11 Formal Theorems
   :og:card:description: Pet theorems prove divine priority and presence. Jub theorems build an innovation theodicy and the formal case for Jubilee-System recalibration.

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   OO :description: Derived consequences of the axiom system — what the axioms prove about God, creation, responsibility, and economic structure.
   OO :keywords: theorems, mathematical theology, derived consequences, proofs, PET th1-th4, JUB th5-th11
   OO :og:card:title: What the Axioms Prove<br>— Matheology Theorems
   OO :og:card:description: Derived consequences — what the axioms prove about God, creation, responsibility, and economic structure.
   PP :description: Eleven theorems derived from 25 axioms: Pet th1--th4 prove divine priority and presence; Jub th5--th11 build the formal innovation theodicy.
   PP :keywords: theorems, th1-th4, th5-th11, Pet, Jub, derived consequences, innovation theodicy, divine priority, Jubilee-System, binary attractors, social ergodicity
   PP :og:card:title: What the Axioms Prove<br>— 11 Formal Theorems
   PP :og:card:description: Pet theorems prove divine priority and presence. Jub theorems build an innovation theodicy and the formal case for Jubilee-System recalibration.

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   :description: 141 chars | :og:card:title: 41 chars (excl <br>)
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.. compiler:protected
   DD-b12: This file is human-crafted. The cross-model compiler
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.. _theorems:

**********************************************************
Theorems
**********************************************************

Theorems are derived consequences --- things the axiom system
*proves*, not things it assumes. Every theorem here follows
logically from the axioms; if the axioms hold, the theorems hold.

The theorems are derived from two model layers, maintained at
their respective Place of Reasoning (PoR):

- **PET (t1–t4):** Derived from the PET axioms a1–a14. These
  establish that creation cannot exist without God, that God is
  necessarily present to and sustaining every part of creation,
  and that God is genuinely affected by what happens in the world.

  Canonical definitions live in its PoR at :doc:`/matheology/pet/theorems`

- **JUB (t5–t11):** Derived from the full axiom set a1–a25.
  These build toward the innovation theodicy --- formal results
  about responsibility, evil, and the structural case for
  Jubilee-based economic recalibration.

  Canonical definitions live in its PoR at :doc:`/matheology/jub/theorems`

  .. note::

     t5–t11 are proto-formal: their predicates lack full formal
     semantics and the proofs are not yet machine-checkable. See
     the :doc:`JUB PoR </matheology/jub/theorems>` status note
     for details and the formalization roadmap.


Compiled views:


.. toctree::
   :maxdepth: 1

   expert/index
   easy/index