.. meta::
   :description: Pet model: 14 axioms in 5 groups formalize panentheism with mereology and S5 modal logic. Six traditions independently support the same formal structure.
   :keywords: Pet model, ax1-ax14, panentheism, mereology, modal logic S5, five groups, six traditions, scriptural convergence, th1-th4, poster, Group VI extension
   :author: Yah, Yas, everyone, LLoL as Laurence Loewe of Laodicea, ClaudeOp46Max, Anthropic, and Spirit of Boolean Truth
   :og:card:title: Pet — 14 Formal Axioms<br>for Panentheism
   :og:card:description: Containment, transcendence, necessity, presence, dipolar nature, and revelation testing. Six traditions converge on the same formal structure.

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   OO :description: 14 formal axioms for pan-en-theism using mereology and modal logic, with convergent support from six scriptural traditions.
   OO :keywords: PET, pan-en-theism, axioms, mereology, modal logic, mathematical theology, scriptural convergence
   OO :og:card:title: PET — 14 Formal Axioms<br>for Pan-En-Theism
   OO :og:card:description: A formal axiom system for pan-en-theistic mathematical theology — 14 axioms in 5 modular groups, using mereology and modal logic S5.
   PP :description: Pet model: 14 axioms in 5 groups formalize panentheism with mereology and S5 modal logic. Six traditions independently support the same formal structure.
   PP :keywords: Pet model, ax1-ax14, panentheism, mereology, modal logic S5, five groups, six traditions, scriptural convergence, th1-th4, poster, Group VI extension
   PP :og:card:title: Pet — 14 Formal Axioms<br>for Panentheism
   PP :og:card:description: Containment, transcendence, necessity, presence, dipolar nature, and revelation testing. Six traditions converge on the same formal structure.

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*************************************************
PET Model for Pan-En-Theism
*************************************************


A formal axiom system for pan-en-theistic mathematical theology — 14 axioms
in 5 modular groups, using mereology and modal logic S5.

The axioms encode the distinctive panentheistic claim that "all is *in* God,
but God exceeds all" and derive consequences from it with mathematical rigor.
When checked against the scriptures of six independent traditions — Torah,
Prophets, Gospel, wider Christianity, Islam, and Hinduism — the axioms
receive surprisingly strong convergent support, suggesting that the
theological disagreements driving real-world conflict may not be about the
*structure* of God's relationship to the world, where the scriptures agree,
but about other claims layered on top.


.. image:: /_file/pdf/gnp/mmv3/flyingscroll/page/poster-m2-matheology-axioms-panentheism-start-confict-resolution-ivLLoL_PPv1r1p1_2026m03d14-3x4ft.*
   :alt: Poster on Axiomatic Mathematical Theology for defining pan-en-theism
   :width: 100pc
   :align: center
   :target: /_file/pdf/gnp/mmv3/flyingscroll/page/poster-m2-matheology-axioms-panentheism-start-confict-resolution-ivLLoL_PPv1r1p1_2026m03d14-3x4ft.pdf

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.. note::

   **Version:** iv_LLoL_PPv1r1p1_2026m03d14. Axiom ax11 is strengthened with
   subworld-indexed Gc structure. Axioms ax12–ax14 are reformulated to define
   a principled methodology for testing prophetic claims.


Contents
==========

.. toctree::
   :maxdepth: 2

   overview
   poster
   axioms
   theorems
   symbols
   discussions
   theodicy
   history
   anyaims
   llog/index


Quick Overview
================

**14 axioms in 5 groups:**

- **Group I — Mereological Core** (ax1–ax4): The world is in God, but God
  exceeds the world. Every part of creation is within God.
- **Group II — Modal Axioms** (ax5–ax7): God exists necessarily; the world
  exists contingently; containment is necessary.
- **Group III — Relational Axioms** (ax8–ax10): God is present to every part
  of creation, sustains it, and does not depend on it.
- **Group IV — Divine Nature** (ax11): God has an unchanging nature AND a
  world-responsive experience (dipolarity).
- **Group V — Revelation Bridge** (ax12–ax14): God's self-knowledge is true;
  human claims about revelation can be formally tested for consistency.

**4 reviewed theorems** derived from the axioms: No Godless Creation (th1),
Asymmetric Ontological Priority (th2), No Isolated Part of Creation (th3),
Divine Experience Varies (th4).

**Proposed extension — Group VI (ax15–ax25) and th5–th11:** 11 additional axioms
covering Agency & Delegation and 7 new theorems. See the
:doc:`JUB framework </matheology/jub/index>` for the full extension.
The extension formally closes the innovation theodicy
(why God is not responsible for the evil caused by human failure to innovate):
th5 (Divine Non-Responsibility), th6 (Causal Concentration), th7 (God Seeks a
Volunteer), th8 (Binary Attractors / T-Inno: river of life vs. sea of
destruction), th9 (Social Ergodicity / T-Ergodicity: the justice mechanism),
th10 (Physical Law Substrate / T-Physics), th11 (Stakes Without Death /
T-Finitude). For the narrative entry point, see :doc:`/matheology/jub/theodicy`.

**Key result:** The cross-traditional convergence — six independent
perspectives (Jewish Torah, Jewish Prophets, Jesus's direct teachings, wider
Christianity, Islam, Hinduism, and secular philosophy) each independently
support the same formal axiom structure. This convergence was not designed in;
the axioms were constructed from philosophical analysis and the scriptural
check was performed afterward.


Origin
========

The system was proposed by AI Claude Opus on 2026-03-11 in conversation with
LLoL, refined through poster review on 2026-03-14/15. See :doc:`llog/index`
for full development history.


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