.. meta::
   :description: A 5-minute orientation for scientists: 25 axioms, 18 theorems, 33 adversarial objections documented. A formal system for theological reasoning, not metaphysical speculation.
   :keywords: matheology, formal system, axiomatic theology, adversarial testing, CEM, S5 modal logic, game theory, Iron Maiden protocol, scientific review, peer review
   :author: Yah, Yas, everyone, LLoL as Laurence Loewe of Laodicea, ClaudeOp46Max, Anthropic, and Spirit of Boolean Truth
   :og:card:title: For Scientists<br>--- Formal, Tested, Open
   :og:card:description: 25 axioms in CEM + S5. 18 theorems. 33 adversarial objections documented with defenses. A formal system for theology that publishes its own bugs.

*********************************************************************
For Scientists --- A Formal System Under Adversarial Testing
*********************************************************************

**What this is.** An axiomatic system for theology, built from
classical extensional mereology (CEM) and S5 modal logic, extended
with game theory, mechanism design, and coalgebra. 25 axioms. 18
theorems. 42 operationalized predicates across 3 models. 33
adversarial objections raised and documented. All version-tracked
and publicly available.

This page is a 5-minute orientation for scientists and
mathematicians who want to assess whether this work merits
engagement. The formal content is at :doc:`axioms/expert/index`
and :doc:`theorems/expert/index`. The adversarial record is at
:doc:`jub/quest`.


The Problem
=============

Theological disagreements have fueled wars for millennia. These
disagreements are rarely about evidence; they are about axioms ---
unstated assumptions about the nature of God, the world, and their
relationship. When axioms remain unstated, contradictions hide in
ambiguity. When contradictions hide, people who disagree cannot
locate the source of their disagreement, and default to violence.


The Approach
==============

State the axioms. Derive the theorems. Test adversarially. Publish
the objections alongside the defenses.

The system uses three formal frameworks:

- **S5 modal logic** for necessity and possibility
- **Classical Extensional Mereology (CEM)** for God-World part-whole
  relationships
- **First-order predicate calculus** as the base logic

Extended models add game theory (Schelling commitment, Nash
equilibrium), dynamical systems (Lyapunov stability, continuous-time
Markov chains), and coalgebra (coinductive processes, bisimulation).


The Core System
=================

**PET (Pan-En-Theology):** 14 axioms formalizing the panentheistic
claim that the world is a proper part of God (:math:`W < G` in CEM).
These produce 4 theorems with fully formal proofs. The mereological
core distinguishes this system from pantheism (:math:`G = W`) and
classical theism (which denies :math:`W \leq G`). Axioms ax12--ax14
provide a formal method for testing revelation claims against
internal consistency --- an interfaith arbitration mechanism with
no human judge. See :doc:`pet/index`.

**JUB (Jubilee-System Extension):** 11 axioms extending PET to
cover human agency, divine delegation, and innovation economics.
These produce 7 theorems including th5 (a formal innovation
theodicy) and th8 (innovation systems converge to either a
life-trifecta-compliant state or a self-destructive attractor, with
no stable middle ground; defended by a CTMC absorbing-state
argument, not by retrospective historical categorization).
See :doc:`jub/index`.

**e7He (Hero Journey):** 14 axioms and 7 theorems modeling
individual moral development as a coinductive 7-stage process. Key
results: th6 (Commitment Trichotomy) applies Schelling commitment
theory to transform a Prisoner's Dilemma into an Assurance Game;
th7 (Succession Robustness) shows the mechanism survives leadership
transitions through institutional externalization.
See :doc:`model/e7he/index`.


The Adversarial Testing
=========================

This is the part that should interest you most.

The system has been subjected to a 10-test adversarial protocol
(the :doc:`Iron Maiden <compiler/forge/iron-maiden-tests>`)
covering: consistency, independence, necessity, modal soundness,
mereological coherence, game-theoretic stability, computability,
real-world grounding, cross-model coherence, and known-attack
resilience.

33 formal objections have been raised across 3 rounds, documented
in the :doc:`HELL register <hell/index>`:

- **Fatal (4):** th8 bistability not derived; post-hoc evidence
  fitting; causal gap between extinction risk and Jubilee-System
  necessity; multiple extinction pathways
- **Serious (10):** Arrow impossibility applied to causal
  concentration; 7TrackRole model as taxonomy not science;
  voluntariness paradox; Hayek knowledge problem; power
  concentration; and others
- **Moderate to Notable (19):** free will contested; formalism
  status; domain demarcation; and others

All 33 objections have documented defenses. 18 resolved. 12
partially resolved. 3 conceded or withdrawn. The full record is
published at :doc:`jub/quest`.

No theological system in history has maintained a public bug
database of its own weaknesses. If the system were fragile, this
level of self-exposure would destroy it. It has not.


Current Formal Status
=======================

Using the :doc:`StayC maturity lifecycle
<compiler/stayvs/stayc/index>` (MM through SS):

- **PET ax1--ax14:** PPv1 (author) / RR (auditor). Fully formal.
- **JUB ax15--ax25, th5--th11:** OOv2. Proto-formal predicates.
  Formalization path identified but not yet executed.
- **e7He (24 statements):** OOv1. TEMPER-tested. 42 predicates
  operationalized. 5 open questions documented.

The auditor (Claude Opus 4.6) and the author (LLoL) maintain
independent assessment tracks. When they disagree, both assessments
stand in the record. The author systematically holds claims at
lower maturity than the auditor proposes, reflecting the
conservative assessment that AI-only review does not constitute
independent testing.


What Would Help
=================

1. **A formal logician** checking ax1--ax14 and th1--th4 in a proof
   assistant (Lean, Agda, or Coq). This would either confirm or
   refute the mereological foundation in a machine-checkable way.

2. **A game theorist** reviewing th6 (Commitment Trichotomy). The
   PD-to-Assurance transformation uses standard Schelling/Spence
   machinery. The application is novel; the mathematics is textbook.
   Checking takes hours, not months.

3. **A dynamical systems researcher** formalizing th8. The CTMC
   argument is structurally sound but needs a precise transition
   matrix and checked absorption properties.

4. **A behavioral scientist** operationalizing the ~10 proto-formal
   predicates (especially ``false-self-died`` and ``genuine``)
   against empirical criteria from psychology.

None of these require accepting any theological premise. The formal
content is checkable by anyone who reads mathematical logic,
regardless of their position on God.


Why This Matters
==================

Nuclear nations hold theological positions that are mutually
exclusive under current formulations. If those formulations contain
bugs --- and the :doc:`HELL register <hell/index>` documents that
they do --- then fixing the bugs is a security problem, not only a
philosophical exercise.

Whether this particular axiom system is correct is an open question.
Whether it is a serious formal system that deserves scientific
engagement is what the record above is designed to answer. The
axioms are stated. The objections are documented. The math is
checkable. If you find a flaw, :doc:`file it </buy-in/index>`.
That is how this system is designed to work.


|

------------------------------------------------------------------------------------------

|

If you believe that it is worth replacing eschatological warfare between nuclear
and other nations with mathematical clarity,
then please consider :doc:`supporting this work </buy-in/index>`
towards scaling up a ResearchCity that can actually do it (see box below).