.. _e7he-axioms:

****************************************************
e7He --- Axioms
****************************************************

14 axioms in two groups: 7 prerequisite axioms (m0) defining the
framework, and 7 stage axioms (m1--m7) defining the journey.

Extracted from FORGE session Sa3_2026m03d28 by PROMY:EXTRACT
on 2026-03-29. See :doc:`/matheology/hell/ll/promy/b/11/promy_ll_2026m03d29_e7he-pipeline-test`.


m0 Prerequisites
==================


.. _e7he-m0-ax1:

m0.ax1 --- Uniqueness
~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \forall h \in H \;:\; \nexists\, h' \in H,\; h' \neq h \;:\;
   \text{profile}(h') = \text{profile}(h)

Every agent has a unique profile. Stereotyping (mapping unique
profiles to standardized templates) is a lossy PERFIDE operation
(e7Day m2.ax2).


.. _e7he-m0-ax2:

m0.ax2 --- FATE Acceptance
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \forall h \in H,\; \forall\, \text{cycle } k \;:\;
   \text{FATE}(h, t_0^k) = \text{state}(h, t_0^k)

   \text{HeroJourney.precondition} \;:\;
   \text{accepts}(h, \text{FATE}(h, t_0^k))

FATE is the agent's full state at cycle start (Markov property).
The hero journey requires acceptance of FATE as its starting condition.
At birth: completely unchosen. Over life: accumulated consequences
of all prior choices, failures, and destinies found.


.. _e7he-m0-ax3:

m0.ax3 --- GOAL Calling
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \forall h \in H \;:\; \exists\, \text{GOAL}(h) \in D_{\text{inno}}

   \text{such that: } H(\text{GOAL}(h, t)) > 0 \;\;\text{(entropy: partially unknown)}

   \text{and: pursuing}(h, \text{GOAL}(h)) \text{ contributes positively to }
   \frac{d\,\text{Ie}_W}{dt}

   \text{and is locally optimal for } h\text{'s comparative advantage}

Every agent has a GOAL in the innovation domain. The GOAL is
partially unknown (positive entropy) and progressively revealed.
Lesser goals are not bad in themselves but become distractions when
they displace the best GOAL.


.. _e7he-m0-ax4:

m0.ax4 --- Cycle Definition
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \text{HeroJourney}(h, k) \;:\;
   \text{FATE}(h, t_0^k) \xrightarrow{s_1, \ldots, s_7}
   \text{DESTINY}(h, t_f^k)

   \text{where DESTINY}(h, t_f^k) \text{ is provisional}
   \;\;(\text{valid until cycle } k+1)

The hero journey is the 7-stage transition from FATE to DESTINY.
DESTINY is a fixpoint of cycle k (mc.ax1), not a permanent state.


.. _e7he-m0-ax5:

m0.ax5 --- Perpetual Reset
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \forall\, \text{cycle } k \;:\;
   \text{FATE}(h, t_0^{k+1}) :=
   \text{DESTINY}(h, t_f^k) \oplus \text{rest}(h, k)

   \text{AND: } \text{self-assessment}(h, t_0^{k+1}) = \text{NOT-OK}

Each cycle's DESTINY becomes the next cycle's FATE (plus rest).
The hero MUST enter the new cycle with NOT-OK self-assessment ("I
should assume the worst about myself that can't be disproven").
OK self-assessment ("I already know") at cycle start triggers
BABL (m6.ax4).

This is the coinductive step function: each cycle produces the
initial conditions for the next.


.. _e7he-m0-ax6:

m0.ax6 --- Stopping Outcome: Irrelevance
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \text{stops}(h, t_{\text{stop}}) \;\wedge\;
   |\beta(h)| \text{ low}
   \;\rightarrow\;
   \frac{d\,\text{Ie}_H}{dt} \leq 0
   \;\;\text{for } t > t_{\text{stop}}

An agent who stops their hero journey with low influence becomes
irrelevant: Ie stagnates, scope freezes, causal influence decays
toward zero.


.. _e7he-m0-ax7:

m0.ax7 --- Stopping Outcome: Supervillain
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \text{stops}(h, t_{\text{stop}}) \;\wedge\;
   |\beta(h)| \text{ high}
   \;\rightarrow\;
   \text{scope}(h) \text{ stagnates at large value}
   \;\wedge\; \text{friendly-fire at scope boundary}

An agent who stops with high influence becomes a supervillain:
large stagnant scope generates misapplied expertise at the
boundaries of what they no longer understand. If h = h*, this is
maximally dangerous for the system (th7 Gate 5).


Stage Axioms (m1--m7)
========================

Each stage axiom defines: (1) the BABL pattern active, (2) the
journey segment content, (3) the milestone condition, and (4) the
bifurcation dynamics.

General form:

.. math::

   \text{e7He.m}_k \;:\;
   \text{step}(\mu_{k-1}) = (\mathcal{J}_k,\; \mu_k)

   \text{where } \mathcal{J}_k.\text{babl\_pattern} = b(m_k)

   \text{and boundary } \mu_k \text{ requires: }
   \mathcal{J}_k.\text{babl\_resisted} \supseteq b(m_k)
   \;\vee\; \beta(h, m_k, t) < 0 \;\text{(BABL path)}


.. _e7he-m1-ax:

m1.ax --- Adventure Calls: Dare (001 = --- --- BA)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_1.\text{babl\_pattern} = 001

   m_1 \;:\; \text{accepts}(h, \text{complexity}(\text{GOAL}))
   \;\wedge\; \text{commits}(h, \text{journey})

The hero accepts that the problem is genuinely complex and commits
to engaging it. The BA temptation to dismiss ("not my problem") has
been faced. Evidence: the hero starts the journey.


.. _e7he-m2-ax:

m2.ax --- Trial Tribulation Training (010 = --- ASH ---)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_2.\text{babl\_pattern} = 010

   m_2 \;:\; \text{skills}(h, t_{m_2}) > \text{skills}(h, t_{m_1})
   \;\wedge\; \text{endurance-tested}(h)

The hero survives genuine trial and emerges with new skills and
courage. Failure is information, not identity. The ASH fog of
"you need to understand everything first" has been cut through.


.. _e7he-m3-ax:

m3.ax --- Gain Advantage Temptation (011 = --- ASH BA)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_3.\text{babl\_pattern} = 011

   m_3 \;:\; \text{holds-advantage}(h) \;\wedge\;
   \neg\text{captured-by}(h, \text{advantage})

The hero holds genuine advantage without being defined by it.
Distinguishes tool from identity. Hears criticism graciously
(message, not messenger). The double temptation (BA: "I've figured
it out" + ASH: "let me build an empire") has been faced.


.. _e7he-m4-ax:

m4.ax --- Meet Your Maker: Infinity Alone (100 = MOL --- ---)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_4.\text{babl\_pattern} = 100

   m_4^{\text{ZION}} \;:\;
   \neg\text{CWA}(h, t_{m_4}) \;\wedge\;
   \text{false-self-died}(h)

   m_4^{\text{BABL}} \;:\;
   \text{CWA}(h, t_{m_4}) \;\wedge\;
   \text{deeper-BABL-servant}(h)

The midpoint bifurcation. The hero confronts infinity and either
lets the BABL-shaped false self die (rejecting Closed World
Assumptions) or clings to it (accepting CWA). Hamming distance
from s3 is 3: the most radical transition. This departure does
not feel radical from inside --- by stage 4, BA and ASH have
normalized the patterns that make MOL's overreach seem necessary.

Two outcomes: become Jonah (ZION agent) or become the whale
(integrated into the Leviathan).


.. _e7he-m5-ax:

m5.ax --- Lucky Ultimate Reward Comedy (101 = MOL --- BA)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_5.\text{babl\_pattern} = 101

   m_5 \;:\; \text{received-without-entitlement}(h) \;\wedge\;
   \text{shared-without-grasping}(h)

The hero receives rewards and shares justly, especially with mercy
for the weak. Maintains commitment to see all views of all the weak
by remembering weakness in light of infinity. Serves the mass market
without creating monopolies that CWAs expect.


.. _e7he-m6-ax:

m6.ax --- Rescue Trip To Resurrection (110 = MOL ASH ---)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_6.\text{babl\_pattern} = 110

   m_6 \;:\; \text{gift-alive-in-others-hands}(h) \;\wedge\;
   \neg\text{institutional-capture}(\text{gift})

The hero fights for truth for truth's own sake. Separates the gift
from all CWAs. Translates for diverse communities. Builds minimal
viable structures that carry the gift forward without becoming its
prison.


.. _e7he-m7-ax:

m7.ax --- Free Reborn Evolving Better (111 = MOL ASH BA)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. math::

   \mathcal{J}_7.\text{babl\_pattern} = 111

   m_7^{\text{ZION}} \;:\;
   \text{full-BABL-resisted}(h) \;\wedge\;
   \text{rest}(h) \;\wedge\;
   \text{open-to-next-call}(h)

   m_7^{\text{BABL}} \;:\;
   \text{insights-weaponized}(h) \;\wedge\;
   \text{Machiavelli-Prince}(h)

Full BABL faced. ZION path: genuine simplification proposed,
hero rests, stays a peacemaker, remains open to next cycle.
BABL path: insights weaponized, corruption perfected, system
persists until self-collapse.