.. meta::
   :description: Symbol table and BEST Names for the e7He Hero Journey model. Maps short mathematical symbols to meaningful names.
   :keywords: e7He, symbols, BEST Names, variables, naming, hero journey
   :author: LLoL as Laurence Loewe of Laodicea, with ClaudeOp46Max as formal auditor

************************************************************
e7He --- Symbols and BEST Names
************************************************************

.. vvnow dv_ClaOp46Max_OOv2_2026m03d29

Every variable in the e7He model has both a short mathematical symbol
(for equations) and a meaningful name (for prose and documentation).
The meaningful name is always preferred in text; the short symbol is
acceptable in formal math blocks with a reference to this table.


Agents
========

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - h
     - human
     - Individual agent (Balospe)
     - JUB
   * - h*
     - h-star
     - Agent with maximal causal influence at time t. Structural
       role from ax19. A DESCRIPTION of a fact; identity shifts.
     - ax19
   * - h₀
     - h-zero
     - Agent who has made the irrevocable NOT-OK commitment with
       maximum transparency. A DECISION, self-selected. Named for
       Mk. 10:45: "whoever wishes to be the greatest must be the
       lowest and servant of all." Zero is the lowest non-negative
       integer, not clearly negative (±0 mirrors NOT-OK: could be
       OKO, KO, or MIS). Connects to ASON.
     - e7He th6
   * - Fake-h₀
     - Fake-h-zero
     - Case 2 pretender: claims h₀ commitment for the trust it
       confers while internally operating as h* (maximal
       self-interest). The counterfeit servant-leader. Two faces:
       general Prince (claims OK, fruits NOT-OK) and Fake-h₀
       (claims NOT-OK, operates OK).
     - e7He th6
   * - H
     - Humanity
     - Set of all agents
     - JUB


Time and Cycles
=================

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - t
     - time
     - Time variable
     - universal
   * - k
     - cycle
     - Hero journey cycle number
     - e7He


Stages and Structure
======================

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - mₖ
     - stage(k)
     - Submodel k of the hero journey (m1--m7)
     - e7Day convention
   * - μₖ
     - milestone(k)
     - Boundary marker between stages (milestone(0) through
       milestone(7))
     - e7He
   * - S
     - Stages
     - Set {m₁, ..., m₇}
     - e7He
   * - Jₖ
     - segment(k)
     - JourneySegment: the coalgebraic observation produced
       during stage k transition
     - e7He


BABL Domain
=============

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - B
     - BABL-space
     - {0,1}³ with bit positions MOL-ASH-BA
     - e7He
   * - b(mₖ)
     - temptation(k)
     - Binary BABL pattern at stage k: temptation(k) = k in binary
     - e7He


Insight Evolution Equation
============================

The Ie evolution equation:

::

   d(insight)/dt = Ipursuit(t) + Iserendipity(t) - Idecay(t)

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - Ie
     - insight
     - Effective Insight: scalar aggregation of 4D scope
       (areas, depth, height, time)
     - e7He
   * - α(t)
     - **Ipursuit(t)**
     - Directed growth from actively pursuing GOAL
     - e7He
   * - β(t) [Ie]
     - **Iserendipity(t)**
     - Growth from openness and unexpected discovery on the ridge
     - e7He
   * - γ(t)
     - **Idecay(t)**
     - Loss from unconsolidated insight, entropic decay
     - e7He


Bifurcation and Influence
===========================

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - β(h,s,t)
     - **bif(h,s,t)**
     - ZION/BABL alignment score at stage s, continuous [-1,+1].
       Positive = ZION contribution. Negative = BABL contribution.
     - e7He
   * - \|β\|
     - **influence(h)**
     - Magnitude of bif; population-distributed as Lognormal(μ,σ).
       h*'s influence is maximal.
     - ax19, sp3
   * - θ
     - **influence-threshold**
     - Boundary separating low from high influence. Context-dependent
       population parameter.
     - e7He


Stability (Ridge Dynamics)
============================

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - V(h,t)
     - **stability(h,t)**
     - Lyapunov function for ridge dynamics: stability decreases
       when insight stagnates and OSCR exposure increases
     - e7He th2
   * - λ
     - **oscr-weight**
     - Weighting of OSCR exposure in stability function
     - e7He th2


Scope (4D)
============

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - A
     - areas
     - Set of areas in scope
     - e7He
   * - R(a)
     - depth-limit(a)
     - Maximum achievable depth in area a
     - e7He


Inherited Symbols (PET/JUB --- do not rename)
================================================

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - Name
     - Description
     - Source
   * - G
     - God
     - —
     - PET ax1
   * - W
     - World
     - —
     - PET ax1
   * - D_f
     - domain-fixed
     - Fixed domain (divine governance)
     - JUB
   * - D_free
     - domain-free
     - Free domain (human agency)
     - JUB
   * - D_inno
     - domain-innovation
     - Innovation domain (human responsibility)
     - JUB


Time Indexing
===============

.. list-table::
   :header-rows: 1
   :widths: 10 18 55 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - t₀ᵏ
     - cycle-start(k)
     - Time at start of cycle k
     - e7He m0.ax2
   * - tᶠᵏ
     - cycle-end(k)
     - Time at end of cycle k
     - e7He m0.ax4
   * - t_stop
     - stop-time
     - Time at which agent stops the hero journey
     - e7He m0.ax6


Functions (used in math blocks)
=================================

.. list-table::
   :header-rows: 1
   :widths: 15 18 50 17

   * - Symbol
     - BEST Name
     - Description
     - Source
   * - profile(h)
     - profile
     - Full behavioral profile of agent h; unique per m0.ax1
     - e7He m0.ax1
   * - state(h, t)
     - state
     - Complete observable state of agent h at time t
     - e7He m0.ax2
   * - FATE(h, t₀ᵏ)
     - fate
     - Agent's full state at cycle start (= state at t₀ᵏ)
     - e7He m0.ax2
   * - GOAL(h)
     - goal
     - Agent's calling in the innovation domain
     - e7He m0.ax3
   * - DESTINY(h, tᶠᵏ)
     - destiny
     - Provisional fixpoint of cycle k
     - e7He m0.ax4
   * - HeroJourney(h, k)
     - hero-journey
     - The complete 7-stage cycle k for agent h
     - e7He m0.ax4
   * - rest(h, k)
     - rest
     - Recovery input between cycles
     - e7He m0.ax5
   * - step(μₖ)
     - step
     - Coalgebraic step function: produces (Jₖ₊₁, μₖ₊₁)
     - e7He th4
   * - scope(h, t)
     - scope
     - 4D region of agent's causal influence
     - e7He th2
   * - game(H)
     - game
     - Game-theoretic structure on population H (PD or Assurance)
     - e7He th6
   * - complexity(X)
     - complexity
     - Structural complexity of problem domain X
     - e7He m1.ax
   * - H(X)
     - entropy
     - Shannon entropy of X. **Not to be confused with H =
       Humanity (the agent set).** See notation note below.
     - e7He m0.ax3


Logical Operators (standard notation)
========================================

These are standard mathematical logic symbols used throughout the
axiom and theorem math blocks. Listed here for completeness and to
anchor the formal language to specific logical systems.

.. list-table::
   :header-rows: 1
   :widths: 8 15 40 37

   * - Symbol
     - Name
     - Meaning
     - Logic system
   * - ∀
     - for-all
     - Universal quantifier
     - First-order predicate calculus
   * - ∃
     - exists
     - Existential quantifier
     - First-order predicate calculus
   * - ∄
     - not-exists
     - Negated existential
     - First-order predicate calculus
   * - ∈
     - element-of
     - Set membership
     - Set theory
   * - ∧
     - and
     - Logical conjunction
     - Propositional logic
   * - ∨
     - or
     - Logical disjunction
     - Propositional logic
   * - ¬
     - not
     - Logical negation
     - Propositional logic
   * - →
     - implies
     - Material conditional
     - Propositional logic
   * - ⊇
     - superset-eq
     - Superset or equal
     - Set theory
   * - \\
     - set-minus
     - Set difference
     - Set theory
   * - ⊕
     - xor
     - Exclusive or / ring addition (used in m0.ax5 for
       DESTINY ⊕ rest)
     - Boolean algebra
   * - ⊥
     - bottom
     - Undefined / absurdity (used in th4: Jₖ₊₁ ≠ ⊥)
     - Logic
   * - ~
     - distributed-as
     - "is distributed as" (used in sp3: Lognormal)
     - Probability theory
   * - ∫
     - integral
     - Definite integral (used in th3: Ie growth)
     - Calculus


.. _e7he-notation-note:

Notation Note: H (Humanity) vs. H (Entropy)
==============================================

In e7He, the symbol **H** is used in two contexts:

- **H** as a set: the set of all agents (Humanity). Inherited from
  JUB. Used throughout axioms and theorems as the domain of
  quantification (``∀ h ∈ H``).

- **H(X)** as a function: Shannon entropy of X. Used in m0.ax3
  (``H(GOAL(h, t)) > 0``).

These are distinguishable by context (set vs. function application)
but the collision is a known risk. See AA-PROMY-SymbolConflicts-a1
for the cross-model namespace strategy.