e7He — Symbols and BEST Names#

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#

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#

Symbol

BEST Name

Description

Source

t

time

Time variable

universal

k

cycle

Hero journey cycle number

e7He

Stages and Structure#

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#

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)

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#

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)#

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)#

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)#

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#

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)#

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.

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

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.