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.