e7Day Symbol Dictionary#

This page defines all symbols used in the e7Day formal statements (axioms and theorems). Only resolved definitions are listed here. For unresolved acronym alternatives, see dict/ambiguities-to-decide.rst.

For the axioms, see e7Day Axioms. For the theorems, see e7Day Theorems.

Entities and Constants#

Symbol

Name

Meaning

Used in

\(\Omega\)

Total domain

Pre-partition domain (VOID state) before scope partition

m0.ax1, m1.ax1

\(L\)

Light / in-scope

The domain within which all construction occurs

m1.ax1 and throughout

\(D\)

Dark / out-of-scope

Complement of L; excluded from construction

m1.ax1

\(W\)

World

The system produced by the construction (W = L)

th1

\(B\)

Balospe

Balance-o-stat species; agent with general intelligence

m6.ax2, m6.ax4

\(h^*\)

Maximally influential agent

The agent with maximal causal influence (per PET ax19)

th7 (Gate 5)

God

God

Distinguished divine entity (boundary condition for th7)

th7

Type Partitions#

Symbol

Name

Meaning

Used in

\(\text{Int}(L)\)

Integer types

Indivisible types within L

m2.ax1, m2.ax2

\(\text{Real}(L)\)

Real types

Divisible types within L

m2.ax1, m2.ax2

\(\text{Ground}(L)\)

Ground values

Unconditionally known values

m3.ax1, m3.ax2

\(\text{Ocean}(L)\)

Ocean values

Conditionally known values

m3.ax1, m3.ax3

Water

Water

Circulation medium (Ocean through programs and back)

m3.ax2, m3.ax3

\(\text{DAY}(L)\)

DAY processes

Directed foreground activity

m4.ax1

\(\text{NIGHT}(L)\)

NIGHT processes

Nondeterministic background guidance

m4.ax1

WorkTime

Work time

Active construction time

m7.ax2

RestTime

Rest time

Periodic consolidation time

m7.ax2

Operators and Functions#

Symbol

Name

Meaning

Used in

\(\text{fix}(\cdot)\)

Fixpoint operator

“It was good” convergence; fix(result(mk)) = result(mk)

mc.ax1

\(\text{result}(m_k)\)

Submodel result

Output of submodel k

mc.ax1, mc.ax4, m7.ax1

\(\text{process}(m_k)\)

Submodel process

The evening-then-morning process of submodel k

mc.ax3

\(\text{input}(m_k)\)

Submodel input

Input to submodel k (includes all prior results)

mc.ax4

\(\text{info-loss}(\varphi)\)

Information loss

Information lost by mapping \(\varphi\)

m2.ax2

\(\text{scope}(\cdot)\)

Scope

Experiential scope of an agent’s compassion

th7 (Gates 2, 5)

\(\text{repair-history}(a, F)\)

Repair history

Agent a’s repair experience for fault class F

th7 (Gates 1, 2)

\(\text{awareness}(a, \cdot)\)

Awareness

Agent a’s information about another’s state/context/trajectory

th7 (Gate 3)

\(\text{noise}(\cdot)\)

Noise level

Noise on a compassion or information channel

m5.ax2, th7 (Gate 4)

Verdicts#

Symbol

Name

Meaning

Used in

OK

OK

Fixpoint convergence; scope-creep-excluded; “it was good”

mc.ax2, m6.ax4

OKO

OKO

Structurally necessary indeterminacy; requires external resolution

m6.ax3, m6.ax4

KO

KO

System failure

m6.th1, th7

\(\text{OK}^+\)

OK-plus

Self-correcting architecture from matched OKO pair

m6.ax3

Named Concepts#

Symbol

Name

Meaning

Used in

PERFECT

PERFECT

Preserve Existence Rights of Functionally Existing Copies of Types

m2.th1, th3

PERFIDE

PERFIDE

Preserve Exchangeability of Resource Functionality in Diverse Environments (double meaning deliberate)

m2.th1

BABL

BABL

Blindly Assuming Blind Leveraging (collapse attractor)

m6.ax4, m6.th1, th3, th5

ZION

ZION

Zoning Investigating Organizing Navigating (innovation attractor)

m6.ax4, th3

UMP

UMP

Unimportant Message Problem (noise threshold for signal collapse)

m5.ax2, th7 (Gate 4)

ASON

ASON

Ambiguous Semantics Of Nothing (semantic trap at VOID)

th7 (Gate 5)

OSCR

OSCR

OK Self-assessment Collapse Route

m6.th1

Mathematical Symbols#

Symbol

Name

Meaning

Used in

\(H(\cdot)\)

Entropy

Shannon entropy function

m0.ax1

\(H_{\max}\)

Maximum entropy

Upper bound of entropy (VOID state)

m0.ax1

\(\varepsilon\)

Epsilon

Minimum information loss bound (strictly positive)

m2.ax2

\(\theta\)

Theta

Noise threshold for channel collapse

m5.ax2, th7

\(F_{\text{all}}\)

All fault classes

The set of all problem/fault classes in the system

th7 (Gates 1, 2, 5)

\(\uplus\)

Disjoint union

Type partition operator (exhaustive, non-overlapping)

m1.ax1, m2.ax1, m3.ax1, m4.ax1, m7.ax2

\(\triangleright\)

Sequential composition

Evening before morning ordering

mc.ax3