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 |