Glossary of Notation

Money: A symbolic token of power that can be transferred between economic agents.

Price: A quantity of money needed to activate or inactivate an economic agent.  “Activate” could mean transfer ownership, or perform a service, while “inactivate” could mean retracting a threat of force.

Capital: A financial asset which is valued according to the discount formula (risk-adjusted expected future earnings discounted to a present value).

Priority Theory of Value: The social value of something is measurable by its centrality to the society.

Generator Paradox: The observation that a system of planning based on energy value can result in generators always being the only rational use of resources.

The following is old information with no plans of being updated:

Resource:
r = (identifier, quantum, dependencies, properties) \in R
\|R\| = n
parameter (abbreviation/alternate abbreviation): Description

identifier (id/id): A hashable and unique identifier to describe r.
quantum (q/q): The standard SI unit of this resource. When choosing this, keep in mind values will truncate below q.
dependencies (で/de): A set of resources that compose r.
superclasses (sup): The set of all resources which could be considered generalizations of this resource.
subclasses (sub): The set of all resources which could be considered specializations of this resource.
surveys (sv): The set of observations of this resource.
properties (ろ/ro): A set of properties defining r

Supply:

s \in S \subset \mathbb{S}
Monoid: s = kr, s_{id} = r_{id}
Domain: 0 \le k < \infty, k \in \mathbb{Z}_+
Sets:
S={s_i}: \left [ s_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n
\mathbb{S} = \{ S_i \} \forall i \le n; \|\mathbb{S}\|=\left (\binom{n}{k} \right )

Demand:

d \in D \subset \mathbb{D}
Monoid:d = \delta r, d_{id} = r_{id}
Domain: -\infty < \delta < \infty , \delta \in \mathbb{Z}
Sets:
D={d_i}: \left [ d_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n
\mathbb{D} = \{ D_i \} \forall i \le n; \|\mathbb{D}\|=\left (\binom{n}{\delta} \right )

Exploitation:

e \in E \subset \mathbb{E}
Monoid: e = \epsilon r, e_{id} = r_{id}
Domain: 0 \le \epsilon \le k, \epsilon \in \mathbb{Z}_+
Sets:
E={e_i}: \left [ e_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n
\mathbb{E} = \{ E_i \} \forall i \le n; \|\mathbb{E}\|=\left (\binom{n}{\epsilon} \right )

Subsets of R:

R \supseteq \{ \mathbb{ M, C, P} \}

m \in \mathbb{M}

The most basic subset of R, the basic and advanced materials.
\mathbb{M}_B: Basic materials: \{m \in \mathbb{M}\}: m_{de} = \{ \O\}
\mathbb{M}_A: Advanced materials: \{m \in \mathbb{M}\}: m_{de} \subseteq \mathbb{M}
Economies are constrained between \mathbb{M} = R\ and\ \mathbb{M} = \{\O\}

c \in \mathbb{C}

The intermediate subset of R, the components.
Components have at least one material dependency:
c_{de} \subseteq \mathbb{M}
Components are members of at least one set of product dependencies:
\exists p \in \mathbb{P}: p_{de} \ni c
Components exist because of a process that acted on one or more materials:
\exists \varphi : f_p(M\subseteq\mathbb{M}, \varphi)\rightarrow c

p \in \mathbb{P}

The highest-level subset of R, the products.
Products are not materials or components:
p \notin \{\mathbb{C,M}\}
Products’ dependency sets are composed of components:
p_{de} \ni r:r\in\mathbb{C}
Products exist because of a process that acted on one more components:
\exists\varphi:f_p(C\in\mathbb{C},\varphi)\rightarrow p

Adaptations of Mainstream Economics Definitions:

Normal good:
\frac{dS_{x.de}}{dt} > 0 \rightarrow \frac{dD_x}{dt} > 0

Ordinary good:
\frac{d(x.de)}{dt} < 0 \rightarrow \frac{dD_x}{dt} > 0

Inferior good:
\frac{dS_{x.de}}{dt} > 0 \rightarrow \frac{dD_x}{dt} < 0

Durable good:
x is a durable good iff:
f(I,O), x\in I \rightarrow x\in O

Non-durable good:
x is a non-durable good iff:
f(I,O), x\in I \rightarrow x\notin O

Agents:

An agent is an individual or organization that acts on or is served by the economy.
a=(id, mutex, history, requests)

id: (id/id) Hashable and unique identifier
mutex: (む/mu) The current mutex, if any, that a has locked.
history: (ひ/hi) The allocation/deallocation and use history of a.
requests: (れ/re) Catalog or feature requests from a.
Set:
A = \{a_i\}\forall i\le N; \|A\|=N
Derivations:
The set D (all demand) is at least the set of all requests for all agents in A.
D \supseteq \{a_{re}\}\forall a\in A
The set E (all exploitation) is at least the set of all allocations and uses of all agents in A.
E \supseteq \{a_{hi}\}\forall a\in A

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