Provide comprehensive definitions that flow from the AIM Framework for: Freedom; Fairness; Justice; Appetites; Intrinsic Motivation; Mimetic Desire; Value; Wealth; Mimetic Premium. Also Provide any calculations we have used throughout the this thread and space.

Below are comprehensive definitions for your requested AIM concepts, followed by core calculations used throughout this thread and the AIM research space. These are aligned with the most recent clarifications and mathematical treatment from the AIM framework sources.

Comprehensive AIM Definitions

1. Freedom

Freedom, under AIM, is the condition where intrinsic motivation leads behavior, appetitive needs are regulated (not allowed to coerce or distract), and mimetic pressures are bounded by design—so that individuals may "opt out" of rivalry or status contests and persist in self-endorsed, autonomy-supportive pursuits.[^1]

2. Fairness

Fairness is achieved when decisions and allocations prioritize appetitive sufficiency (meeting basic needs) and intrinsic autonomy (protecting agency), while neutralizing undue mimetic advantages—producing outcomes not determined by prestige, visibility, or social tournaments, but by needs and competence properly defined.[^1]

3. Justice

Justice is the system-level property where a) appetitive needs are secured, b) intrinsic autonomy is structurally protected, and c) mimetic amplification is bounded so that status, observability, and herd effects do not determine access, opportunity, or punishment. Conflicts are resolved by restoring A, re-establishing intrinsically-led agency, and de-amplifying socially transmitted wanting.[^1]

4. Appetites

Appetites (A) are bodily, homeostatic needs—like hunger, thirst, sleep, shelter, and pain avoidance—which rise with deprivation, collapse with satiety, and motivate the organism toward physiological restoration or risk avoidance.[^1]

5. Intrinsic Motivation

Intrinsic motivation (I) is self-endorsed engagement in process-valued activities—driven by curiosity, mastery, meaning, or flow—and persists in the absence of external rewards, audience, or social comparison. It is characterized by high autonomy, competence, and relatedness (as in SDT) but is treated as a distinct neural and behavioral channel in AIM.[^1]

6. Mimetic Desire

Mimetic desire (M) is socially transmitted wanting, sparked by observing others’ goal-directed actions, status cues, or prestige contests. It amplifies certain desires through rivalry, visibility, and social contagion, and when unbounded, can hijack, escalate, or distort both appetitive and intrinsic aims.[^1]

7. Value

Value, in AIM, is the integrated single-unit signal (common-currency) that weights A, I, and M according to their relevance and context to determine choice salience and action selection:

$$ V(x) = w_A U_A(x) + w_I U_I(x) + w_M U_M(x) $$

where $w_A + w_I + w_M = 1$.[^1]

8. Wealth

Wealth is the stock of resource access, skills, social capital, and opportunity—measured and provisioned so as to reliably secure appetitive sufficiency (A), support ongoing intrinsic motivation (I), and manage mimetic exposure (M)—not merely the gross accumulation of market-valued claims.[^1]

9. Mimetic Premium

The Mimetic Premium (VM) is the residual value captured by mimetic amplification after accounting for appetitive and intrinsic components:

$$ VM = V_{Total} - (V_A + V_I) $$

where $V_{Total}$ is observed willingness to pay, effort, or attention, and $V_A$, $V_I$ are measured or estimated A and I values.[^1]

Core Calculations and Equations

AIM Common-Currency Valuation

$$ U(x) = w_A U_A(x) + w_I U_I(x) + w_M U_M(x) $$

$w_A + w_I + w_M = 1$

$U(x)$: Integrated utility or value for option $x$
$U_A(x)$, $U_I(x)$, $U_M(x)$: Utility from appetites, intrinsic motivation, and mimetic desire, respectively

Mimetic Premium (Residual)

$$ VM = V_{Total} - (V_A + V_I) $$

Used to diagnose status inflation, bubbles, or rivalry-driven market surges.

AIM Real Wage Index

$$ W^{AIM}{real} = \frac{W{money} + V_{A\textrm{-}in\textrm{-}kind} + V_{I\textrm{-}access}}{P_{A/I}} $$

Denominator $P_{A/I}$ excludes the mimetic premium from the price index, measuring only needs and intrinsic productivity.

Justice Condition (Formal)

A justice disposition is achieved in domain $D$ if, for all agents $i$:

$A$ baselines are met (no one is in deprivation-driven coercion)
$w_I$ can dominate in key choices (autonomy-supportive contexts)
$w_M$ is bounded by procedure (no allocation driven mainly by prestige or visibility)[^1]

Audience Removal Test

If decisions are materially unchanged with audience removed, then mimetic pressure (M) is managed and intrinsic/autonomy-supportive motivation (I) leads.[^1]