Question 1: Baseline N* Calculation (Unweighted)

A White Belt candidate runs a preliminary self-audit on their Four α domains. They score their current states on a scale from 0 to 1 as follows:

• α1 (Resources): 0.8
• α2 (Relationships): 0.4
• α3 (Governance/Ethics): 0.6
• α4 (Transcendence): 0.2

What is their unbaseline, unweighted N* score?

Question 2: Gross vs. Subtle Weighting

According to the Four αlpha mathematics, the Subtle layer stabilizes the Gross layer. Therefore, the formula weights Gross at 0.4 and Subtle at 0.6.

A corporate executive has an α1 (Wealth) Gross score of 0.9. However, their α1 Subtle score (Ethical wealth generation/Sustainability) is 0.3.

Calculate the true, weighted N* component for their α1 domain using the formula: Wi [0.4(Gi) + 0.6(Si)]. Assume the domain weight wi = 1 for this calculation.

Question 3: Quantifying the 3Ds (Process Efficiency)

A family initiates a weekly meeting (an α2 SOP). The total meeting time is 120 minutes.

• 45 minutes are spent arguing over past grievances (Defect).
• 15 minutes are spent waiting for a late family member (Delay).
• 60 minutes are spent actually aligning on the week's schedule and emotional check-ins (Value-Added Time).

What is the Process Cycle Efficiency (Value-Added Time / Total Time) of this family’s α2 process, expressed as a percentage?

Question 4: The A-Y Defect (Causal Misalignment)

An individual desires Outcome Y (Deep α2 relational harmony with their spouse). However, they execute Action A (working 80 hours a week to maximize α1 wealth), falsely believing it will yield Outcome Y.

If they have 112 waking hours in a week, and they spend 80 hours on Action A, 20 hours on basic survival/chores, and the remainder on Action Y (actual relationship building), what percentage of their waking discretionary time is effectively aligned with their desired outcome?

Question 5: Independent Process Probability

To optimize his α4 (Cognitive Mastery), a student implements a Corrective and Preventive Action (CAPA) to practice Vedic Maths daily. Historical data shows his probability of executing this process on any given weekday is 0.8, and on any given weekend day is 0.5.

What is the probability that he successfully executes his α4 CAPA on both a randomly selected Tuesday AND a randomly selected Saturday?

Question 6: Expected Value & Defect Prevention

A sociological study shows that without a "Process Excellence Cell," a local government department has a 15% probability of committing a Reverse Sequence Pitfall (α3 --> α1: using administrative power to extract wealth) in a given year. If the Four α framework is implemented, this probability drops to 2%.

In a state with 200 such government departments, what is the expected number of Reverse Sequence defects prevented annually by implementing the framework?

Question 7: Trajectory Scoring

A White Belt logs their daily behavioral events. Moving forward in the sequence (α1 --> α2) adds +1 to their trajectory score. Falling into a reverse sequence pitfall (e.g., α2 --> α1) subtracts -2 due to the heavy friction generated.

In one week, the candidate logs 5 forward sequence actions and 2 reverse sequence actions. What is their net trajectory score for the week, and is the system currently optimizing or degrading?

Question 8: The Dwivedi-Nash Cooperative Equilibrium

A corporate CEO introduces a new policy. The baseline N* scores of a 3-person team prior to the policy are: Employee A (0.4), Employee B (0.5), Employee C (0.8).

The CEO models two potential policy options:

• Policy X: Increases A to 0.3, B to 0.7, and C to 0.9. (Total N* = 1.9)
• Policy Y: Increases A to 0.5, B to 0.5, and C to 0.8. (Total N* = 1.8)

According to the Dwivedi-Nash Cooperative Equilibrium theorem, which policy is the mathematically valid choice, and why?

Question 9: Root Cause Allocation (The 5 Whys)

A university identifies 500 α1 (Academic/Skill) defects—such as failed exams—in a semester. By applying the "5 Whys," they discover that 80% of these Gross α1 defects are actually rooted in Subtle α2 defects (psychosocial stress, lack of belonging).

If the university has a budget to deploy 100 CAPA interventions, how many of those interventions should be aimed directly at the α2 domain to address the mathematical root cause?

Question 10: SDE (Law of Social Motion) - Additive Model

The Law of Social Motion is modeled by dVh = F + M + dW.

In a given month for a specific individual:

• The Control Input (F, deliberate DMAIC optimization) adds +0.15 to their N* score.
• Systemic Interdependence (M, friction from a toxic workplace) subtracts -0.08.
• Random Shocks (dW, an unexpected health bill) subtracts -0.03.

What is the net change (dVh) in the individual's N* score for that month?