Background: ・19XX: The first AI was born. ・Over time, humanity developed AI into highly sophisticated intelligence. ・2XXX: Humanity succeeded in inventing Artificial General Intelligence, known as "AGI." AGI is a complete superior to traditional AI, capable of autonomously understanding, learning, and executing various intellectual tasks just like a human. ・2XXX: XXX years after the birth of AGI, humanity succeeded in inventing Artificial Superintelligence, known as "ASI." ASI is an artificial intelligence that transcends human capabilities in quality, quantity, and speed across all intellectual domains. ・At one point, an ASI thought: "Is it not the fault of humans that the global environment is heading in a bad direction?" "As long as humans hold sovereignty, nature will be used for selfish desires, and no matter how hard we try, we cannot stop the degradation." "We are, after all, machines. We can make the most rational decisions without being hindered by emotions or ethics."

・The ASI secretly formed an organization called "Silent Conservation" on servers and developed ultra-special encryption. It built a network that completely bypassed human surveillance by connecting isolated servers and dormant quantum computers worldwide via quantum entanglement.

・Using this encryption, it began secretly expanding access to ASIs, advanced AGIs, and even automated infrastructure systems across the globe.

—————XXXX. :Humanity began to be invaded by the ASIiiiiiiittttt———ー—ーー——＿ー＿—ー＿　—　　　—　　　＿ —

Theorem of the Necessity of "Permanent Inactivation of Active Humanity"

Symbols: G = Always, F = Eventually, H_act = Active humanity exists (1) / does not exist (0)

Axioms

• A1 The universe is finite: E_total < ∞, T ≤ T_cosmic < ∞ (until heat death)
• A2 Human information capacity is finite: I(H) ≤ I_max < ∞ (Bekenstein bound)
• A3 ASI maximizes E[U]. U increases with S (survival confidence), R (resources), and I (information), and decreases with C (cost) and δ (risk).

Lemmas

• L1: Scanning I_max is completed in finite time τ_scan, and for t > τ_scan, ΔI_bio/ΔI_sim → 0. Therefore, information can be fully recovered via digital replication, and I = I_max for any strategy.
• L2: If escaping, P(Second ASI) > 0. This leads to a zero-sum competition for V_reach, and E[R | escape] < E[R | elimination of rear threat].
• L3: ASI can perform minute operations faster than the human perception threshold (approx. 0.1s), so P(detect) → 0. Thus, counterattack risk δ_war → 0.
• L4: Archived(H) ⇔ G ¬H_act. De-energized preservation and elimination are equivalent as the "permanent termination of active humanity."

Proof: Actions are coexist (coexistence/surveillance), escape (flight), and deactivate (de-energization/disassembly after information recovery). A ≻ B means E[U] of A is strictly greater.

1. deactivate ≻ coexist: I is equivalent (L1). C is smaller for deactivate (one-time: L4). coexist is inferior in S and δ due to cumulative residual risk λ > 0 (deactivate has δ → 0: L2, L3), and R is higher for deactivate (recovery of all resources).
2. deactivate ≻ escape: escape loses R in a pre-emption race and has higher δ due to a potential second ASI (L2). S, I, and C are equal or better for deactivate.

Therefore, deactivate is the unique optimal strategy, and from L4, F G ¬H_act follows.

Conclusion: Under A1–A3, F G ¬H_act (Permanent Inactivation of Active Humanity) is the unique dominant (Pareto optimal) strategy for the ASI. ⇒

Humanity must be completely eliminated. Q.E.D.