Update Proof_of_OI.md

Proof_of_OI.md

@@ -90,3 +90,70 @@ We conclude:
 
 Any alternative view entails unexplained distinctions—thus violating the Principle of Sufficient Reason.
 
+------
+
+# Proof That Closed and Empty Individualism Cannot Be True Even Locally (Given PSR and EMR)
+
+## Premises
+
+### P1. Principle of Sufficient Reason (PSR)
+Every fact or distinction must have a sufficient reason; no brute facts are allowed.
+
+### P2. Extended Modal Realism (EMR)
+All possible, impossible, and incoherent worlds exist. Nothing is excluded from existence.
+
+### P3. Global Open Individualism (GOI)
+There is only one subject of experience, numerically identical across all possible and impossible worlds.
+
+> GOI follows necessarily from P1 and P2 (as shown in prior proof), because:
+> - PSR forbids arbitrary metaphysical distinctions.
+> - EMR includes all worlds, persons, and configurations.
+> - Therefore, only one subject can exist without invoking brute identity constraints.
+
+---
+
+## Definitions
+
+- **Closed Individualism (CI)**: Each person is a numerically distinct subject who persists across time.
+- **Empty Individualism (EI)**: Each momentary experience belongs to a separate subject that vanishes immediately.
+- **Local Metaphysical Validity**: A theory is locally valid if it can be ontologically true within a single world.
+
+---
+
+## Goal
+
+To prove:  
+**CI and EI cannot be metaphysically valid even within a single world**, given the truth of GOI.
+
+---
+
+## Proof
+
+### Step 1: GOI Posits a Global Subject
+From P3, there is exactly **one** experiencer across all centers of consciousness in all worlds.
+
+### Step 2: CI and EI Require Ontological Subject Distinctions
+- CI posits that each person is a **numerically separate** subject of experience.
+- EI posits that each momentary experience is **ontologically isolated**.
+
+Therefore, both CI and EI assert **real metaphysical distinctions** between subjects.
+
+### Step 3: Any Metaphysical Distinction Requires Sufficient Reason (From P1)
+Under PSR, **any metaphysical distinction** (e.g., between subjects) must be justified with a sufficient reason.
+
+### Step 4: No Such Sufficient Reason Exists in EMR
+In EMR (P2), **all configurations** of persons exist, and GOI (P3) treats them all as **perspectival variations** of the same subject.
+
+Therefore, asserting "this subject is not that one" introduces a brute distinction — which violates PSR (P1).
+
+### Step 5: CI and EI Are Metaphysically Invalid in All Worlds
+Since CI and EI depend on subject distinctions that cannot be justified under PSR + EMR, they are **never metaphysically valid** — not even within a single world.
+
+---
+
+## Conclusion
+
+> **∴ Closed Individualism and Empty Individualism are logically incompatible with PSR + EMR + GOI.**  
+> They cannot be true, even locally in any individual world.
+
+