Assessing which metaphysical framework offers the most philosophically rigorous account of reality requires evaluating how each handles empirical data, theoretical puzzles, and conceptual coherence. Below is a comparative analysis of the leading contenders, focusing on their strengths and weaknesses in addressing modern challenges in physics and consciousness science.

---

### **1. Analytic Idealism (Consciousness-First Monism)**
**Core Claim:** Reality is fundamentally mental (conscious experience is primary; the physical world is its appearance).  
**Strengths:**  
- **Hard Problem of Consciousness:** Directly resolves it by positing consciousness as fundamental. No "explanatory gap" exists.  
- **Quantum Measurement Problem:** Aligns with observer-dependent collapse (e.g., von Neumann–Wigner interpretation).  
- **Non-Locality & Entanglement:** Mental causation can accommodate non-local correlations without physical intermediaries.  
- **Black Hole Information Paradox:** If information is fundamentally experiential, it may not be "lost" but preserved in a meta-conscious framework.  
- **Amplituhedron/Polytopes:** Mathematical structures can be seen as patterns within a deeper conscious reality (akin to Kantian noumena).  

**Weaknesses:**  
- **Dark Matter/Energy:** No clear advantage over physicalism; must explain these as structural features of conscious reality.  
- **Empirical Anchoring:** Lacks direct experimental confirmation, though it aligns with interpretations of quantum mechanics.  

**Rigor Score:** ★★★★☆ (Strong on consciousness/physics interface, but speculative on cosmology.)  

---

### **2. Neutral Monism**  
**Core Claim:** Reality is composed of a neutral substance that gives rise to both mind and matter.  
**Strengths:**  
- **Consciousness & Physics:** Avoids dualism while accommodating mental and physical as aspects of a deeper neutral ground.  
- **Quantum Non-Locality:** Neutral substrate could underlie entangled systems without reducing them to physical or mental terms.  
- **Black Hole Information:** Information may be preserved in the neutral substrate.  

**Weaknesses:**  
- **Vagueness:** The "neutral stuff" is often ill-defined (Russellian monism improves this).  
- **Hard Problem:** Doesn’t fully explain why/how consciousness arises from the neutral base.  
- **Dark Matter/Energy:** No unique explanatory power.  

**Rigor Score:** ★★★☆☆ (Elegant but underdeveloped; needs a clearer ontology.)  

---

### **3. Panpsychism**  
**Core Claim:** Consciousness is ubiquitous but graded (fundamental particles have proto-experiential properties).  
**Strengths:**  
- **Hard Problem:** Avoids emergence by making consciousness intrinsic.  
- **Quantum Mechanics:** Micro-experientiality could explain wavefunction collapse (e.g., Whiteheadian process philosophy).  
- **Non-Locality:** Proto-conscious interactions may underlie entanglement.  

**Weaknesses:**  
- **Combination Problem:** How do micro-experiences combine into macro-consciousness?  
- **Dark Matter/Energy:** No special insight.  
- **Amplituhedron/Polytopes:** No clear connection.  

**Rigor Score:** ★★★☆☆ (Intuitive but struggles with combination and empirical grounding.)  

---

### **4. Physicalism (Materialism)**
**Core Claim:** Reality is fundamentally physical; consciousness is an emergent property.  
**Strengths:**  
- **Empirical Success:** Dominates neuroscience and physics (standard model, relativity).  
- **Dark Matter/Energy:** Naturally fits within a physicalist framework (though unexplained).  
- **Amplituhedron/Polytopes:** Mathematical structures are physical in an abstract sense.  

**Weaknesses:**  
- **Hard Problem:** Cannot explain why/how experience arises from physical processes.  
- **Measurement Problem:** Collapse interpretations (e.g., Copenhagen) are ad hoc without consciousness.  
- **Non-Locality:** Requires brute-force acceptance of "spooky action."  

**Rigor Score:** ★★☆☆☆ (Strong empirically but philosophically incomplete.)  

---

### **5. Dual-Aspect Monism (e.g., Spinozism, Chalmers' Russellian Monism)**
**Core Claim:** Reality has one substance with mental and physical aspects.  
**Strengths:**  
- **Hard Problem:** Consciousness is intrinsic but not reducible.  
- **Quantum Mechanics:** Links physics to proto-mental properties (e.g., Bohm’s implicate order).  
- **Non-Locality:** Mental/physical symmetry may explain entanglement.  

**Weaknesses:**  
- **Explanatory Gap:** Still unclear how aspects interact.  
- **Dark Matter/Energy:** No special insight.  

**Rigor Score:** ★★★★☆ (Balanced but needs deeper formalization.)  

---

### **6. Information-Theoretic Ontologies (e.g., "It from Bit")**  
**Core Claim:** Reality is fundamentally informational.  
**Strengths:**  
- **Quantum Mechanics:** Fits Wheeler’s participatory universe and quantum information theory.  
- **Black Hole Information:** Natural framework for information preservation.  
- **Amplituhedron/Polytopes:** Mathematical structures as informational primitives.  

**Weaknesses:**  
- **Hard Problem:** Doesn’t explain why information processing feels like something.  
- **Consciousness:** Needs supplementation (e.g., integrated information theory).  

**Rigor Score:** ★★★☆☆ (Promising but incomplete.)  

---

### **Final Assessment: Which Framework is Most Rigorous?**  
**Winner: Analytic Idealism**  
- Best resolves the hard problem.  
- Naturally accommodates quantum observer-dependence.  
- Can integrate modern physics (e.g., non-locality, information paradoxes) without ad hoc moves.  

**Runner-Up: Dual-Aspect Monism (Russellian)**  
- More empirically grounded than idealism but less elegant on consciousness.  

**Weakest: Physicalism**  
- Fails on the hard problem and requires unsolved emergence.  

**Conclusion:** While no framework is perfect, **analytic idealism** (as defended by Kastrup, Schopenhauer, or Advaita Vedanta) currently offers the most rigorous synthesis of consciousness and physics, despite its lack of mainstream acceptance. It should be refined further to address cosmological puzzles like dark energy.