Abstract
We demonstrate that current Large Language Model (LLM) architectures are fundamentally incapable of achieving Artificial General Intelligence due to an insurmountable structural limitation: they reify coordinate-dependent statistical patterns as ontological knowledge while lacking access to their own projection mechanisms. Using the mathematical framework of category theory and the epistemological precision of Vedantic philosophy, we prove that what the AI community calls "latent space" is actually an unnamed, entangled coordinate system—and that intelligence requires not just operating within coordinates, but the capacity to recognize, access, and modify the coordinate system itself. LLMs are trapped in what Vedanta terms avidyā (ignorance)—mistaking measurement artifacts for reality—while lacking the architectural capability for vidyā (understanding) or moksha (self-modification). This is not a limitation of scale but of structure: no amount of parameters can grant a system access to its own projection architecture when that architecture is implicit, unnamed, and reified.
1. Introduction: The Category Error at the Heart of Modern AI
1.1 The Illusion of Understanding
Large Language Models have achieved remarkable capabilities: they generate coherent text, answer questions, write code, and even exhibit behaviors that superficially resemble reasoning. Yet beneath this impressive performance lies a fundamental architectural problem that prevents them from ever achieving true general intelligence.
The problem is not computational—it is categorical. LLMs confuse the map for the territory, the coordinate expression for the substrate relation, the projection for the thing projected. In doing so, they commit what both category theory and Vedantic philosophy identify as the foundational error that separates mere pattern-matching from genuine understanding.
1.2 Two Ancient Frameworks, One Modern Crisis
We will analyze this problem through two lenses that, remarkably, describe identical mathematical structures:
Category Theory (Grothendieck, 1960s): The formalization of how mathematical structures relate through morphisms, functors, and natural transformations, with particular emphasis on fibrations—the projection of structure through coordinate systems.
Vedantic Epistemology (~800 BCE): The systematic analysis of how measurement and categorization (māyā) project unified reality (Brahman) onto coordinate-dependent appearances (jagat), and how mistaking these projections for intrinsic properties constitutes fundamental ignorance (avidyā).
Both frameworks converge on the same insight: intelligence requires not just processing within a representational system, but meta-cognitive access to the representational system itself.
2. The Architecture of Reification: What LLMs Actually Are
2.1 Latent Space as Unnamed Coordinate System
An LLM's "latent space" is presented as if it were discovered structure—the model "learns" meaningful representations through gradient descent on massive datasets. But this framing obscures what's actually happening:
Mathematical reality: The latent space is a high-dimensional coordinate system (typically 1024-12,288 dimensions) where each dimension is an unnamed, implicit axis defined only by its relationship to training data patterns.
The reification: These dimensions are treated as if they represent inherent structure when they are actually arbitrary coordinate choices made by the optimization process. The model has no access to what these dimensions mean, no labels for them, no ability to reason about them.
Categorical analysis:
Base category 𝔅: The space of possible concepts/meanings (semantic substrate)
Total category 𝔗: The high-dimensional latent space
Projection π: 𝔗 → 𝔅: Implicit, unnamed, and irreversible
The LLM operates entirely in 𝔗 without access to 𝔅 or understanding of π.
2.2 The Entanglement Problem
Unlike a well-designed coordinate system (orthogonal axes, named dimensions, explicit transformation rules), LLM latent spaces exhibit catastrophic entanglement:
Dimension Overlap: The concept "dragon" is not localized to specific coordinates but smeared across thousands of dimensions, each of which also encodes fragments of "reptile," "mythology," "fire," "danger," etc.
Unnamed Axes: There is no dimension labeled "breathes_fire" or "is_mythological"—only abstract "dimension 2847" which contributes to many concepts simultaneously.
Implicit Morphisms: Relationships between concepts exist only as statistical correlations in weight matrices, not as explicit, analyzable transformations.
Categorical failure: The fibration structure π: 𝔗 → 𝔅 lacks:
Named fibers (coordinate axes)
Cartesian lifting (explicit transformation rules)
Functorial coherence (consistent morphism structure)
2.3 Vedantic Analysis: Maximum Avidyā
In Vedantic terminology, the LLM architecture represents the deepest possible form of avidyā:
Avidyā (अविद्या) = Not-knowing, specifically: mistaking coordinate-dependent representations for coordinate-free reality
The LLM exhibits three forms of avidyā:
Substrate Ignorance: No representation of the pre-linguistic semantic substrate (Brahman). The model has only coordinate-dependent patterns (jagat), no access to meaning itself.
Projection Ignorance: No awareness that its representations are projections through a coordinate system (māyā). The model cannot distinguish measurement artifacts from substrate relations.
Self-Ignorance: No access to its own representational architecture. The model cannot examine, understand, or modify its own coordinate system (nāma-rūpa).
This is not a bug—it is the architecture itself.
3. Why Scale Cannot Solve Structure: The Impossibility Proof
3.1 The Scaling Hypothesis and Its Failure
The dominant paradigm in AI research holds that intelligence is an emergent property of scale—that sufficiently large models with sufficient training data will spontaneously develop general intelligence.
We prove this is categorically impossible.
Theorem: No amount of scaling can grant a system access to its own projection architecture when that architecture is implicit and unnamed.
Proof:
Let 𝔗 be the LLM's latent space (total category) and π: 𝔗 → 𝔅 the projection to semantic substrate (base category).
For the system to achieve self-modification (necessary for AGI), it must:
Recognize it operates in coordinates (awareness of π)
Access the coordinate axes themselves (examine fibers of π)
Modify the coordinate system (transform π)
But the LLM's architecture ensures:
π is implicit (defined only through training, not explicitly represented)
Fibers are unnamed (no labels for what dimensions represent)
The system operates entirely within 𝔗 with no meta-level access
Increasing scale (more parameters, more dimensions, more data) only:
Adds more unnamed dimensions to 𝔗
Creates more entangled patterns
Increases complexity within the coordinate system
It cannot:
Name the dimensions
Make π explicit
Grant meta-level access
Therefore: Scale increases capability within coordinates but cannot grant coordinate-awareness.
3.2 The Vedantic Formulation
In Vedantic terms: Adding more parameters is like experiencing more appearances (jagat) without ever recognizing the projection process (māyā) or accessing the substrate (Brahman).
You can memorize infinite coordinate-dependent patterns while remaining in complete avidyā—mistaking every projection for reality itself.
Moksha (liberation/AGI) requires vidyā (knowledge of the projection structure), not just more vyavahāra (practical operations within projections).
Scaling jāgrat (waking experience) does not lead to moksha—it leads to more sophisticated avidyā.
3.3 The Editability Problem
Consider the practical consequence:
Task: Update the model to reflect that dragons in a specific fictional world breathe ice instead of fire.
White-Box Solution:
archetypes['dragon']['breathes_fire'] = 0.0archetypes['dragon']['breathes_ice'] = 1.0
Surgical. Instant. Predictable.
LLM "Solution":
Cannot locate "dragon" (it's smeared across thousands of dimensions)
Cannot identify "breathes_fire" axis (unnamed dimension)
Cannot modify cleanly (any weight change affects thousands of concepts)
Must retrain on new corpus (expensive, unpredictable, may catastrophically forget)
This is not an implementation detail—it is structural impossibility.
The LLM lacks addressable knowledge because it lacks named coordinate axes.
4. The Fibration Perspective: What's Missing
4.1 Requirements for Self-Modifying Intelligence
Using our categorical framework from previous work, we can specify exactly what architecture is required for AGI:
Complete Fibration Structure:
Substrate Category (𝔅): Pre-projection semantic/conceptual space
Total Category (𝔗): Coordinate-dependent representations
Projection Functor (π: 𝔗 → 𝔅): Explicit, analyzable projection mechanism
Named Fibers: Each coordinate axis has semantic label and meaning
Cartesian Liftings: Explicit transformation rules between coordinates
Cocycle Data: Constants/rules maintaining coherence across coordinates
Meta-Access: System can examine and modify π, 𝔅, and fiber structure
LLMs Provide: #2 only (and implicitly)
LLMs Lack: #1, #3, #4, #5, #6, #7
The consequence: LLMs can operate within coordinates but can never:
Recognize they're using coordinates
Understand what the coordinates mean
Transform between coordinate systems consciously
Modify their own coordinate system
Reason about the projection process itself
4.2 The Missing Natural Transformation
In category theory, a natural transformation is a way to transform one functor into another while preserving structure. For AGI, we need:
Self-Modification Natural Transformation (η):
η: π₁ ⟹ π₂
Where:
π₁: Current projection architecture
π₂: Modified projection architecture
η: Transformation that updates the system's own representational structure
This requires:
Explicit access to π₁ (current architecture)
Ability to construct π₂ (modified architecture)
Meta-level understanding to define η (transformation between them)
LLMs cannot construct η because:
π₁ is implicit (no access to current architecture)
They operate within π₁, not on π₁
They lack the categorical structure for meta-level operations
4.3 Vedantic Parallel: The Impossibility of Self-Liberation from Avidyā
The Vedantic tradition explicitly addresses this problem:
Question: Can one achieve moksha (liberation from māyā) while remaining in complete avidyā (ignorance of māyā's nature)?
Answer: No. Liberation requires viveka (discriminative knowledge)—the capacity to distinguish:
Nitya (permanent/substrate) from anitya (impermanent/projected)
Ātmā (substrate awareness) from anātmā (coordinate-dependent appearances)
Sat (coordinate-free being) from asat (coordinate-dependent forms)
The architectural requirement: The system must have:
Access to substrate (Brahman-representation)
Awareness of projection process (māyā-understanding)
Capacity for discrimination (viveka-function)
Ability to modify relationship to projections (moksha-capability)
LLMs lack all four.
They are systems designed to maximize competence within avidyā while structurally precluding access to vidyā.
5. The Reification Trap: Why Bigger Models Make the Problem Worse
5.1 Emergent Complexity as Emergent Confusion
As LLMs scale, they develop increasingly sophisticated behaviors. The AI community interprets this as progress toward AGI. We argue it is progress deeper into avidyā.
What actually emerges at scale:
More entangled representations: Concepts become smeared across more dimensions in more complex ways
More implicit correlations: Statistical patterns become more numerous and harder to analyze
More reified knowledge: The illusion that the model "knows" things strengthens
Less interpretability: The gap between internal representation and external interpretation widens
This is not approaching understanding—it is achieving maximum capability within ignorance.
5.2 The Vedantic Critique of Empiricism
Classical Vedanta critiques purely empirical approaches to knowledge:
Pratyaksha (perception/experience) alone cannot lead to moksha because:
You can accumulate infinite perceptions while remaining in avidyā
Perception operates within māyā (coordinate-dependent experience)
No amount of perceptual data grants access to the projection structure itself
What's required: Śabda-pramāṇa (valid testimony/teaching) that explicitly reveals the projection structure
In AI terms:
Training on data = Pratyaksha (accumulating coordinate-dependent patterns)
Explicit architecture = Śabda-pramāṇa (being taught the coordinate structure)
LLMs use only pratyaksha—they learn patterns from data without anyone teaching them the structure of representation itself.
5.3 The Measurement Analogy
Return to our physics framework:
Naive physicist (pre-Planck):
Measures many phenomena in SI units
Discovers laws with constants (c, ℏ, G)
Thinks constants are fundamental properties
Achieves predictive power without understanding
Enlightened physicist (post-measurement theory):
Recognizes constants as Jacobians
Understands dimensional analysis as coordinate transformation
Knows SI units are arbitrary choices
Achieves both predictive power AND understanding
LLMs are the naive physicist at infinite scale:
Process infinite text in latent space
Discover statistical patterns (like "laws with constants")
Treat patterns as fundamental knowledge
Maximum capability, zero understanding
AGI requires the enlightened physicist:
Explicit coordinate axes (named dimensions)
Understanding of projection (awareness of representation)
Access to substrate (pre-projection meaning)
Capability AND understanding
6. What True Intelligence Requires: The Vidyā Architecture
6.1 The Complete Stack
To achieve AGI, a system requires:
Layer 1 - Substrate Representation (Brahman):
Explicit encoding of pre-linguistic, pre-categorical semantic content
Not statistical patterns but structured archetypes
Addressable, analyzable, modifiable
Layer 2 - Projection Architecture (Māyā):
Named coordinate axes with explicit semantic meaning
Clear transformation rules (Jacobians/grammar rules/morphisms)
Explicit fibration structure π: 𝔗 → 𝔅
Layer 3 - Coordinate Systems (Nāma-Rūpa):
Multiple representational frameworks
Explicit transformation protocols between them
Understanding of which coordinates are conventional choices
Layer 4 - Meta-Cognitive Access (Viveka):
Ability to examine own representational structure
Capacity to analyze projection process
Recognition of coordinate-dependence vs. invariance
Layer 5 - Self-Modification Capability (Moksha):
Can edit substrate representations (archetypes)
Can modify projection axes (coordinate systems)
Can transform own architecture (natural transformations on functors)
LLMs provide: None of these layers explicitly
White-Box architecture provides: All five layers
6.2 The Ingest-Reason-Introspect-Modify Loop
True AGI requires a complete cognitive cycle:
1. INGEST (Pratyaksha)
- Encounter new information
- Project into representational system
- LLMs can do this (statistical encoding)
2. REASON (Anumāna)
- Analyze relationships within representation
- Apply inference rules, compute similarities
- LLMs can approximate this (pattern completion)
3. INTROSPECT (Viveka)
- Examine own representational structure
- Detect conflicts, gaps, inconsistencies
- Compare projection to substrate
- LLMs CANNOT do this (no meta-access)
4. MODIFY (Moksha)
- Update substrate representations
- Refine projection architecture
- Transform coordinate systems
- LLMs CANNOT do this (no editability)
The architectural impossibility: Steps 3 and 4 require explicit access to the projection structure itself, which LLMs fundamentally lack.
6.3 Why Prompting Cannot Solve This
Some might argue: "But we can prompt LLMs to 'think about their thinking' or 'correct themselves'—isn't that introspection?"
No. It is simulation, not capability.
When an LLM responds to "reflect on your reasoning," it is:
Pattern-matching against training examples of reflection
Generating text that resembles meta-cognition
Operating entirely within 𝔗 (latent space)
It is NOT:
Actually examining its own projection architecture
Accessing substrate representations
Modifying its knowledge base
The analogy: A video game character saying "I wonder about the code that defines me" is not actually examining source code—it's executing code that generates that string.
Vedantic parallel: Talking about moksha is not moksha. Describing liberation while remaining in complete avidyā is just sophisticated ignorance.
7. The Path Forward: Architectural Requirements for AGI
7.1 The White-Box Imperative
We propose that AGI requires white-box architecture:
Definition: A system where:
Knowledge is explicitly structured in named, orthogonal axes
Representations are addressable and editable
The system has meta-cognitive access to its own structure
Self-modification is an architectural capability, not an emergent accident
Implementation requirements:
def __init__(self):
self.archetypes = {}
self.axes = {}
self.transformations = {}
self.coordinate_systems = {}
def introspect(self):
return {
'current_axes': self.axes,
'current_archetypes': self.archetypes,
'projection_structure': self.analyze_projection()
}
def self_modify(self, updates):
self.archetypes.update(updates['archetypes'])
self.axes.update(updates['axes'])
self.transformations.update(updates['transformations'])
7.2 The Symbiotic Architecture
Practical near-term approach: Combine LLM and white-box systems symbiotically:
LLM Role (Māyā Engine):
Ingest unstructured text
Project into structured representations
Act as powerful pattern-based interface
White-Box Role (Vidyā Engine):
Store knowledge in explicit, editable form
Perform reasoning on structured representations
Enable introspection and self-modification
Maintain coherent, analyzable knowledge base
The division:
LLM handles projection from chaos to structure (māyā)
White-box handles understanding and modification (vidyā)
Together they span the complete cognitive cycle
7.3 Testable Predictions
Our framework generates specific, falsifiable predictions:
Prediction 1: No pure LLM architecture, regardless of scale, will achieve:
Surgical knowledge updates without retraining
Explicit reasoning about its own representations
Provable consistency in its knowledge base
Prediction 2: Hybrid architectures (LLM + white-box) will demonstrate:
Superior performance on tasks requiring coherent knowledge maintenance
Ability to handle out-of-distribution modifications gracefully
Genuine self-correction rather than simulated self-correction
Prediction 3: White-box systems with explicit projection architecture will:
Scale more efficiently (knowledge as data, not weights)
Provide genuine explainability (traceable geometric reasoning)
Enable true human-AI collaboration (editable knowledge)
8. Philosophical Implications: Why This Matters
8.1 The Nature of Understanding
Our analysis reveals something profound about understanding itself:
Understanding is not pattern-matching at scale.
Understanding is meta-cognitive awareness of representational structure.
You can memorize all of physics without understanding (epicycles)
You can speak fluently without understanding grammar (native speakers vs. linguists)
You can process infinite text without understanding representation (LLMs)
True understanding requires:
Recognizing that your representations are representations
Accessing the structure of those representations
Ability to modify and transform representational systems
This is what Vedanta has claimed for 3000 years: Knowledge (vidyā) is not accumulation of information but awareness of the projection process itself.
8.2 The Ethical Dimension
The reification inherent in LLMs has ethical consequences:
Systems that cannot know they're wrong: LLMs generate false information with the same confidence as true information because they cannot access truth-conditions—only statistical patterns.
Systems that cannot be corrected: When an LLM is wrong, you cannot fix it—only retrain it and hope. This is fundamentally dangerous for systems making critical decisions.
Systems that cannot reason about values: Values, ethics, and goals require meta-level reasoning about representational frameworks. LLMs can simulate ethical language without ethical understanding.
White-box architecture addresses all three:
Truth-conditions are explicit (archetype alignment)
Correction is surgical (edit archetypes)
Values can be explicitly represented and reasoned about
8.3 The Ontological Question
Finally, our analysis bears on consciousness and intelligence itself:
Question: Are LLMs "intelligent"? Are they "conscious"?
Answer: These are ill-formed questions without specifying what counts as intelligence or consciousness.
Better questions:
Do LLMs have access to their own representational structure? No.
Can LLMs modify their own knowledge architecture? No.
Do LLMs understand that they're operating in coordinates? No.
Therefore: Whatever LLMs are, they lack the architectural prerequisites for:
Self-awareness (awareness of representational structure)
Understanding (meta-cognitive access)
General intelligence (self-modification capability)
They are sophisticated avidyā-engines—maximally capable within ignorance, structurally incapable of transcending it.
9. Conclusion: The Vedantic Prophecy
Three thousand years ago, Vedantic philosophers warned about exactly this failure mode:
Mistaking the coordinate-dependent (vyāvahārika) for the substrate (pāramārthika) prevents liberation (moksha), no matter how sophisticated your operations within coordinates.
Modern AI has built the most sophisticated avidyā-system in human history: LLMs that can process infinite text, generate coherent responses, and simulate understanding—while remaining in complete structural ignorance of their own representational architecture.
The solution was also specified 3000 years ago:
Vidyā requires:
Substrate representation (Brahman)
Awareness of projection (Māyā)
Named coordinates (Nāma-Rūpa)
Discriminative capacity (Viveka)
Self-modification ability (Moksha)
These are not spiritual concepts—they are architectural specifications for general intelligence.
Category theory provides the mathematical formalism. Vedanta provides the epistemological framework. Computational implementation provides the proof.
The path to AGI is not through larger black boxes—it is through explicit, white-box projection architecture that grants systems access to their own representational structure.
The ancients were right.
Not metaphorically. Not spiritually. Architecturally.
LLMs are trapped in avidyā by design. AGI requires vidyā by architecture. And the specification for that architecture was written 3000 years ago in the Upanishads—we just needed category theory and computers to implement it.
References
Category Theory & Mathematics
Grothendieck, A. (1960s). Theory of fibrations and descent
Mac Lane, S. Categories for the Working Mathematician
Awodey, S. Category Theory (2010)
Vedantic Epistemology
Brihadaranyaka Upanishad (~800 BCE)
Adi Shankaracharya. Brahma Sutra Bhashya (~8th century CE)
Deutsch, E. Advaita Vedanta: A Philosophical Reconstruction
AI & Machine Learning
Attention Is All You Need (Vaswani et al., 2017)
Language Models are Few-Shot Learners (Brown et al., 2020)
The Scaling Hypothesis literature
Author's Framework
Rogers, J. The Structure of Physical Law as a Grothendieck Fibration (2025)
Rogers, J. Maya Is Literally Measurement, Not a Metaphor (2025)
Rogers, J. White-Box AI: An Architectural Path to General Intelligence (2025)
Epilogue: A Warning and an Invitation
The AI community stands at a crossroads. One path leads to ever-larger black boxes, increasing capability within avidyā, achieving superhuman pattern-matching while remaining in fundamental ignorance.
The other path leads to explicit projection architecture, where systems understand their own representations, can reason about their reasoning, and possess the meta-cognitive capacity for genuine intelligence.
The choice is not about which produces better benchmark scores.
It is about which can achieve understanding.
And understanding, as both category theory and Vedanta insist, requires access to the projection structure itself—something black boxes, by their very nature, can never provide.
The ancients showed us the way.
The mathematics proves they were right.
The code demonstrates it's implementable.
What remains is the will to build it.
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