Abstract:
We introduce Induced AI-Theory Expansion (IAI-TE), a formal methodology for developing scientific theories in collaboration with large language models (LLMs). IAI-TE reframes LLM "hallucination" as unfiltered statistical fantasy  analogous to human imagination but devoid of innate reality-checking mechanisms. The methodology counteracts this by constructing a framework of artificial reality filters: (1) a lossless, context-window-optimized Axiomatic Core (A-Core), (2) a predefined Structural Template (S-Template), and (3) an iterative Consistency-Enforcement Protocol (CE-Protocol) that integrates both textual and symbolic verification. We demonstrate IAI-TE's efficacy by detailing its role in constructing the Temporal Theory of the Universe (TTU), a coherent, ~50-page theoretical manuscript. IAI-TE provides a blueprint for transforming LLMs from sources of confabulation into disciplined engines for logical extrapolation, establishing a new paradigm for human-AI co-authorship in fundamental science.

Keywords: artificial intelligence, theory development, large language models, scientific methodology, human-AI collaboration, theory architecture, axiomatic systems, hallucination, imagination, reality filters, prompt engineering, temporal theory of the universe.

1. Introduction: From Hallucination to Guided Imagination

Large language models (LLMs) are revolutionizing human-computer interaction, yet their tendency to "hallucinate" generate plausible but ungrounded content remains a critical barrier to their use in rigorous science [1]. This paper proposes a paradigm shift: we reconceptualize LLM hallucination not as a mere error, but as a form of unfiltered statistical fantasy.

This fantasy is functionally analogous to human imagination: both processes generate novel, coherent information by interpolating and recombining prior experience (training data for LLMs, lived experience for humans). The crucial divergence lies in the absence of innate reality filters in LLMs. Humans possess layered corrective mechanisms: a physical filter (sensory feedback) and a cognitive filter (critical self-reflection). LLMs possess neither; their primary drive is linguistic coherence within a given context, not correspondence with an external world.

We present Induced AI-Theory Expansion (IAI-TE), a methodology that engineers and installs these missing filters onto the LLM's generative process. By providing a rigorous axiomatic, structural, and procedural framework, IAI-TE transforms the LLM's uncontrolled statistical fantasy into a directed, self-correcting engine for scientific theory-building. This work details the IAI-TE protocol and demonstrates its successful application in developing the Temporal Theory of the Universe (TTU), positioning it as a novel, formal contribution to the methodology of human-AI collaborative science.

2. The IAI-TE Framework: Engineering Artificial Reality Filters

IAI-TE is built on the principle that a productive AI collaborator must be endowed with proxies for the reality-checking capabilities it inherently lacks. The methodology operationalizes this through three engineered components, each acting as a specific filter.

2.1. The Three Engineered Filters of IAI-TE

Filter 1: The Axiomatic Core (A-Core) The Theory's Immutable Physics
The A-Core is a minimal (typically 7-15 statements), self-contained set of foundational postulates. This size is strategically chosen: it is sufficient to define a novel theoretical ontology (e.g., "Time is a physical field") while being compact enough to be losslessly compressed and held entirely within the context window of contemporary LLMs throughout the entire expansion cycle. This ensures the A-Core's immutability and constant accessibility, functioning as a non-negotiable "constitution" for the theory. It includes ontological axioms, definitional axioms (e.g., E=E=), and correspondence rules to established knowledge (0000).

Filter 2: The Structural Template (S-Template) The Theory's Logical Anatomy
The S-Template is a predefined schema that outlines the theory's architecture. It specifies sections (e.g., Foundations, 5D Mathematics, Electrodynamics), their required logical components (e.g., "Derivation of displacement current"), and the dependency graph between them. This template confines the LLM's generative search space to a productive, causally coherent pathway, preventing it from generating conclusions before premises.

Filter 3: The Consistency-Enforcement Protocol (CE-Protocol) The Theory's Immune System
The CE-Protocol is the operational heart of IAI-TE, implementing the metacognitive filter. It is a recursive Generate Verify Integrate/Correct loop. The verification step is not merely textual; it is a hybrid analytical process:

• • Textual Consistency Check: A dedicated LLM instance (or a separate verification pass) acts as a "critic," checking for logical flow, definitional adherence, and narrative coherence against the A-Core and prior text.
  • Symbolic & Dimensional Check: For mathematical content, the protocol mandates a symbolic verification step. This can involve: a) explicit prompting of the LLM to perform and show dimensional analysis, b) integration with external symbolic algebra systems (e.g., via API calls to Wolfram Alpha), or c) manual human oversight at key junctures. In the TTU case study, this involved rigorous checking that derived equations like jdisp=(t)jdisp=(t) maintained correct units (A/m') and reduced to known identities (Maxwell's displacement current).
    

3. The IAI-TE Workflow: A Protocol for Constrained Creativity

The following diagram illustrates the iterative, filter-driven workflow of IAI-TE:

Workflow Description:

• 1. Phase 1: Filter Construction (Human). The researcher defines the compact A-Core and the detailed S-Template.
  2. Phase 2: Seeding. The LLM generates the initial section. The CE-Protocol verifies it (textually and symbolically, if applicable) and integrates it into the theory body.
  3. Phase 3: Iterative Expansion Loop. This is the core cycle. For each subsequent component in the S-Template:
     a. The LLM is prompted with the full context: the original A-Core and all previously verified text.
     b. It generates new content.
     c. The CE-Protocol scrutinizes the output. Textual checks ensure narrative and definitional consistency. Symbolic checks (for equations) verify dimensional homogeneity and mathematical correctness.
     d. If verification fails, a corrective prompt is issued, and the loop reiterates. If it passes, the content is integrated.
  4. Phase 4: Global Audit. The LLM performs a final self-consistency review across the complete manuscript. The human researcher then conducts a high-level review for physical plausibility, depth, and originalityaspects beyond the protocol's automated checks.

4. Case Study: Constructing the Temporal Theory of the Universe (TTU)

The development of TTU serves as a comprehensive proof-of-concept for IAI-TE.

• 1. A-Core as Immutable Law: The TTU_CORE_RECALL file (7 axioms) was designed to fit a single LLM context window. Its immutability was enforced throughout. For example, any drift from the core definition of the electric field was flagged by the CE-Protocol.
  2. S-Template as Guiding Scaffold: The CODEX outline enforced a strict logical order: Definitions Lagrangian Variation Field Equations Limits. This prevented the common LLM failure of "putting the cart before the horse."
  3. CE-Protocol in Action (Hybrid Verification): During the derivation of the TTU form of Maxwell's equations, the protocol mandated:
     1. Textual Check: Is the argument logically derived from the provided Lagrangian?
     2. Symbolic/Dimensional Check: The LLM was explicitly prompted: "Show that the derived equation for displacement current, jdisp=(t)jdisp=(t), has dimensions of A/m' when has units of . Then, show the algebraic steps to demonstrate its equivalence to 0E/t0E/t." This forced a step-by-step, verifiable derivation.

Result: The generation of CODEX TTU V1, a coherent, self-consistent theoretical manuscript where the LLM's "fantasy" was successfully channeled to interpolate and elaborate within the rigid bounds of the artificial filters, producing novel, consistent derivations.

5. Philosophical & Mechanistic Analysis: Transformation of Unfiltered Fantasy

5.1. The Default State: Unfiltered Statistical Fantasy
An LLM's default operation is a random walk through the space of linguistic plausibility. Its "imagination" is unbounded, optimized for local coherency, not global truth or logical soundness.

5.2. IAI-TE: Implementing Directed, Filtered Fantasy
IAI-TE fundamentally changes the LLM's objective function. It does not eliminate the generative mechanism but constrains its search space to a high-likelihood manifold defined by the filters.

• 1. The A-Core acts as a hard boundary condition.
  2. The S-Template defines a preferential path (a "loss landscape" gradient).
  3. The CE-Protocol acts as a rejection-sampling mechanism, discarding steps that violate constraints.

The LLM is no longer solving: "What is a statistically likely next sentence?"
It is now solving: "What is a sentence that is statistically likely given that it must satisfy constraints A, B, and C from the A-Core and fit into logical slot D of the S-Template?"

This reframing turns a liability into a capability. We leverage the LLM's power to explore combinatorial spaces, but only within a carefully constructed, truth-constrained subspace.

6. Discussion: Implications and the New Division of Labor

IAI-TE formalizes a new paradigm for human-AI partnership in theoretical science, establishing a clear division of labor:

• 1. The Human as Intuition Engineer & Filter Designer: Provides the seed of genius (the A-Core) and the blueprint for reasoning (S-Template). This is a high-level, strategic, and creative role focused on ontology and architecture. The human also holds final responsibility for the external validity (empirical correspondence) of the theory, a task beyond the protocol's scope.
  2. The AI as Deductive Power & Consistency Engine: Brings immense speed, perseverance, and combinatorial power to the task of exhaustively exploring the deductive consequences within the defined, filtered search space. It is a tireless, precise executor of logical implications and a vigilant guardian of internal consistency.

This partnership mirrors and amplifies the ideal scientific process: human intuition proposes, and systematic logic disposes. IAI-TE makes this dichotomy explicit, operational, and scalable.

7. Advantages, Limitations, and Future Work

Advantages:

• 1. Guaranteed Internal Coherence: The CE-Protocol embeds automated consistency checks into the generative process, producing theories with a high degree of internal logical soundness.
  2. Explicitness & Reproducibility: Forces explicit declaration of axioms and structure, making the theoretical foundation clear and the methodology reproducible.
  3. Scalability: Manages the complexity of large-scale theory development, maintaining coherence across dozens of pages and interlinked concepts.
  4. AI-Resilient Output: Naturally produces theories that are easily reconstructible and verifiable by AI systems.

Limitations & Critical Considerations:

• 1. Garbage In, Garbage Out (GIGO) & The Validity Boundary: IAI-TE is a powerful engine for internal coherence, but it is not an engine for external validity. If the human-provided A-Core is physically incorrect, the LLM will efficiently construct a perfectly coherent, elaborate, and entirely wrong theory. IAI-TE guarantees logical soundness within the defined axiomatic system, but the ultimate truth of that system remains the sole responsibility of the human researcher.
  2. No Autonomous Paradigm Shifts: The AI cannot propose a new A-Core; it can only elaborate within the given paradigm. Major conceptual breakthroughs remain a human domain.
  3. Computational & Technical Overhead: The iterative verification loops, especially with hybrid symbolic checks, require significant computational resources and careful technical setup.

Future Directions:

• 1. Development of Specialized Agents: Fine-tuning or prompting strategies to create dedicated "Generator-under-Constraints" and "Critic/Auditor" LLM instances optimized for their IAI-TE roles.
  2. Integrated Symbolic-Verification Platforms: Building software that seamlessly integrates LLM generation with calls to symbolic mathematics engines (e.g., SymPy, Wolfram Engine) within the CE-Protocol loop.
  3. Cross-Disciplinary Application: Applying IAI-TE to fields like legal reasoning (building consistent arguments), mathematical conjecture exploration, or complex policy modeling.
  4. Quantitative Analysis of Coherence: Developing metrics to quantitatively measure the improvement in theoretical coherence (e.g., reduction in logical contradictions, increase in cross-referential accuracy) when using IAI-TE versus standard LLM use or human-only drafting.

8. Conclusion

The Induced AI-Theory Expansion methodology represents a significant advance in formalizing human-AI collaboration for science. By recognizing LLM "hallucination" as unfiltered statistical fantasy and proactively engineering a system of artificial reality filters (A-Core, S-Template, CE-Protocol), we can harness this generative power for disciplined, logical theory-building. IAI-TE provides a concrete, reproducible protocol for this transformation.

Crucially, IAI-TE establishes a clear boundary in the division of labor: the human remains the Intuition and Ontology Engineer, responsible for the initial axioms (A-Core) and the external validity (empirical truth) of the theory. The AI, conversely, acts as the Deduction and Consistency Engine, ensuring internal logical integrity. This guarantees that while the resulting theory is perfectly coherent, its correspondence to the real world remains exclusively the domain of critical human judgment.

The successful construction of the Temporal Theory of the Universe stands as a testament to the method's efficacy. We are no longer merely using AI as a tool; we are engineering cognitive architectures for it  providing the missing filters for reality, logic, and self-correction that allow it to become a constructive, reliable partner in the fundamental scientific endeavor. IAI-TE establishes a new standard for how humans and machines can co-create complex, coherent knowledge systems.

References

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