Computational Complexity-Driven Investment(CDN): Avoid Unsolvable AI SaaS Models, Classify NP-Complete Product-Led Organic Growth

Disclaimer: This note is not about pure computing complexity theory but rather utilizes its framework meta-semantically to materialize startup growth.

Disclaimer: This note is not about pure computing complexity theory but rather utilizes its framework meta-semantically to materialize startup growth.

1. Introduction: Applying Computational Complexity to Startup Investment

? Why Some Startups Are Fundamentally Unsolvable and Will Always Burn Capital ? Why Investors Should Prioritize NP-Complete/NP-Easy hybrid Startups for Competitive Scaling ? How Founders Should Identify Undecidable Problems Before Building an AI SaaS Startup

Artificial Intelligence (AI) SaaS startups promise exponential growth, but many venture-backed companies unknowingly operate in fundamentally unsolvable problem classes, leading to infinite capital burn cycles. This article proposes a Computational Complexity-Informed Investment Framework (CCM: Complexity Classification Model) that helps classify AI startups by problem complexity, avoid undecidable cases, and systematically scale NP-Complete/NP-Easy hybrid products toward logarithmic efficiency.

2. The Startup Cash Burn Paradox: The Three-Body Problem of Capital Destruction

One of the biggest traps for AI SaaS startups is entering an unsolvable cash burn cycle, similar to the classical Three-Body Problem.

2.1 What is the Three-Body Problem?

In physics, the Three-Body Problem describes the chaotic and unpredictable motion of three gravitational bodies interacting under Newtonian mechanics. Unlike the Two-Body Problem, which has a closed-form analytical solution, the Three-Body Problem requires numerical simulation and is inherently unstable.

? Key Insight: The Three-Body Problem is an analogy for startups that have no stable path to profitability, require continuous funding, and cannot achieve operating leverage.

2.2 Typical Cash Burn Example: A Three-Body Problem in Startups

Breaking Down the Three-Body Problem into a Two-Body Problem

? The Three-Body Problem is a chaotic and unsolvable problem in classical mechanics where three gravitational bodies interact unpredictably over time. ? The Two-Body Problem, however, has an analytical solution, meaning it can be modeled and predicted efficiently. ? In AI SaaS startups and investment, the analogy translates to eliminating unstable dynamics (capital inefficiency, unscalable AI models, market unpredictability) and focusing on structured, solvable models.

Key Strategy: Convert Three-Body startup problems (high complexity, infinite capital burn) into Two-Body models (scalable, predictable, capital-efficient growth) that converge to least action.

3. Applying the Least Action Principle to Startup Growth

? The Least Action Principle (LAP): In physics, systems evolve to minimize the action (energy expenditure over time). ? In startups, this means minimizing unnecessary capital burn, avoiding unproductive complexity, and ensuring maximum efficiency per investment dollar.

3.1 What the Least Action Principle Looks Like in Startups

Tools & Frameworks: The best AI SaaS startups operate on the Least Action Principle—optimizing capital allocation, computational efficiency, and revenue scaling.

4. The Complexity Landscape of AI SaaS Startups

Startups operate in different computational complexity classes, which directly impact scalability, cost structure, and profitability. Before investing, one must identify which complexity classes lead to solvable/unsolvable output after resources input.

4.1 Classifying AI SaaS Startups by Computational Complexity

Constraints: ? Undecidable and Unsolvable classes (UNSAT, EXPSPACE) should be immediately rejected for investment. ? NP-Complete/NP-Easy hybrid startups provide defensibility and high scalability potential. ? The basic strategy is getting first mover advantage to find NP-Complete proof toward logarithmic scalability (NL, N).

4.2.Classification of Game Theory Problems by Complexity

5. Identifying and Avoiding Undecidable and Unsolvable Startup Models

5.1 What Are Undecidable Class Problems and Why Should Investors Avoid Them?

? An undecidable problem is one where no algorithm exists that can guarantee a solution in finite time. ( Usually EXPSPACE, EXPTIME, PSPACE, NP-Hard) ? This means an AI SaaS startup based on an undecidable problem will require infinite resources (TIME, SPACE, RANDOMNESS) with no clear path to scaling.

Example: The AI Halting Problem Startup

• Startup Claim: "We are building an AI that can predict whether any given AI model will ever stop learning or continue training forever."
• Computational Reality: This is equivalent to Turing’s Halting Problem, which is undecidable.
• Investor Outcome: This startup will burn capital indefinitely without ever reaching product-market fit.

Tools & Frameworks: "Undecidable" class startups should be avoided at all costs. They are venture capital "black holes".

5.2 Unsolvable Startups: EXPSPACE and EXPTIME Pitfalls

? EXPSPACE (Exponential Space Complexity) and EXPTIME (Exponential Time Complexity) problems require impractical computational resources, making them fundamentally unsustainable as SaaS businesses.

Example: AI-Based Theorem Proving at Scale

• Startup Claim: "We use AI to generate and prove any mathematical theorem, ensuring automated research breakthroughs."
• Computational Reality: This is equivalent to EXPSPACE-hard problems, where theorem proving may require exponential memory growth.
• Investor Outcome: Even with quantum computing, this startup cannot scale profitably.

Tools & Frameworks: Startups in EXPSPACE or EXPTIME should be treated as high-risk, capital-intensive ventures that may never reach operating leverage.

6. The Correct Investment Playbook: Exponential Product Earnings Growth While Maintaining Logarithmic Resource Requirement

6.1 How to Identify NP-Complete/NP-Easy hybrid AI SaaS Startups

? NP-Complete problems have a balance between computational difficulty (moat), NP-Easy problems have practical heuristic solutions (scalability). ? Investors should use computational tools to verify whether a startup’s core problem is NP-Complete/NP-Easy hybrid.

Tools & Frameworks: By applying SAT Solvers and Cook’s Reduction, investors can mathematically verify if an AI startup is solving a valuable NP-Complete problem.

6.2 Scaling NP-Complete Startups Toward Brachistochrone Curve

The best AI SaaS startups follow the Brachistochrone Curve of Computational Scaling, transitioning from NP-Complete to NP-Easy to Logarithmic Scaling (NL, N).

Tools & Frameworks: Successful AI SaaS startups scale their computational complexity down from NP-Complete to NL, achieving logarithmic capital efficiency.

7. Complexity Scaling Model? (CSM?)

To systematically invest in the right AI SaaS startups, TANAAKK and HITSERIES CAPITAL introduce the Complexity Scaling Model? (CSM?):

CSM Framework

1. Classify Complexity Early Use SAT Solvers, Cook’s Reduction, and Kolmogorov Complexity to verify if a startup’s core problem is NP-Complete.
2. Reject Undecidable and Unsolvable Startups If a startup is tackling an UNSAT (Undecidable) or EXPSPACE-class problem, it’s a capital sink.
3. Prioritize NP-Complete Startups Focus on AI SaaS solving NP-Complete problems, as these provide computational moats and defensibility. Quickly verify its statement by E-ZKP? Zero-Knowledge Proof (ZKP) This is a standard term from computational complexity theory where a prover can demonstrate knowledge of a value without revealing it. While traditionally used in cryptographic authentication, TANAAKK adapts its principles to startup investment. Extended Zero-Knowledge Proof? (E-ZKP?) Extended interpretation of ZKP in computational complexity. By ZKP, prover stating propositnon is true without revealing any sensitive infomation to verifier. By E-ZKP?, prover can convince truth meta-semantically without adding any knowledge in verifier. Mutual Zero-Knowledge Proof (M-ZKP?)
4. Enable Logarithmic-Resource Scaling Guide NP-Complete startups towards NP-Easy, NL, and N-class problems within 10 years.
5. Use Mutual-ZKP? to Validate Revenue & Growth Investors and founders should use Mutual-ZKP? (Zero-Knowledge Proof) technique to validate revenue and AI model claims without exposing sensitive data. Mutual-ZKP? (M-ZKP?) is TANAAKK and HITSERIES CAPITAL's original Product-Led Organic Growth? verification models.

?? Conclusion: By systematically applying the Complexity Scaling Model (CSM), investors and founders can optimize capital efficiency while ensuring sustainable AI SaaS startup growth.

8. Conclusion: The Future of Complexity-Driven Investment?

? Investors must systematically classify AI SaaS startups by computational complexity before committing capital. ? Undecidable and Unsolvable problem classes (UNSAT, EXPSPACE) should be immediately rejected. Some problems are too abstract or too complex to ever be monetized. Investing in such startups leads to permanent capital destruction. ? NP-Complete startups provide defensibility but require structured scaling toward NP-Easy and Logarithmic Efficiency (NL, N). ? The Complexity Scaling Model? (CSM?) ensures AI startups follow an optimal computational trajectory, avoiding capital inefficiency and maximizing investor returns.

Final Thought: The next trillion-dollar AI company will master complexity reduction—scaling from NP-Complete toward logarithmic growth while optimizing capital efficiency. This is the future of Complexity-Driven Investment?

9. Advanced Toolkits & Frameworks

Mathematics and physics often define idealized states to enhance understanding and inspire groundbreaking innovation. TANAAKK introduces a suite of frameworks designed to optimize Complexity-Driven Investment?, integrating computational principles, physics-inspired least energy models, and economic scaling logarithmic resource strategies(Gravity Assurance?).

A key innovation is the development of a language-independent verification algorithm—a Meta-Semantic Reasoning? approach that transcends linguistic and computational boundaries. This methodology is applicable across natural languages, programming languages, and even theoretical interplanetary, intergalactically or inter-meta spacetime civilizations（potential theoretical metaverse civilization ）.

At the core of this initiative, TANAAKK is pioneering the GAAS? (Gravity-as-a-Service?)—a meta-physical and computational framework that leverages ideal gravitational principles to model and accelerate exponential earnings growth, Product-Led Organic Growth?. Inspired by general relativity, entropy minimization, and space-time optimization, GAAS? applies these fundamental laws to business scaling, startup investment, and AI decision-making. A next-generation suite of meta-semantic reasoning models. These models enable decision-making for true value without requiring domain-specific linguistic explanations.

GAAS?(Gravity-as-a-Service?): Next-Generation Investment Frameworks

1. GAAS?(Gravity-as-a-Service?) It is TANAAKK proprietary toolkits comprised of creative frameworks and products series. Aming to provide creative framework utilizing converged ground state as theoretical toolkits.
2. Zero-Knowledge Proof (ZKP) This is a standard term from computational complexity theory where a prover can demonstrate knowledge of a value without revealing it. While traditionally used in cryptographic authentication, TANAAKK adapts its principles to startup investment.
3. Extended Zero-Knowledge Proof? (E-ZKP?) Extended interpretation of ZKP in computational complexity. By ZKP, prover stating propositnon is true without revealing any sensitive infomation to verifier. By E-ZKP?, prover can convince truth meta-semantically without adding any knowledge in verifier.
4. Mutual E-Zero-Knowledge Proof (M-E-ZKP?) A proprietary product viability checking tool developed by TANAAKK to prove there is Gravity Assurance. Unlike traditional ZKP in computational complexity, M-E-ZKP? enables sellers and buyers to mutually verify the feasibility of a product without revealing sensitive proprietary details. which can quickly check product market fit existence meta-semantically by matchning truth of product and truth of initial buyer's "Connoisseur" capability. It is the part of Meta-Semantic Reasoning Model? – A universal, language-independent decision framework. The meta-semantical process would be interactive without limitation of language. It is a key component of TANAAKK Complexity Scaling Model? (CSM?) during conducting Complexity-Driven Investment? (CDI). After product owner conduct NP-Complete Sourcing? product owner should conduct Mutual-ZKP? to quickly verify if the problem tackled by product is solvable within 10 years time limit.ensuring that AI startups tackle solvable problems within a 10-year timeframe.
5. Complexity-Driven Investment? (CDI) A structured investment framework developed by TANAAKK that applies computational complexity principles to AI startup evaluation. It focuses on assessing scalability and problem solvability within a decade.
6. Complexity Scaling Model? (CSM?) CSM? is core model in GAAS?(Gravity-as-a-Service?), TANAAKK's proprietary approach to scaling AI startups by transitioning their computational challenges from NP-Complete to logarithmic efficiency, ensuring long-term viability and scalability.
7. Meta-Semantic Reasoning Model? A universal, language-independent decision framework.
8. NP-Complete Sourcing? The process by which a product owner identifies high-complexity solvable problems that require advanced computation. ZKP verify NP-Complete problem. After NP-Complete Sourcing? finished, M-E-ZKP? will make Product-Led Organic Growth? to determine if the problem can be efficiently solved within 10 years.
9. Gravity Assurance? (GA?) Traditional Quality Assurance (QA) Traditional QA focuses on validating a product’s specification and correctness by ensuring it meets predefined customer requirements. It ensures quality control, reliability, and consistency based on agreed-upon standards. Gravity Assurance? (GA?), developed by TANAAKK, extends beyond traditional QA by evaluating a product’s ability to solve newly generated NP-Complete problems and scale efficiently. It assesses whether a product can maintain performance while scaling exponentially with logarithmic resource increments in additional production supply. Gravity Assurance? ensures that solutions are not only functional but also computationally scalable for long-term technological advancements. Gravity Assurance? Key Features: Capital Efficiency Validation: Ensures the product operates with higher capital efficiency compared to market benchmarks. Earnings Growth Assessment:Evaluates the product's ability to drive consistent earnings growth over time. Operating Leverage Optimization:Measures how efficiently the product scales while maintaining or improving profitability margi</li>
10. Product-Led Organic Growth? Product-Led Organic Growth? is ideal state of least action state of customer acquisition after Gravity Assurance? step. Verified by E-ZKP? and M-ZKP? , which can materialize exponential product growth without proactive selling & marketing activities while having logarithmic resource.
11. NTM Sales? – Non-Deterministic Turing Machine (NTM) is ideal ultimate state of classical deteministic turing machine that can calculate any pattern at once and select correct answer without any trials and errors. NTM Sales? is ultimate state of product sales that experience no trial and no errors, calculate all of the possible patterns and output right maximized option at once. If NTM Sales? is account executive, that personel proberbility of win is 100% without any failure. NP-Complete Sourcing? finds products solvability of newly discovered problems. M-E-ZKP? quickly verify early adopters and strategic accredited verifiers among various customer categories. NTM Sales? quickly acquire customers. These sales process decision would be done by Inter-Spacetime Analysis?(Examine action influence through past-present-future simlutaniously without any distance). Byometimes NTM Sales? action alters the meaning of past-present-future, then there will be newly updated versions of past-present-future sets. The change will be recorded to Meta-Spacetime Memory?. Meta-Spacetime Computing? will process multiple memories and datasets semantics in Meta-Spacetime Memory? , NTM Sales? can maximize performance by comparing various influence that will be invoked by alternative patterns of actions. This ideal NTM Sales? maximizes product selling performance by Meta-Spacetime Selling?. These best practices will be eventually stocked and optimal alghorythm will be stored in the layer of Inter-Meta Spacetime Computing?
12. Meta-Spacetime Version Control?- refers to a structured collection of past-present-future "versions" of spacetime that interact as a memory-like system. A computational framework for accessing and referencing spacetime-based datasets
13. Meta-Spacetime Selling?-Advanced sales optimization framework using past-future AI-driven projections
14. Meta Spacetime Computing? – AI modeling beyond conventional time and space constraints.
15. Inter-Meta Spacetime Computing? – Exploring well architected states that function across theoretical multi-universe, multi-timespace beyond single universe and single spacetime, analogy in monolithic vs cloud multi tenant modular architecture. It is Best practices will be eventually stocked and optimal alghorythm will be stored in the layer of Inter-Meta Spacetime Computing?

for detail, see GAAS glossary.

Why GAAS??

Just as gravity governs the motion of celestial bodies, GAAS? assure a fundamental scaling force (GA?)for AI SaaS businesses. By minimizing entropy, optimizing capital efficiency, and leveraging computational complexity, GAAS? enables startups to achieve logarithmic scalability and exponential earnings growth. TANAAKK’s GAAS? initiative redefines the intersection of physics, computation, and venture capital, paving the way for next-generation AI infrastructure, scalable SaaS models, and trillion-dollar market opportunities.