©2026_NKTg = f(x,v,m)
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©2026_NKTg = f(x,v,m) 1. English (English) 5. German (Deutsch) 2. French (Français) 6. Japanese (日本語) 3. Vietnamese (Tiếng Việt) 7. Spanish (Español) 4. Chinese (简体中文) 8. Russian (Русский) 1. English (English) ANNOUNCEMENT OF SOFTWARE SPECIFICATION AND ALGORITHM FOR THE NKTg LAW OF VARIABLE INERTIA © 2026 Nguyễn Khánh Tùng. All rights reserved. I. GENERAL INFORMATION • Software Name: NKTg Variable Inertia Computing System (NKTg Dynamics Calculator). • Author: Nguyễn Khánh Tùng • Programming Languages: C++ (ISO/IEC 14882) and Assembly (x64). II. THEORETICAL BASIS: NKTg LAW OF VARIABLE INERTIA The software is implemented based on the principles of the NKTg Law: • Fundamental Relationship: Movement tendency depends on position (x), velocity (v), and mass (m). Formula: NKTg = f(x, v, m). • Core Product Quantities: o Momentum (p): p = m * v o NKTg_1 Quantity: Product of position and momentum (NKTg_1 = x * p). o NKTg_2 Quantity: Product of the mass variation rate and momentum (NKTg_2 = (dm/dt) * p). • Unit of Measurement: NKTm (Unit of variable inertia). III. DETAILED ALGORITHM DESCRIPTION 1. Data Processing Workflow The algorithm performs movement tendency analysis through logical steps: • Step 1: Receive input parameters: position (x), velocity (v), mass (m), and mass change rate (dm/dt). • Step 2: Calculate linear momentum p = m * v. • Step 3: Calculate variable inertia values NKTg_1 and NKTg_2. • Step 4: Classify the tendency (Tendency) based on the sign of the value: o NKTg_1 > 0: Moving away from stable state. o NKTg_1 < 0: Moving toward stable state. o NKTg_2 > 0: Mass variation supports movement. o NKTg_2 < 0: Mass variation resists movement. 📜 License NKTgLaw is available under a dual licensing model: 1. GPL-3.0 License (Open Source) You can use, modify, and redistribute NKTgLaw under the terms of the GPL-3.0 License. This version is free and requires that any derivative works are also released under GPL-3.0. 2. Commercial License (Proprietary) For commercial use without the GPL obligations, a commercial license is required. See LICENSE-commercial.txt for terms and conditions. Contact Nguyen Khanh Tung (traiphieu.com@gmail.com) for licensing and support. Note: Each user must choose either the GPL license or the Commercial license. Combining both is not permitted for the same use case.
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VI. QUANTUM EXPANSION: NKTg ALGORITHM ON QUANTUM COMPUTING PLATFORMS 1. Quantum Theoretical Basis The quantum expansion preserves all core quantities of the NKTg Law: • Momentum (p): p = m * v • NKTg_1 Quantity: Product of position and momentum (NKTg_1 = x * p) • NKTg_2 Quantity: Product of the mass variation rate and momentum (NKTg_2 = (dm/dt) * p) • Unit of Measurement: NKTm (Unit of variable inertia) Instead of calculating each combination (x, v, m, dm/dt) sequentially as in the classical model, the quantum model encodes the entire parameter space into a superposition state and exploits quantum parallelism for searching. 2. Quantum Problem Statement • Input: Parameter space (x, v, m, dm/dt), each variable is discretized into N = 2^n value levels, encoded using n qubits. Total search space consists of M = N^4 = 2^{4n} combinations. • Problem: Given a tendency condition f selected from the set: Condition f Tendency NKTg_1 > 0 Moving away from stable state NKTg_1 < 0 Moving toward stable state NKTg_2 > 0 Mass variation supports movement NKTg_2 < 0 Mass variation resists movement NKTg_1 > 0 and NKTg_2 < 0 Combination of two conditions Find all combinations (x, v, m, dm/dt) ∈ {1..N}^4 satisfying the chosen condition f. • Output: The set of parameter combinations satisfying f, obtained after quantum measurement. 3. Quantum State Space The entire parameter space is encoded into a 4n-qubit quantum register: |q⟩ = |x⟩ ⊗ |v⟩ ⊗ |m⟩ ⊗ |dm/dt⟩ The initialization state is a uniform superposition via Hadamard gates: |s⟩ = H^{⊗ 4n} |0⟩^{4n} = (1/√M) ∑ |x, v, m, dm/dt⟩ Each combination exists simultaneously with an initial probability amplitude of 1/√M. 4. Quantum Processing Algorithm The algorithm performs NKTg tendency analysis through logical steps: • Step 1: Receive and encode input parameters (x, v, m, dm/dt) into the 4n-qubit register. Apply Hadamard gates to create uniform superposition across all M = N^4 combinations. • Step 2: Build an Oracle Ô̂ parameterized according to the chosen tendency condition f. The Oracle performs three reversible operations: o Compute: Calculate p = m * v, NKTg_1 = x * p, NKTg_2 = (dm/dt) * p onto the ancilla register. o Phase kickback: Flip the phase of states satisfying f. o Uncompute: Restore ancilla to |0⟩. Ô̂ |x,v,m,dm/dt⟩ = -|x,v,m,dm/dt⟩ if f(x,v,m,dm/dt) = 1 Ô̂ |x,v,m,dm/dt⟩ = +|x,v,m,dm/dt⟩ if f(x,v,m,dm/dt) = 0 • Step 3: Apply the Diffusion operator — amplify the amplitudes of solution states and suppress non-satisfying states: D̂ = 2|s⟩⟨ s| - I • Step 4: Repeat Step 2 and Step 3 for T optimal rounds. With k being the number of solutions in space M: T = ⌊(π/4) * √{M/k}⌋ iterations. After T rounds, the probability of measuring the correct solution approaches 1. • Step 5: Measure the 4n-qubit register — obtaining combination (x, v, m, dm/dt) satisfying condition f with high probability. Repeat O(k) times to collect all k solutions.