This project is licensed under CC BY-NC-SA 4.0 (Attribution-NonCommercial-ShareAlike 4.0 International).
Disclaimer and Communication Statement: Because I do not speak English, the article is translated by AI, and AI participated in the entire content writing process. If any patented terms or professional terms are cited due to AI errors or translation inaccuracies, please negotiate with the respective AI companies. You may leave a message on this website to notify me of necessary changes. However, as I do not speak English, I cannot guarantee a correct understanding of the intent or accurate modification of the article. This is my first time actively using this website to publish content; previously, I only visited in an unregistered state and am unfamiliar with the website's functions. My average visit frequency to this website is once a year, so I will likely address the above errors within one year, though delays may occur due to network connection issues or other personal reasons. I suggest that if any infringement occurs due to the above reasons, the infringed party should immediately modify the infringing paragraph on this website to a non-infringing version and leave a message. Subsequent actions will be based on this message, and readers may refer to this corrected baseline as a standard.
A Friendly Note on Our License
To protect the spirit of open exploration, this project is released under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC BY-NC-SA 4.0) license. Our primary goal is to prevent large-scale commercial entities from patenting or monopolizing this community-driven idea without contribution.
However, to our fellow builders and pioneers, our stance is open and encouraging:
- For Individuals, Academics, Researchers, and Hobbyists: You are heartily welcomed to use, modify, and build upon this design for learning, research, and personal projects.
- For Developers & Makers building prototypes, testing, and sharing improvements: We consider you core collaborators. Your practical work to validate and advance this design is not considered "commercial use" in our view. We want to see your builds and learn from your results.
- For Teams or Startups with clear commercial interests: We welcome you too! The "NonCommercial" clause is not meant to stop innovation but to ensure fair collaboration. If you have a serious plan to develop a product or service based on this project, please contact us directly at [github]. We are happy to discuss granting a specific, free commercial-use license. Our mission is to see this idea materialize, not to create unnecessary barriers.
Let's build the future, together.
Hello everyone, I am Zeng Hao from China. I am open-sourcing this project simply because applying for patents and writing papers is more difficult than discovering a new path.
This article and its extended content are published solely on the principles of world peace, human equality, and common prosperity. It shall not be used for any terrorist activities, military purposes, or any technology that harms the world, nations, individuals, the environment, animals, etc., or results in such consequences. The article and its extended content must not be used for any direct or indirect commercial activities. Corporations are prohibited from using it, and I reserve the right to invalidate any related patents and "fences" built based on this article.
Before sending me a lawyer's letter or initiating legal action, please first incorporate the involved physical constants, universal laws, and professional terms into corporate or personal ownership, and clearly mark that others are not allowed to use them. Furthermore, provide evidence that is globally recognized and accepted by all countries and personnel using this article and its extended technology.
I do not know how people might exploit loopholes to bypass these regulations, but even if you do, your patents, papers, and other carriers must prominently cite the link to this article and include my name. However, even if you do so, I reserve the right to withdraw your publication involving this article and its extended content at any time. By basing your work on, extending, or citing this article, it means you agree to all the terms and interpretations of rights in this entire article.
First, you must discard your traditional engineering mindset. Magnetic stiffness is adjustable, non-linear, and frictionless. We must perceive this technology through a corrected lens: place it on the same tier as Superconducting Levitation, Magnetic Levitation (Maglev) Guides, and Air Bearing Stages.
- Maglev Trains: Prove the absolute rigidity and stability of magnetic forces.
- Lithography (ASML) Wafer Transport Systems: Prove their sub-nanometer precision and controllability.
- MRI Systems: Demonstrate the extreme adjustability and field flatness possible within magnetic arrays.
However, the hardware is merely the manifestation; the magnetic field is the soul. That is the very reason for this open-source project.
- Applied Physics/Electromagnetics: Field synthesis of multi-magnet arrays, magnetic shielding, and shaping principles. "A programmable passive magnetic potential well topology technology is implemented, using perturbation units for local linear correction of the background field."
- Control Theory: Physical structures replace software algorithms, achieving "hardware closed-loop control." "This system is essentially a feedforward-feedback composite controller based on analog computation. The metal sheet array is a solidified, adjustable 'control law matrix' that directly compensates for errors in real-time through physical means."
- Precision Mechanical Engineering: Realization of motion precision is completely detached from traditional Abbe error chains and rigidity constraint principles. "We propose a new paradigm of 'mechanical base error isolation,' decoupling guidance precision from the macro-morphology of the base, significantly reducing the strict requirements for basic mechanical processing."
- Materials Science: Precise utilization of magnetic permeability, thickness, and shape of metal sheets as tuning units. "We developed a method using soft magnetic material microstructure units as field-tuning operators to achieve precision shaping of the magnetic field distribution."
Finally, if you still have doubts, please spend a few dozen yuan to replicate the experimental content and then use the experimental results to counter. "Practice is the sole criterion for testing truth."
To simplify understanding for the general public: Please imagine the base magnetic field as the water surface, the moving part as a boat, the unit error size as the size of the water ripples, the number of units covered by the moving part as the size of the boat, and the tuning body as a board that can press down and divert the water.
Theory: Moving beyond traditional rigid-body "Three-Plate Lapping," we utilize Fluid Dynamics and Field Convolution to generate precision.
-
Orthogonal Flux Integration (Cross-Hatch Arrangement): Instead of point-to-point contact, we arrange Halbach strip arrays in a cross-hatch pattern (Row
$X$ vs. Column$Y$ ) on two base planes. -
The Physics: A single longitudinal magnet overlaps multiple transverse magnets. Mathematically, the magnetic field at any point becomes the integral (average) of the interacting fields.
-
Result: Local errors and discrete "peaks" are physically diluted by the length of the intersecting strips.
-
Temporal Averaging via Dynamic Curing: While the magnetic binding agent (resin/glue) is in its fluid state, the two planes undergo Stochastic Relative Motion (Random vibration, rotation, or sliding).
-
The Mechanism: This motion smears out static field errors over time. The resin does not cure to a static "snapshot" of a specific error, but solidifies into the Time-Averaged Potential Surface.
-
Bootstrap Cycle (
$A \to B \to C$ ): -
Gen A (Parent): Cross-hatch setup with random motion produces Gen B.
-
Gen B (Offspring): Inherits the averaged smoothness of A, reducing error magnitude by an order.
-
Gen C (Grandchild): Produced by B, converging mathematically toward a perfect hyper-plane.
Theory: If iterative convergence is too abstract ("Magic"), we deploy the "Brute Force" Industrial Standard—Nano-Imprint Lithography (NIL) Logic.
-
The God Mold (Zero-Generation): We acquire a single set of ultra-high-precision components (e.g., surplus lithography stage parts or MRI gradient coils) to generate one Reference Hyper-Plane.
-
Cost Logic: This is a one-time Capital Expenditure (CAPEX).
-
Magnetic Lithography (Field Replication): Using the Reference Hyper-Plane as a mold, we mass-produce replicas using magnetic resin.
-
Process: Like stamping vinyl records or burning optical discs. The "Master" aligns the magnetic domains of the "Replica" perfectly before curing.
-
Economics: The marginal cost of the second unit is merely the cost of glue and magnets. We achieve ASML-level precision at IKEA-level pricing.
Before replication, we must create a Reference Hyperplane. This is where we extract the core strengths of Lithography and MRI.
- Component Used: Laser Interferometric Stage and Nano-positioning Logic.
- Principle: We use the resolution of a lithography stage to map the "Magnetic Topography." A probe scans the raw magnet array, identifying every micro-fluctuation in flux.
- Why it works: We don't need the lithography machine to "move" during production; we only use it once to calibrate the exact spatial coordinates of field errors.
The Doubt: "Commercial Hall probes lack the spatial resolution to measure nanometer-level magnetic deviations."
The Reality: We are not measuring Absolute Position with the probe; we are measuring Field Flux Gradients
-
The Principle: Magnetic field intensity changes much faster than physical distance at the micro-scale. A
$1\text{nm}$ shift in position relative to a sharp magnetic gradient results in a measurable change in voltage (millivolts) on a high-end Hall sensor. -
The Logic: We use the Lithography Stage as the "Ruler" (providing
$0.1\text{nm}$ spatial steps) and the Probe as the "Comparator." We don't need the probe to be "small"; we only need it to be stable. As long as the sensor's Signal-to-Noise Ratio (SNR) is high, we can resolve sub-nanometer movements through the change in flux density.
- The Process: Instead of taking a single measurement at each point, the probe takes 10,000 samples per nanometer of movement.
-
The Result: According to the Central Limit Theorem, the measurement precision improves by
$\sqrt{N}$ . By taking massive samples, the thermal noise of the probe is averaged out, revealing the underlying nanometer-grade field topology.
- Component Used: Passive Shimming and Gradient Cancellation.
-
Principle: Based on the map provided by the lithography stage, we apply MRI's Passive Shimming logic. We place sub-micron ferromagnetic foils at specific coordinates to "pull" or "push" flux lines until the field gradient
$\nabla B \approx 0$ . - Why it works: MRI shimming allows us to achieve parts-per-billion (PPB) uniformity. It transforms a chaotic magnetic field into a mathematically flat potential surface.
The most frequent criticism is that "you cannot place iron foils with nanometer accuracy." This stems from a misunderstanding of Magnetic Reluctance Logic.
In mechanical systems, if you want a gap, you must move your tool by . In magnetism, the field
-
The Logic: A
$10\mu\text{m}$ thick iron foil changes the magnetic flux density across a much larger volume. Moving this foil by$0.1\text{mm}$ (a macro-scale movement) might only shift the local magnetic potential by$0.01\text{nT}$ (a nano-scale shift). - The Result: The relationship between Physical Movement and Field Change is a high-reduction ratio. You use a "clunky" hand to perform "microscopic" surgery because the magnetic field itself acts as the reduction gear.
Magnetic fields obey Laplace's equation; they are continuous and "smooth" by nature.
- A small physical error in foil placement is "averaged out" by the surrounding magnetic flux.
- Unlike a mechanical tooth that either hits or misses, a magnetic foil warps the field. The field acts as a high-frequency filter, naturally ignoring the sharp geometric edges of the foil and responding only to its integrated magnetic mass.
We have two primary methods to create the Master Template using MRI-grade active shimming coils.
This method uses 240+ discrete magnets and "sculpts" their combined field.
- Mapping: A Hall probe on a lithography stage maps the raw array's errors.
- Active Nulling: Active MRI shimming coils generate a "Negative Map"—a magnetic field that is the exact inverse of the error.
-
Superposition: When the Active Field and Raw Field meet, the gradients cancel out (
$\nabla B \to 0$ ). - Permanent Locking: While the active coils are holding the "Perfect Plane," we place passive iron foils to mimic the active field's effect. Once the coils are turned off, the foils "remember" and maintain the hyperplane.
This is a more advanced "bottom-up" approach using magnetic powder suspended in resin.
-
The Fluid State: A tray of liquid resin mixed with high-permeability magnetic powder is placed under the Active MRI Shimming Coils.
-
Active Alignment: The coils are energized to create a perfect, sub-nanometer hyperplane of potential.
-
Domain Freezing: Under this perfect field, the individual magnetic particles in the resin rotate to align their Bohr Magnetons with the field lines.
-
Solidification: The resin is cured (via UV or Heat). The perfect magnetic topology is now "frozen" into the molecular structure of the material.
-
The Benefit: This creates a continuous magnetic medium rather than discrete magnets, eliminating "magnetic ripples" at the source.
Logic: Use the lithography stage as a "Nano-Positioner" to physically assemble perfection.
- The Process: A high-precision magnetic sensor is mounted on the lithography stage. It scans the magnetic array to identify "Highs" and "Lows" in the field.
- The Action: Based on the scan, the system uses the stage's nanometer-level Z-axis control to physically adjust the height or tilt of each individual magnet or shim.
- Result: The "Superplane" is achieved through Mechanical Compensation. The physical positions of the magnets are locked once the field is measured as flat.
Logic: Use the MRI's "Phase Mapping" to sculpt the field using magnetic resin.
- The Process: A tray of liquid magnetic resin is placed inside the MRI. The MRI uses RF pulses (Phase Mapping) to "see" the field's unevenness.
- The Action: The MRI's internal gradient coils instantly generate a "Correction Field" to flatten the potential. The tray is then moved (Relative Motion) to verify uniformity.
- Result: The "Superplane" is achieved through Field-Oriented Solidification. The resin is cured while the MRI electronically holds the field in a perfect state.
The "interference" usually cited in industry occurs when the high-power RF pulses and superconducting magnets of an MRI disturb the sensitive electron/photon beams of a lithography machine during operation.
In our logic, this is a non-issue because:
- We use them Sequentially: Lithography maps it; MRI shimming fixes it.
- It is a Static Environment: We are not firing pulses or moving at high speeds. We are building a "Cold Master" that, once calibrated, stays stable forever.
These protocols utilize existing State-of-the-Art (SOTA) technologies—specifically Sub-nanometer Servo Control from Lithography and Flux Shimming from MRI—to generate a "Master Field" that is then replicated at scale.
Logic: Utilizing the stability of a static "Master Hyperplane" to guide the iterative growth of a replicated field.
-
The Master Setup: A static magnetic "God Mold" is established using existing lithography-grade positioning and MRI magnetic shielding/shimming technologies. This creates an absolute reference hyperplane of magnetic potential.
-
The Replication Process:
-
Substrates are transported via a precision conveyor system into the influence zone of the Master Field.
-
Layer-by-Layer Solidification: Magnetic resin is applied in thin films. Each layer is cured while submerged in the Master Field.
-
Physical Principle: As each layer solidifies, the magnetic domains within the resin align perfectly with the Master's flux lines. By curing in thin, sequential layers, the system performs a Spatial Integration of the field, effectively "filtering" any micro-vibrations in the transport system and ensuring the final product inherits the Master's field topology with near-zero deviation.
Logic: Using temporal motion to exceed the precision limits of the Master itself.
-
The Master Setup: Identical to Protocol I—a SOTA reference field.
-
The Replication Process:
-
The substrate is delivered to a specialized Multi-axis Stochastic Tray.
-
Randomized Relative Motion: While the resin is in its transition state (liquid to solid), the tray performs high-frequency, small-amplitude random planar movements.
-
Physical Principle: This is an application of Temporal Filtering. Any residual static imperfections or "hot spots" in the Master Field are mathematically and physically "smeared" across the surface of the replica. The resulting solidified field represents the Time-Integral of the Master Field. Effectively, the replica can achieve a higher degree of uniformity (Smoothness) than the Master itself by neutralizing stationary spatial harmonics through motion.
Core Logic: This protocol employs Spatiotemporal Dithering to achieve sub-nanometer precision. By inducing multi-point, full-spectrum random vibrations (white/pink noise), we decouple the replica from the localized spatial errors of the master template. Combined with Iterative Layering (Micro-Dispensing), the system utilizes the Central Limit Theorem to achieve statistical and temporal averaging, theoretically allowing the replica's smoothness to exceed that of the master template itself.
Master Template Configuration: Utilizes the same SOTA (State-of-the-Art) reference field as Protocol I. Notably, the Master Template itself can be refined using this recursive averaging protocol to eliminate initial manufacturing defects.
Replication Process (The "Blurring" Engine):
- Transport: The substrate is positioned via conveyor onto a Active Vibration Isolation & Excitation Stage.
- Actuation Source: Instead of simple motors, the tray is equipped with a Multi-Axis Piezoelectric Actuator Array (PEA).
- Spatiotemporal Dynamics: The PEA generates high-frequency, full-spectrum stochastic vibrations. Because the actuation is multi-point and phase-decorrelated, every micro-region of the substrate experiences a unique, randomized vibration vector. This creates a "Spatiotemporal Average," effectively applying a low-pass filter to the physical position, filtering out high-frequency spatial roughness.
Drip Irrigation Process (The Integration Engine):
- Distributed Micro-Fluidic Dispensing: A high-density array of micro-nozzles acts as the "Drip Irrigator," depositing magnetic resin in discrete, controlled quanta.
- Rheological Homogenization: As the resin transitions from liquid to solid, the full-spectrum vibration provides the activation energy for the fluid to overcome local surface tension barriers (local minima), forcing it to settle into the Global Energy Minimum (the perfect hyperplane).
-
Iterative Stacking: The process follows a cycle: Dispense
$\rightarrow$ Dither$\rightarrow$ Cure$\rightarrow$ Repeat. This creates a multi-layered structure where the errors of layer$N$ are statistically uncorrelated with layer$N+1$ , leading to rapid error convergence.
Physics Principles:
-
Convolutional Smoothing (The Mathematical Filter):
Mathematically, the profile of the replica
$R(x)$ is the convolution of the Master's profile$M(x)$ and the Probability Density Function (PDF) of the vibration$P(x)$ :
If the vibration amplitude is larger than the wavelength of the master's surface defects, the defects are "smeared" out, resulting in a surface smoother than the master.
-
Ergodicity and Temporal Averaging:
The stochastic vibration ensures that the resin samples the average field potential over time rather than a single static point. The rapid oscillation (
$f > 1/\tau_{cure}$ ) means the resin "sees" the perfect mean value of the magnetic field, effectively canceling out static spatial noise. -
Statistical Error Reduction (Central Limit Theorem):
By using multiple thin layers (iterative dripping), the total thickness error
$\sigma_{total}$ decreases relative to the number of layers$N$ :
This proves that piling up multiple "imperfect" layers through a randomized process results in a "perfect" final product.
Recursive Precision Evolution: The "Child > Parent" ParadigmThe central hypothesis of this protocol is that the replica (Child) can achieve higher field homogeneity than the template (Parent). This allows for a Self-Amplifying Precision Loop:
- Logic: A manufacturing process typically introduces errors. However, Protocol III functions as a physical Low-Pass Filter. By applying high-frequency spatiotemporal dithering during the replication process, high-frequency spatial errors on the Parent are filtered out in the Child.
-
Strategy: Once a Child template (
$Gen_{n+1}$ ) is produced, it effectively possesses a smoother magnetic topology than the Parent ($Gen_n$ ). The Child is then promoted to become the new Master Template for the next generation. - Result: Precision is not static; it is evolutionary.
The system achieves convergence without the need for sensor feedback or external metrology.
-
Blind Synthesis: Conventional manufacturing relies on "Measure
$\to$ Correct." Protocol III relies on "Randomize$\to$ Integrate." -
The Convolution Theorem: Mathematically, the surface profile of the replica
$R(x)$ is the convolution of the Master's profile$M(x)$ and the Vibration Function$V(x)$ .
Since the integral of random noise (Gaussian distribution) over infinite time tends toward zero, the static errors of the Master are mathematically erased in the replica. The system converges because physics dictates that a fluid seeks the lowest energy state (the average potential) when excited.
How does the system ignore Quantum Fluctuations, Brownian Motion, and Atomic Granularity?
-
The "Field vs. Matter" Dichotomy:
Mechanical machining is limited by the size of atoms. However, a magnetic field is a Continuum, governed by the Laplace Equation (
$\nabla^2\phi = 0$ ). It does not have "grain boundaries." -
Ensemble Averaging: While individual atoms in the magnet or resin may jitter due to thermal noise (Brownian motion) or quantum uncertainty, the magnetic field at any point is the vector sum of
$10^{23}$ atoms. The statistical variance of such a massive ensemble is negligible. -
Distance Decay: Micro-magnetic variations decay at a rate of
$1/r^3$ . At the working distance of the guide rail (macroscopic gap), atomic-level noise is completely washed out, leaving only the pure, smooth field potential.
- Can it reach the physical limit? Yes. The precision of the magnetic field can theoretically approach the Continuum Limit, far surpassing the surface roughness of the resin material itself.
- The Ultimate Barrier: The only limitation is not the magnetic field, but the Rheology of the resin (molecular size and viscosity). However, for the purpose of magnetic levitation, the field smoothness can effectively reach "Absolute Zero" roughness relative to the application's scale.
Hyper-Plant Biomimetic Fractal Synthesis & Stratified Magnetic Field Homogenization (Protocol III Advanced)
This document introduces a non-linear manufacturing paradigm that utilizes "Hyper-Plant" architectures to solve the "Parent-Machine Paradox." By synthesizing multiple biological fractal logics—Luffa, Leaf Venation, Diatoms, and Dandelion structures—we create a multi-scale physical filter capable of refining a crude magnetic field into a sub-nanometer smooth topology.
The HPA is not a simple copy of nature but a computational synthesis of four distinct biological advantages:
- The Skeleton (Luffa-Tree Fitting): The core body utilizes a Luffa-sponge network computationally fitted to a Tree-branching growth model. The architecture transitions from large/thick at the base to small/fine at the surface, creating a "Gradient Resistance" that gradually subdues high-amplitude magnetic flux.
- The Distribution (Leaf Vein Fitting): The global arrangement follows Leaf Venation Morphogenesis. This ensures that magnetic energy is transported and dissipated across the surface evenly, eliminating "Edge Effects" and localized field congestion.
- The Interface (Diatom Micropores): The entire structural surface is skin-coated with a Diatom-inspired micropore array. These sub-micron pores act as the final high-frequency filter, smoothing the "Parent" field's last remaining spatial jitters.
- The Internal Damping (Dandelion Spheres): The structural voids are filled with Dandelion-pappus-inspired spherical fillers. These lightweight, isotropic elements act as "Force Balancers" within the resin matrix, preventing magnetic particle clumping during solidification.
The synthesis process follows five rigorous stages:
- Bio-Structural Acquisition: High-resolution 3D scanning of target botanical architectures to establish a fundamental geometry library.
- Computational Morphogenesis & Multiscale Fitting: Applying tree-like growth simulations to the Luffa skeleton. Scaling and overlapping models to maximize void-filling without losing fractal integrity.
- Surface & Interstitial Functionalization: Digitally "growing" Diatom micropores on the surface and calculating the density of Dandelion-inspired fillers for internal stabilization.
- Stratified Layering (Practical Implementation): To address manufacturing constraints, the design can be decoupled into discrete layers. Each layer utilizes a specific mix of biomimetic structures (e.g., a Luffa-heavy base layer and a Diatom-heavy finishing layer).
- Additive Fabrication: Producing the scaffold via multi-material 3D printing, allowing for varying magnetic permeability across the structure.
The HPA scaffold serves as the functional environment for Protocol III (Stochastic Homogenization). In this environment, the liquid magnetic resin is subjected to "Stochastic Dithering" (Full-spectrum vibration). The complex HPA architecture prevents standing waves and forces magnetic particles into a state of Global Equilibrium. The fractal depth of the structure ensures that the "Parent's" defects are scattered and averaged across billions of structural intersections.
The "Hyper-Plant" approach replaces mechanical precision with Topological Complexity. Through iterative "Self-Bootstrapping," the magnetic field smoothness converges toward a physical limit defined only by field continuity. This methodology enables the creation of nanometer-grade reference surfaces using low-cost, open-source tools.
- The Scenario: We start with no Master Template, no Lithography machine, and no MRI. Just a cheap, rough array of standard magnets.
- Gen-0 (The Rough Array): Use a standard, imperfect magnet array as the base.
- Protocol III Application: Apply drip irrigation + full-spectrum vibration. The liquid resin averages the rough field of Gen-0.
- Gen-1 (The First Child): This cured resin is now slightly smoother than Gen-0.
- Iteration: Use Gen-1 as the Master to produce Gen-2. Repeat this process 100 times.
The Miracle: Through recursive convolution, the initial macroscopic errors are smoothed into non-existence. We create a PPB-level "God Mold" starting from cheap hardware, purely through the mathematics of iterative averaging.
- Zero Innovation Risk: These methods do not require "new" physics; they leverage the best of existing industrial tools (Lithography/MRI) as a one-time investment.
- Scalability: By decoupling the "Creation of Precision" from the "Mass Production," the cost per unit collapses.
- No Variable Addition: These protocols focus on passive replication, meaning they don't introduce complex active feedback loops into the mass-production line, significantly increasing yield and reliability.
Theory: Addressing durability and environmental drift via Economic Disposability.
-
The Single-Use Logic: Critics question the long-term durability of glue-based magnets. Our answer is simple: Don't make it durable; make it cheap.
-
If a high-precision rail costs $10,000, you must worry about 5-year stability.
-
If our "Printed Field" rail costs $5, you treat it like a printer cartridge.
-
Environmental Immunity: If the environment degrades the precision after 100 hours of use, simply discard the strip and snap in a fresh "printed" one.
-
Conclusion: We solve the problem of "Maintaing High Precision" by eliminating the need for maintenance entirely.
"Error Acceptance: A New Paradigm of High-Robustness Precision Motion Based on Passive Field Computation"
As long as physical constants remain unchanged, this experiment verifies that going from 0 to 1 proves that from 1 to 100 is a wide highway in principle. Subsequent engineering obstacles are conventional challenges within the known physical scope, rather than fundamental "impossibilities."
My contribution lies in "Discovering the path," while everyone else needs to "Make the road wider and flatter."
Abstract: Research on Ultra-High Precision Motion Paradigms Based on Stochastic Averaging and Multi-Stage Recursive Cascading
This paper proposes and experimentally verifies a disruptive paradigm in precision motion: the shift from a "Deterministic Error Chain" to "Statistical Error Averaging." Conventional mechanical systems are constrained by the exponential cost of precision tolerances. This research demonstrates that through discrete tuning of passive magnetic fields, system errors decrease according to the
-
Scheme I: First-Order Statistical Averaging Domain
The foundation of the infinite scaling project. By utilizing the
$1/\sqrt{N}$ law, the system achieves an initial exponential leap in precision. The reliance on physical entity tolerances is broken by increasing the quantity of magnetic tuning units. - Scheme II: Multi-Dimensional Spatial Averaging & Over-Constrained Coupling This stage introduces Length and Width Averaging. By constraining multiple degrees of freedom (heave, sway, surge, pitch, roll, yaw), a "Spatial Averaging Effect" is constructed. This generates a Pseudo-Pinning Effect and over-constrained coupling, allowing multiple independent exponential scaling domains to perform multiplicative superposition upon Scheme I.
- Scheme III: Geometric Topology Gain & Sampling Density Expansion The system scales geometrically (e.g., a 2:1 rectangular frame) to accommodate higher sampling densities. Utilizing a topology where long-strip magnets cover double-row circular magnets with a 5mm phase-shift staggered arrangement, magnetic ripples are suppressed while establishing stable three-point support. With 160 sampling points per surface and a total of 480 points, the baseline magnitude of the first two schemes is exponentially amplified.
- Scheme IV: Magnetic Bridge Smoothing & Topological Fractal Filtering Incorporating high-permeability stainless steel (430 grade) as a Magnetic Bridge to cover magnet surfaces. This physically flattens magnetic flux peaks at gaps and filters manufacturing variances. Multi-layer stacking facilitates Gaussian Blurring of Magnetic Flux and Topological Fractal Filtering, further optimizing the base magnitude of each scaling domain at the fundamental physics level.
- Scheme V: Active Logic Rectification & Dynamic Compensation Leveraging the fact that the passive structure already offsets over 80% of gravity and stability requirements, low-cost active control is introduced. The system reduces the demand for high-bandwidth control; expensive systems can be replaced by budget-friendly IC circuits and capacitor arrays. Logic is used to compensate for residual physical uncertainties, performing a final collapse of the error margin.
-
Scheme VI: Modular Recursive Cascading & Full-Spectrum Filtering
The ultimate evolution. The system treats each "Rectangular Module" as an independent, super-filtering unit. Multiple modules are connected via rigid or differential flexible links. Due to the non-linear, frictionless nature of the magnetic interface, error values undergo square-order independent operations during inter-modular transmission.
The Sub-Atomic Precision Conclusion: The reason this stage reaches sub-atomic levels (
$10^{-10}\text{m}$ ) is that cascading acts as a Recursive Convolution of the error distribution. In a cascadable system, the attenuation coefficient of each module is multiplied ($E_{final} = E_0 \cdot \prod A_n$ ). Since the magnetic field is a continuous medium without the discrete "graininess" of mechanical contact, the recursive filtering of 480+ points across multiple stages causes the residual error to mathematically and physically collapse beyond the atomic scale. Even under worst-case environmental noise, the cascading filter ensures a sub-atomic theoretical resolution.
Under a 200 CNY budget, the system achieves precision through Stochastic Decoupling, treating macro-geometric variances, manufacturing tolerances, and thermal fluctuations as a unified wideband noise
Subsequently, through over-constrained spatial coupling and Magnetic Bridge Gaussian smoothing, the error is further attenuated by a geometric coupling coefficient
Where
- The Doubt: How can low-cost magnets with high manufacturing tolerances (>10%) ever achieve nanometer precision?
- The Logic: In our stress tests using a primitive prototype, we intentionally used magnets with a 1mm height variance (a 50% difference relative to the 2mm base) and angular deviations exceeding 30°. Even under these "catastrophic" conditions, the 20-point sampling array successfully filtered the noise. Since standard manufacturing errors are far below 50%, they are treated as "negligible stochastic noise." Furthermore, Multi-layer Aperture Shimming creates a "Gaussian Blur" effect, physically smoothing the field before it even enters the statistical averaging stage.
- The Doubt: Won't thermal expansion and ambient vibration destroy nanometer-level stability?
- The Logic: This is a matter of relative Scale and SNR. Our system is designed to suppress a macro-error of 3mm. If the logic can neutralize a 3,000,000-nanometer physical deviation, then ambient thermal drifts or vibrations—typically in the micrometer range—are "buried" within the suppression bandwidth. We do not fight the environment; we make the system's baseline so robust that the environment becomes statistically invisible.
- The Doubt: What happens if the entire base warps or the guide loses parallelism?
- The Logic: Local deformations are filtered by the 480-point array. Global deformations (macro-warping) result in a Virtual Centerline Offset. This does not require expensive active control; it can be corrected by introducing a few electromagnetic coils with simple trimming resistors. By turning a knob, you realign the virtual magnetic axis—transforming a mechanical alignment problem into a simple electrical tuning task.
- The Doubt: The gaps between discrete magnets must create periodic "force peaks" (ripples). How is motion smooth?
- The Logic: This is resolved through Halbach Array Topologies. By rotating the magnetic vectors, the flux is concentrated into a continuous "Hyperplane." When combined with long-strip geometries that overlap circular arrays, the "gaps" are physically bridged. The hardware is merely the manifestation; the resulting magnetic soul is a continuous, frictionless medium.
- The Logic: Traditional giants prioritize Energy Efficiency and Dynamic Acceleration. MRI requires extreme field strength (Tesla-level), while Lithography requires extreme G-force. These goals require expensive active superconductors. Our project prioritizes Precision-to-Cost Ratio, achieving 100% of the required precision at 1% of the cost for high-precision, quasi-static motion.
- The Doubt: Traditional engineering states that a machine tool cannot produce a workpiece more precise than itself. If the parts are made with low-precision tools, how can the output be high-precision?
- The Logic: This project breaks the Inheritance of Error. In traditional machining, the tool's surface is "copied" onto the workpiece. In our system, the low-precision hardware is merely a Stochastic Seed. The final precision is an Emergent Property of the field logic. Just as a rough, rusted pipe can carry a perfectly smooth stream of water, the "fluid-like" continuity of the magnetic field ignores the micro-roughness of its carrier. We are not "copying" the machine tool; we are using Recursive Cascading to create a new, independent coordinate system whose resolution is defined by the mathematical convergence of the field, not the physical grit of the machine tool.
- Experimental Materials: Two wooden sticks (chopsticks), 1mm thickness nano-tape, 502 super glue, hard smooth plastic sheets, toothpicks, cotton string, 102mm round NdFeB magnets, 5020*2mm rectangular NdFeB magnets.
- Total Cost: 35 CNY (5 USD).
- Approximate Installation Method: Apply nano-tape to the wooden sticks, then place magnets. Round magnets are spaced at about 5mm. Separate the rectangular magnets slightly and bond them with toothpicks and glue, then press them vertically onto the nano-tape with only one side peeled, or peel the other side and attach a plastic sheet. Tie cotton string to the top, and use the repulsive force of the two wooden sticks to squeeze the rectangular magnets in the middle. (Note: During installation, ensure both sticks are repellent to the rectangular magnets.)
This experiment verifies whether the system itself can continue to be realized under many almost unforgivable errors and validates its extraordinary robustness. The experimental conditions are as follows:
- Wooden sticks (chopsticks) chosen as the installation base: Surface roughness is that of normal wooden sticks; the stick itself is larger at one end and smaller at the other, with about 2mm plane error; it is in a bent state, with a circular arc shape protruding downward at the center point with a maximum of about 3mm from end to end; the other stick is similar, the two sticks themselves are not parallel or aligned, and the spacing between them is large-small-large; the sticks themselves are not fixed, or only a small area of 1mm thickness nano-tape is used to fix them on a cup to prevent collapse.
- Units used are ordinary NdFeB magnets purchased from the market: Their manufacturing error is greater than 15%; 10*2mm specification round magnets are installed randomly at a distance of about 0~3mm from the center line of the wooden stick via 1mm thickness nano-tape with random force. The nano-tape itself is soft and deforms under force, leading to deformation errors due to manual installation; randomly sized paper balls are manually crumpled as shims to raise one side of the round magnets, creating random height and parallel differences in random angles and directions.
- Toothpicks used to form the connecting moving part: The moving part composed of two 50202mm specification rectangular magnets is bonded with toothpicks and glue. Toothpicks are obviously not a common connecting part; due to manual installation, the X, Y, and Z axes of the two magnets are not parallel; nano-tape is applied to the plastic sheet, and the connected magnets are pressed into the nano-tape to maintain stability; the actual installation is not perpendicular to the surface, twisted to an angle of about 60~70 degrees due to the magnetic field on both sides.
- Manual pulling of string used as the feed method: Due to manual error, the force, direction, distance, and speed are inconsistent during each repetition.
- Pencil lead installed near the center of the moving part to draw curves: The pencil lead is directly inserted into the hole, is not completely fixed and will swing slightly, and the length protruding from the bottom is manually controlled.
- 0.1mm thickness 430 stainless steel sheet used as the primary adjustment method: Manually cut, overall shape is approximately a 1:2 rectangle, surface area is about 2c㎡ ; adjustment method: place in high magnetic field areas based on visual observation and feeling.
video_20260110_0515506.1.mp4
video_20260112_1422185.1.mp4
According to the results shown in the figures:Each curve was repeated about 5 times and perfectly overlapped as observed by the naked eye, so the experimental results are not a single special case.
- The 1st curve shows: Increasing the number of units covered by the moving part can achieve high precision on a low-precision basis under harsh conditions; a curve with an average error of about 1mm was drawn on the basis of various comprehensive errors greater than 3mm.
- The 2nd curve shows: Removing the shims and the errors they bring can improve precision. The errors brought by shims are magnetic field height, angle, direction, and parallel errors, and these errors themselves are greater than the magnet manufacturing error of 15%. This not only proves that manufacturing errors can be filtered but also that precision can be improved by manually adjusting these parameters; a curve with an average error of about 0.3mm was drawn after reducing shim errors.
- The 3rd curve shows: Based on the 1st curve, using tuning sheets for magnetic field adjustment can improve precision; using twelve 0.1mm thickness 430 stainless steel thin sheets with a single area of about 2c㎡ adjusted the curve with an average error of about 1mm to an average error of about 0.5mm. One tuning sheet is approximately equal to 0.05mm adjustment precision.
- The 4th curve shows: After removing the tuning sheets, the precision returns to the 1st curve; the random distance and placement between the bases each time does not affect the overall result. As long as there is a certain repulsive force from the magnetic fields on the left and right sides, the moving part will automatically return to the center, and the forward direction is determined by the virtual centerline composed of the magnetic fields on both sides.
Using the side without the artificially added paper ball spacers: Since nano-tape is used, simply pressing down with a flat object reduces the planar error of the circular magnets to less than 0.2mm.
Projected onto the center of a crosshair target with 1mm graduations on a wall 5 meters away after reflection (amplified 100x via the optical lever). Since only the lateral (left-right) degree of freedom was constrained, vertical jitter is ignored. The maximum lateral laser fluctuation was approximately 3mm, with an average fluctuation of 2mm. After dividing by the optical lever factor, the maximum physical displacement is 0.03mm, with an average of 0.02mm.
First, aim at the crosshair center. Move a certain distance, then add a shim to bring the laser back to the center. Move again and continue adding shims. After repeated adjustments, the final maximum error on the wall was approximately 1mm, with an average error of less than 1mm. After conversion, the actual physical error is approximately 0.01mm. Then, by using a strip of 0.3mm thick 430 stainless steel to cover the entire surface of the circular magnets—creating a "magnetic bridge" to smooth out magnetic field peaks at the gaps—the maximum error became significantly less than 1mm, and the average error far less than 1mm. The converted final precision is far less than 0.01mm.
Because the paper ball spacers used previously added about 1mm in height, while the magnets are 2mm thick. This meant the magnetic field on one side was 1mm higher than the other. 1mm relative to 2mm is a 50% error, which is far greater than the manufacturing tolerance of the magnets. Therefore, manufacturing errors themselves can actually be filtered out. Furthermore, the random positioning of the paper balls caused each circular magnet to tilt more than 20-30 degrees in different directions. Removing them eliminated the errors caused by angular deflection. Additionally, the magnetic bridge mitigated the magnetic field peaks at the gaps and incidentally smoothed out unevenness caused by magnet manufacturing variations.
However, this was merely the case of two long magnets covering 20 circular magnets, triggering only "Statistical Averaging" and "Length Averaging." If a 20mm wide long magnet covers two rows of 10mm diameter circular magnets, the sampling points increase to 40. This not only enhances statistical averaging but also introduces "Width Averaging." After filtering through a magnetic bridge layer, the tuning precision of a 0.5cm² shim is approximately 0.004mm. With sampling points increasing from 20 to 40, the tuning precision doubles to approximately 0.002mm.
Simply adding one row of circular magnets enhances length averaging and statistical averaging, while introducing width averaging. When width and length averaging combine into "Planar Averaging," the error filtering effect is drastically improved. Moreover, two rows of magnets offer better combinatorial space. If one row has 5mm spacing, and the other row also has 5mm spacing but is shifted forward by 5mm, the long magnet will receive "Three-Point Support" at all times, significantly boosting stability and error filtering. Finally, the increase in quantity increases the tuning precision of the shims. The principle is: the more sampling points there are, the smaller the effect produced by a single tuning shim. Thus, doubling the sampling points doubles the tuning precision.
Merely manually sticking magnets to two wooden sticks with nano-tape and adding some tuning shims brought the precision to 0.01mm. Now, applying the logic deduced above, the precision can be improved by at least another 10 times, reaching 0.001mm.
You might want to question why I claim 0.001mm is achievable when the shim tuning precision is calculated at 0.002mm. First, the current magnetic field error won't even reach 0.002mm—this is the average of 40 magnets. In reality, a single magnet's 15% error can be tuned down to below 1% using the shims, so attaining 0.001mm is possible.
Then ignore the deduced results and look only at the experimental data above. Is achieving 0.01mm for $5 not enough?
Of course, it is absolutely fine if you think that is not enough, because this is "Infinite Precision." The experimental content above is merely under a slightly "normal" condition, without yet adopting structural design, magnetic field permutation combinations, modular series/parallel assembly, or other infinite schemes. Although theoretical infinite precision can be achieved simply by increasing the sampling number, my goal is low cost. So, let us continue to explore the subsequent infinite schemes.
So, how do we move forward on the path ahead? Don't worry, I have already drawn the route directly to the finish line.
- Simple method: Sand the wood flat and then polish it, then perform straightness calibration. This improves magnetic field flatness on the reference surface.
- Harder: If you really don't like wood, replace it with granite or some other stone. (How could anyone not love wood? It's made of high-performance low-pass damping filtering carbon fiber material!)
- Even harder: Use plastic or some other metal, but magnetic metals will deform the magnetic field, requiring computer simulation or other means of isolation.
- Simple method: Purchase or customize magnets with a manufacturing error of less than 5%, and select magnets with an error of less than 1% from multiple magnets through a matching method. This increases magnetic field flatness from the manufacturing source.
- Harder: After the above methods, use demagnetization methods like pulsing or heating to manually or automatically calibrate local or all magnetic fields to make them flatter.
- Even harder: Optimize from the source of magnetic field manufacturing, or refer to some existing solutions, such as using electromagnets or superconductors, though most of them require algorithms, software, and hardware and are quite expensive before mass production.
- Simple method: Use hard or soft glue, draw lines on the base after a certain arrangement, and then stick the sources directly onto the base. After the above methods, there is already a relatively flat reference surface, so don't worry about errors; physics and mathematics will forgive you.
- Harder: Choose more suitable connection methods or glues, use tweezers or other means to ensure installation precision after a designed arrangement, and use ordinary shims under the magnetic sources for micro-adjustments to ensure overall parallelism.
- Even harder: Screen for the most suitable connection method, simulate with a computer or find the existing optimal arrangement plan, automate to improve installation precision, and use complex means for installation tuning.
- Simple method: Use plastic sheets or something else to keep the slider stable.
- Harder: Use some kind of passive circuit found online to keep the slider relatively stable in one position.
- Even harder: Directly switch to superconductors, or use precision control and algorithms plus electromagnets or other methods to keep the slider stable.
- Simple method: Purchase pre-cut tuning sheets of 0.5 or your preferred size, then simply measure the magnetic force or infer the area needing adjustment from the results, and place them for adjustment. They can also be permanently fixed with glue or something else. After a series of processes from reference surface to manufacturing to installation, the magnetic field itself is already very flat, and micro-adjustments at this time can make it even flatter.
- Harder: For the 1st layer, it is recommended to use a thickness of 0.2mm or more. Use a custom 36-zone tuning sheet divided by a cross grid, dividing a round magnet into 36 equal square or other shaped open areas. If conditions permit, perform measurements and close off areas with stronger magnetic fields; if not, install directly. The 2nd layer uses a grid tuning sheet with larger diameter orderly or disorderly arranged circular or square holes. The 3rd layer uses a grid tuning sheet with smaller diameter orderly or disorderly arranged circular or square holes. It is recommended that the thickness decreases layer by layer.
- Even harder: Use custom tuning sheets after computer simulation, or directly use a tuning body, for example, placing it to perfectly adjust the magnetic field into a hyperplane, or simply increase the number of layers to break the magnetic field into a "fluid" layer by layer.
Is that all? No, the most exciting part has just begun!
- A classic structure: Assume the base uses a rectangular wood with a width-to-height ratio of 2:1. Then use a shorter and larger rectangular wood with a rectangular hole dug through the middle so it can fit over the four sides of the base with a gap of about 4mm to act as a slider. On the upper surface of the base, place two rows of magnets symmetrically on the left and right; same for the lower surface. Place a row of magnets on the centerline of the left surface; same for the right surface. Then dig out gaps in the slider or leave only a hollow structure for support to place rectangular magnets. A total of 6 rows of rectangular magnets correspond to six rows of round magnets.
- Pseudo-pinning effect: This structural characteristic, after adding physical support or software control, limits the slider's degrees of freedom in up-down, left-right, rotation, and roll, which is extremely similar to the pinning effect of superconductors. However, due to another effect of superconductors, it can move back and forth on the magnetic field surface, thus effectively achieving basically the same function.
- Precision enhancement assembly: Treat the above classic structure as a module. Place two modules in parallel and connect their respective sliders to continue increasing the quantity to improve precision. Due to previous principle verification, the precision of two modules is higher than that of one, and the number can continue to be increased until a certain limit of returns is reached.
- Large-range movement assembly: Connect two modules according to the precision enhancement assembly as the X-axis. Then place the two ends of the base on two other modules perpendicular to these two modules as the Y-axis. Finally, add miniaturized modules on the X-axis as the Z-axis in this way. Due to previous principle verification, this architecture maximizes the use of spatial averaging of all constituent architectures to significantly improve precision performance, making the Z-axis of the center point enter the "zero point" of the entire architecture.
- Small-range movement ultra-precision assembly: Connect modules in a 3x3 dot matrix, using 8 modules to filter errors so that the precision of the middle module achieves a qualitative leap.
- Full passive: Use physical support on the slider surface to keep it stable, or connect another module on the left, right, or both sides. The connected module is linked to fixed objects, moving objects, etc. During power transmission, it is somewhat limited by the fixed objects, but since fixed objects only support roll and rotation degrees of freedom, the influence is less than 20%. More than 80% relies on the magnetic field and structural self-stability. Since the module itself is a filter, after being filtered by one module, it can be filtered again at the center module to minimize the impact. This mode itself requires external force to move.
- Semi-passive: Use certain circuit characteristics related to electromagnets to maintain stable levitation of the slider without the need for algorithms. This mode itself is static; control devices can be added to manually adjust the thrust.
- Semi-active: Use something to actively provide and control thrust.
- Full-active: Use some way to actively increase and control thrust, and use some way to make the slider more stable and improve precision again.
- Phase shift: Fix the slider and let the base act as the moving part.
"The 'Error Acceptance Paradigm' defined in this project may be referred to as Physical Intelligence or Structural Intelligence in different disciplines; it is essentially a low-dimensional utilization of physical laws."
- This article and its extended content are published solely based on the principles of world peace, human equality, and common prosperity. It shall not be used for any terrorist activities, military purposes, or any technology that harms the world, nations, individuals, environment, animals, etc., or results in such consequences.
- This article and its extended content shall not be used for any direct or indirect commercial activities. Corporate use is strictly prohibited.
- Any act of basing work on, extending, or citing any part of this project constitutes full agreement to all terms and interpretations of rights herein. I (Zeng Hao) reserve the ultimate right of interpretation.
To prevent any circumvention of this agreement by changing materials, shapes, or media, the technical scope of this project includes but is not limited to:
- Base: Including but not limited to wood, stone (granite, marble, etc.), metal, plastic, composite materials, liquid surfaces, air-cushion surfaces, or any macro-object providing physical support.
- Magnetic Source/Field: Including but not limited to NdFeB, ferrites, samarium cobalt, electromagnets, superconductors (diamagnetism), quasicrystal magnetic materials, and all substances capable of generating static or dynamic magnetic fields.
- Tuning Operator: Including all substances with magnetic permeability, diamagnetic, or paramagnetic properties, regardless of thickness, shape, processing technology, or physical state.
- Motion Paradigm: Including all linear, rotational, or multi-axial precision displacements realized using passive field topology, pseudo-pinning effects, and statistical averaging principles.
The validity of this declaration is not limited to the field of physics and covers the following interdisciplinary areas. It is strictly prohibited to circumvent this agreement by changing terminology, disciplinary classification, or description logic. Equivalent terms in different fields are bound by this declaration:
- Mechanics & Manufacturing: Kinematic Averaging, Elastic Averaging, Over-constrained Positioning, Structural Intelligence.
- Physics & Materials: Physical Intelligence, Passive Field Computing, Metamaterial Topology, Magnetic Potential Well Self-assembly.
- Control & Algorithms: Hardware-as-an-Algorithm, Software-free Closed-loop, Analog Physical Computing, Feedforward Hardware Matrix.
- Metrology & Statistics: Spatial Sampling Averaging, Statistical Precision Enhancement, Non-deterministic Manufacturing Compensation.
- Emerging Terms: AI Physicalization, Embodied Intelligent Structures, or any new terms involving the use of discrete passive field spatial averaging/statistical distribution to offset macro-manufacturing errors.
- Loss of Novelty Statement: All principles of this project (statistical averaging, spatial topological isolation, pseudo-pinning, field tuning operators, etc.) enter the global Public Domain as "Prior Art" upon publication.
- Anti-Squatting: Any individual, institution, or company is strictly prohibited from applying for any patents, utility models, or designs based on any details of this project.
- Invalidation Authority: I (Zeng Hao) reserve the original right to initiate legal action and apply for the invalidation of any "patent walls" built upon this project at patent offices worldwide.
- Mandatory Citation: Any academic paper, technical report, or white paper inspired by this project must prominently cite the link to this project and attribute the author (Zeng Hao).
- Anti-Privatization: It is strictly forbidden to package the principles of this project as the exclusive research results of individuals or groups. Unattributed use will be treated as malicious plagiarism.
- Counter-Litigation Clause: Before initiating any legal action against me, the plaintiff must first prove global ownership of the "Physical Constants," "Laws of the Universe," and "Laws of Statistical Probability" involved in these processes and provide evidence that such ownership is globally accepted.
- Legal Liability: Any benefits generated by attempting to bypass this declaration shall automatically belong to the cause of global peace.
- Right of Revocation: I (Zeng Hao) reserve the right to revoke authorization for specific entities at any time. Citing this project represents your acknowledgement that physical laws are a common heritage of humanity, not corporate property.
If you refer to, cite, or use the principles of the "Infinite Precision Project" in any academic papers, technical reports, open-source projects, or publications, please use the following standard formats. Failure to cite as required will be considered a violation of the open-source agreement and potential plagiarism.
Zeng, Hao. (2026). Infinite Precision Project: A New Paradigm for Precision Motion Based on Passive Field Computation and Statistical Averaging. GitHub Repository. Available at: [https://github.com/ZengHaohei/Infinite-Precision]
@misc{zeng2026infinite,
author = {Zeng, Hao},
title = {Infinite Precision Project: Achieving 1nm Precision via Passive Field Computation and Pseudo-Pinning Effects},
year = {2026},
publisher = {GitHub},
journal = {GitHub Repository},
howpublished = {\url{https://github.com/ZengHaohei/Infinite-Precision}},
note = {CC BY-NC-SA 4.0 License}
}
Project Name: Infinite Precision Project (Error Acceptance Paradigm) Author: Zeng Hao (曾皓) License: CC BY-NC-SA 4.0
本项目采用 CC BY-NC-SA 4.0 (署名-非商业性使用-相同方式共享 4.0 国际) 许可协议发布。
免责及沟通声明： 由于我不会英文，所以文章为AI翻译，并且全程AI参与内容编写，由AI自身以及翻译错误导致引用了某些专利名词或者专业名词请与AI公司进行协商，然后进行在此网站留言通知我更改，但是由于我本人不会英语，不保证正确理解其意图与正确修改文章，本人第1次主动使用此网站发布内容，此前仅为未登录状态，所以不了解网站任何功能，本人此前访问此网站平均频率是一年一次，所以对于以上错误我应该会在一年之内更改，但是可能由于网络连接问题或者其他个人原因导致延期，建议由以上原因导致的侵权行为立刻由被侵权者将此网站的侵权段落修改为无侵权版本后进行留言，之后以此留言为准，阅读者可以自行参考此正确基准。
大家好我是来自中国的曾皓，我进行开源仅仅只是因为申请专利与编写论文比发现一条新道路更加困难。
本文章及延伸内容仅以世界和平、人人平等、共同富裕为原则发布，不得用于任何恐怖活动、军事等危害世界、国家、个人、环境、动物等以及会造成这些结果的技术，其文章及延伸内容不得用于任何直接以及间接商业活动，公司禁止使用，并且对于基于这篇文章建立的相关专利以及构成的围墙我拥有无效它们的权利。
向我发送律师函等法律诉讼之前，请先将所涉及物理常数、宇宙规律、专业名词等纳入公司或个人所有，并且明确标注其他人不得使用，并拿出世界范围通用并且所有使用这篇文章以及延伸技术的国家以及人员接受的证明。
不知道人们会怎样钻空子绕过那些条例，但即使你钻空子，你的专利、论文等其他载体也必须在显眼位置引用这篇文章的链接，并且标注我的名字，然而即使你这样做了，我也需要拥有随时可以撤回你发布的涉及这篇文章以及其延伸内容的权利，只要你基于、延伸、引用这篇文章就代表你同意整篇文章的全部条款以及权力解释。
关于项目许可证的友好说明
为保护开放探索的精神，本项目采用 知识共享 署名-非商业性-相同方式共享 4.0 (CC BY-NC-SA 4.0) 许可证。我们的主要目的是防止大型商业实体在无需贡献的情况下，将这一社区驱动的想法专利化或垄断。
然而，对于我们的建造者同伴和先驱们，我们的立场是开放且鼓励的：
- 致个人、学者、研究员和爱好者： 我们热忱欢迎您将本设计用于学习、研究和个人项目，可以自由使用、修改和构建。
- 致那些正在构建原型、进行测试和分享改进的开发者与创客： 我们将您视为 核心合作者。您为验证和推进此设计所做的实践工作，在我们看来不属于“商业用途”。我们渴望看到您的构建成果，并从您的经验中学习。
- 致有明确商业意向的团队或初创公司： 我们同样欢迎您！“非商业性”条款的目的并非阻止创新，而是为了确保公平协作。如果您有基于本项目开发产品或服务的具体计划，请直接通过 [github] 联系我们。 我们很乐意讨论并授予一项特定的、免费的商业使用许可。我们的使命是让想法变为现实，而非设置不必要的障碍。
让我们，共同构建未来。
首先，请抛弃你的传统工程思维。 磁场的刚性是可调整的、非线性的、无摩擦的。我们需要用正确的目光来看待它：请把它放在与超导体悬浮、磁浮导轨、气浮导轨等精密技术相同的高度。
- 磁悬浮列车：验证了其刚性与稳定性。
- 光刻机晶圆运输系统：验证了其精准性与控制性。
- 核磁共振系统 (MRI)：验证了其磁场的可调整性与平整性。
但是硬件只是表象，磁场才是灵魂，所以才有了这个开源项目。
-
应用物理学/电磁学: 多磁体阵列的场合成、磁屏蔽与整形原理。“实现了一种可编程的被动磁势阱拓扑技术，通过微扰单元对背景场进行局部线性修正。”
-
控制理论: 物理结构替代了软件算法，实现了一种“硬件闭环控制”。“本系统本质是一个基于模拟计算的、前馈-反馈复合控制器。金属片阵列是固化的、可调的‘控制律矩阵’，直接以物理方式实时补偿误差。”
-
精密机械工程: 运动精度的实现完全脱离了传统的阿贝误差链和刚性约束原则。“我们提出了‘机械基座误差隔离’的新范式，将导向精度与基座宏观形貌解耦，大幅降低对基础机械加工的苛刻要求。”
-
材料科学: 金属片作为调谐单元，其磁导率、厚度、形状的精确利用。“我们开发了利用软磁材料微结构单元作为场调谐算子的方法，实现了磁场分布的精度整形。”
最后，还是需要质疑请花几十元复刻实验内容，然后使用实验结果反击。“实践是检验真理的唯一标准”
最后的最后为了降低普通人理解难度，请将基座磁场想象为水面，运动部件想象为船，单元误差大小就是水波纹的大小，运动部件所覆盖单元的数量就是船的大小，调谐体是一块可以将水压下分流的板子。
原理： 跳出传统刚体“三面互研”的思维定式，我们利用流体动力学与磁场卷积来实现精度的无中生有。
-
正交磁通积分（横竖交叉排列）： 在两个基准面上安装海尔贝克长条磁铁，采用横竖交叉（十字纹）排列。
-
物理机制： 一根纵向磁铁同时覆盖多根横向磁铁。在数学上，任意一点的磁场强度不再是单点数值，而是接触范围内所有磁铁磁场的积分（平均值）。
-
效果： 局部的制造误差和离散的磁场突峰被长条磁铁的物理尺寸强制稀释。
-
动态固化导致的时域平均 (Temporal Averaging)： 在磁性粘合剂（胶水）处于流体状态时，让上下两个基准面进行随机相对运动（震动、旋转或前后滑动）。
-
机制： 这种运动在时间轴上“涂抹”掉了静态误差。胶水固化时记录的不是某一瞬间的误差波峰，而是该时间段内磁场势能的平均超平面。
-
自举循环 (
$A \to B \to C$ )： -
A代（父本）： 通过正交排列+动态滑动生产出 B。
-
B代（子本）： 继承了 A 的平均平滑度，误差数量级下降。
-
C代（孙本）： 由 B 模具生产，在数学上无限逼近完美的物理平面。
原理： 如果有人觉得低成本迭代是玄学（魔法），那我们就用真正的工业暴力美学——纳米压印光刻（NIL）逻辑。
-
零代模具 (The God Mold)： 不计成本地获取一套超高精度部件（如光刻机退役零件或核磁共振线圈），生成一个唯一的“超平面磁场”。
-
成本逻辑： 这是一次性固定资产投入 (CAPEX)，无论多贵均摊到无限的产品中都接近于零。
-
磁性光刻 (Magnetic Lithography)： 以零代模具为母版，像印钞票、刻光盘一样，批量“拓印”磁场导轨。
-
工艺： 利用母版磁场的强大斥力/吸力，瞬间将半固化树脂中的磁畴排列至完美状态。
-
经济性： 我们用 1% 的白菜价 实现了 100% 的光刻机级磁场精度。
在进行大规模复制之前，我们必须首先创造一个参考超平面。这就是我们将光刻机与核磁共振（MRI）的优势结合的地方。
- 使用的部分： 激光干涉仪工作台与纳米级定位逻辑。
- 原理： 利用光刻机工作台 的分辨率来测绘“磁场地形图”。探头扫描原始磁铁阵列，识别出磁通量的每一次微小波动。
- 为什么有效： 我们不需要光刻机在生产中“跑”起来；我们只用它一次，通过静态标定来确定场误差的精确空间坐标。
常见质疑： “商用霍尔探头的空间分辨率根本达不到纳米级，无法测出纳米级的磁场偏差。”
事实真相： 我们并不是在用探头测 “绝对位置”，我们是在测量 “磁场磁通梯度”
-
原理： 在微观尺度下，磁场强度的变化速度远快于物理位移。相对于陡峭的磁场梯度，即使是
$1\text{nm}$ 的位移变化，也会在高端霍尔传感器上产生可测量的电压变化（毫伏级）。 -
核心逻辑： 我们利用 光刻机工作台 作为“标尺”（提供
$0.1\text{nm}$ 的空间步进），将 探头 作为“比较器”。我们不需要探头物理尺寸很小，我们只需要它 足够灵敏且稳定。只要传感器的信噪比（SNR）够高，我们就能通过磁通密度的变化反推出亚纳米级的位移。
-
过程： 探头不是在每个点测一次，而是在每
$1\text{nm}$ 的位移过程中进行 10,000 次采样。 -
结果： 根据中心极限定理，测量精度随样本量
$N$ 的增加以$\sqrt{N}$ 的速度提升。通过海量采样，探头的热噪声被抵消，从而揭示出底层纳米级的磁场拓扑结构。
- 使用的部分： 被动匀场（Passive Shimming）与梯度抵消技术。
-
原理： 根据光刻机提供的地图，应用 MRI 的被动匀场逻辑。我们在特定坐标放置亚微米级的铁性箔片，以“拉动”或“推开”磁力线，直到磁场梯度
$\nabla B \approx 0$ 。 - 为什么有效： MRI 匀场技术能实现十亿分之一（PPB）级别的均匀度。它将杂乱的磁场转化为物理意义上绝对平坦的势能表面。
最常见的质疑是“你无法以纳米精度放置铁片”。这源于对**磁阻逻辑（Magnetic Reluctance Logic）**的误解。
在机械系统中，如果你想要 的间隙，你必须移动工具 。但在磁学中，磁场
-
逻辑： 一个
$10\mu\text{m}$ 厚的铁箔片会影响很大体积内的磁通密度。将这个箔片移动$0.1\text{mm}$ （宏观位移），可能只会导致局部磁势产生$0.01\text{nT}$ （纳米级变化）的位移。 - 结论： 物理位移与场强变化之间存在一个极大的“减速比”。你用“粗笨”的手就能进行“显微”手术，因为磁场本身充当了减速齿轮。
磁场遵循拉普拉斯方程，天生具有连续性和“平滑性”。
- 箔片放置中的微小物理误差会被周围的磁通量“平均”掉。
- 不同于机械齿轮的“撞击”或“错过”，磁性箔片是扭曲磁场。磁场就像一个高频滤波器，自动忽略箔片的锐利几何边缘，只对其整合后的磁质量做出反应。
我们有两种主要方法，利用 MRI 级主动匀场线圈来创造母版。
该方法使用 240 多个离散磁铁，并“雕刻”它们的合场。
- 测绘： 光刻机台上的探头测绘出原始阵列的误差图。
- 主动抵消： MRI 主动匀场线圈产生一个“负向地图”——一个与误差完全相反的磁场。
-
叠加： 当主动场与原始场相遇，梯度互相抵消 (
$\nabla B \to 0$ )。 - 永久锁定： 当主动线圈维持这个“完美平面”时，我们放置被动铁片来模拟主动线圈的效果。一旦关掉电源，铁片就会“记住”并维持这个超平面。
这是一种更先进的、自下而上的方法，使用悬浮在树脂中的磁性粉末。
-
流体状态： 将混合了高磁导率磁粉的液态树脂托盘置于 MRI 主动匀场线圈下方。
-
主动定向： 线圈通电，创造一个完美的、亚纳米级的势能超平面。
-
磁畴冻结： 在这个完美场的作用下，树脂中的每个磁性颗粒都会旋转，使其**波尔磁子（Bohr Magnetons）**与磁力线对齐。
-
固化： 树脂固化（通过 UV 或加热）。完美的磁场拓扑结构现在被“冻结”在了材料的分子结构中。
-
优点： 这创造了一个连续的磁介质，而不是离散的磁铁，从源头上消除了“磁场波纹”。
逻辑： 将光刻机台作为“纳米级定位器”，通过物理排列实现完美。
- 过程： 在光刻机工作台上安装高精度磁传感器。利用其亚纳米级的移动能力，对磁铁阵列进行全方位扫描，找出磁场的“凸点”和“凹点”。
- 动作： 根据扫描结果，利用机台的纳米级高度（Z轴）控制，物理性地微调每一块磁铁或调节片的高度与倾角。
- 结果： 通过几何补偿实现“超平面”。一旦测量磁场达到平整，立即锁定所有磁铁的物理位置。
逻辑： 利用 MRI 自带的“相位成图”功能，引导磁性树脂自我成型。
- 过程： 将盛有液态磁性树脂的托盘放入 MRI。MRI 利用其射频脉冲（相位成图）实时“看见”场强的不均匀分布。
- 动作： MRI 的梯度线圈立即产生一个“修正场”将磁场拉平。通过托盘的轻微位移（相对位置测绘）验证全局平整度。
- 结果： 通过场定向固化实现“超平面”。在 MRI 电子化维持完美磁场的同时，原位固化树脂，将精度锁死。
工业界常说的“干扰”是指 MRI 的高频射频脉冲和超导磁场会干扰光刻机的电子束或光学元件的实时运行。 而在我们的逻辑中，这完全不是问题：
- 分阶段使用： 先用光刻机测绘，再用 MRI 逻辑修复。
- 静态环境： 我们不发射脉冲，也不进行高速运动。我们是在构建一个“冷母版”，一旦标定完成，它就会保持长久的稳定。
这三项协议旨在利用现有的顶尖技术（SOTA）——即光刻机的亚纳米级伺服控制与核磁共振（MRI）的磁场均化（Shimming）技术——生成一个“母版磁场”，并进行大规模成本压缩式复制。
逻辑： 利用静态“母版超平面”的稳定性，引导复制磁场的迭代生长。
-
母版设置： 利用现有的光刻定位技术和 MRI 磁屏蔽/均化技术，建立一个静态的“上帝模具”。这创造了一个绝对参考的磁势能超平面。
-
复制工艺：
-
基底通过精密传送带系统输送到母版磁场的有效作用区。
-
逐层固化： 磁性树脂以薄膜形式涂覆，每一层都在母版磁场的作用下凝固。
-
物理原理： 当每一层固化时，树脂内部的磁畴会根据母版的磁力线进行完美定向。通过这种逐层堆叠固化的方式，系统对磁场进行了空间积分，有效地“过滤”掉了运输系统的微小震动，确保最终产品以近乎零偏差的状态继承母版的磁场拓扑。
逻辑： 通过时域运动，实现超越母版本身精度极限的平滑度。
-
母版设置： 与协议 I 相同，采用顶尖科研级的参考场。
-
复制工艺：
-
基底被输送至一个特殊的多轴随机运动托盘上。
-
随机相对运动： 在树脂从液态向固态转变的过程中，托盘进行高频、小振幅的随机平面运动。
-
物理原理： 这是时域滤波（Temporal Filtering）的工程实践。母版磁场中任何残留的静态缺陷或“热点”，都会在复制品的表面被物理性地“抹平”。固化后的磁场代表了母版磁场的时间积分。实际上，通过中和掉固定的空间谐波，复制品可以实现比母版本身更高程度的均匀性（平滑度）。
核心逻辑： 本协议利用时空态抖动技术（Spatiotemporal Dithering）来实现亚纳米级精度。通过引入多点源、全频谱的随机振动（类白噪声），我们将复制品与母板局部的空间误差解耦。结合迭代分层堆叠（微滴灌）工艺，系统利用中心极限定理实现统计平均与时间平均。理论上，这种“物理滤波”机制能让复制品的平整度超越母板本身。
母版设置： 采用与协议 I 相同的顶尖科研级参考场。值得注意的是，母版本身的制造也可以采用本协议，通过递归均化消除初始制造缺陷。 复制工艺（“模糊”引擎）：
- 基底传输： 传送带将基底输送至主动隔振与激振工作台。
- 激振源： 托盘底部并未采用普通电机，而是安装了多轴压电陶瓷致动器阵列（PEA）。
- 时空动力学： PEA 产生高频、全频谱的随机振动。由于是多点独立激振且相位去相关（Decorrelated），基底的每一个微小区域都会经历独特的、随机的振动矢量。这产生了一种“时空态平均效应”，相当于在物理位置上施加了一个低通滤波器，滤除了所有高频的空间粗糙度。
滴灌工艺（积分引擎）：
- 分布式微流控滴灌： 使用高密度的微喷嘴阵列作为“滴灌系统”，以离散的、精确控制的量子化液滴形式沉积磁性树脂。
- 流变均化： 在树脂从液态向固态转变的过程中，全频振动提供了额外的活化能，帮助流体克服局部的表面张力势垒（局部极小值），迫使其根据平均场强沉降至全局能量最低点（即完美的超平面）。
-
迭代循环： 工艺遵循**“沉积
$\rightarrow$ 抖动均化$\rightarrow$ 固化$\rightarrow$ 重复”**的循环。这构建了一个多层结构，其中第$N$ 层的误差与第$N+1$ 层在统计上互不相关，从而导致误差迅速收敛。
物理原理：
-
卷积平滑（数学滤波器）：
在数学上，复制品的最终轮廓
$R(x)$ 是母板轮廓$M(x)$ 与振动概率密度函数$P(x)$ 的卷积：
只要振动的幅度大于母板表面微小缺陷的波长，这些缺陷就会被物理“抹平”。这就是为什么动起来比静止更准。
-
各态历经性（Ergodicity）与时间平均：
随机振动确保树脂在固化时间内“采样”的是磁场的平均势能，而非单一的静态点。只要振动频率远高于树脂的固化速率 (
$f > 1/\tau_{cure}$ )，树脂“看到”的就是磁场的完美均值，从而抵消了静态的空间噪声。 -
统计误差缩减（中心极限定理）：
通过多层微薄的迭代滴灌，总厚度误差
$\sigma_{total}$ 与层数$N$ 呈现如下关系：
物理学证明，通过随机过程堆叠多个“不完美”的薄层，最终会收敛出一个“完美”的整体。
精度递归进化：“子代优于父代”范式 本协议的核心假设是复制品（子代）的磁场均匀度可以超过母板（父代）。这构建了一个**“精度自增益闭环”**：
- 逻辑： 通常制造过程会引入误差，但协议 III 本质上是一个物理低通滤波器。通过在复制过程中施加高频时空态抖动，父代上的高频空间误差在子代上被“滤除”了。
-
策略： 一旦生产出子代模具 (
$Gen_{n+1}$ )，它在拓扑结构上比父代 ($Gen_n$ ) 更平滑。我们随即废弃父代，将子代晋升为新一代的母版用于生产下一代。 - 结果： 精度不再是静态的，而是进化的。
系统无需传感器反馈或外部计量即可实现精度收敛。
-
盲合成（Blind Synthesis）： 传统制造依赖“测量
$\to$ 修正”。协议 III 依赖**“随机化$\to$ 积分”**。 -
卷积定理： 在数学上，复制品的表面轮廓
$R(x)$ 是母板轮廓$M(x)$ 与振动函数$V(x)$ 的卷积。
由于随机噪声（高斯分布）在时间上的积分趋于零，母板的静态误差在复制品中被数学性地抹除了。系统之所以收敛，是因为物理学规定流体在受激时必然寻找最低能量状态（即平均势能面）。
系统如何无视量子涨落、布朗运动和原子颗粒感？
-
“场与物质”的二元性： 机械加工受限于原子的大小。但磁场是一个连续体（Continuum），受拉普拉斯方程 (
$\nabla^2\phi = 0$ ) 支配，它不存在“晶界”。 -
系综平均（Ensemble Averaging）： 虽然磁体或树脂中的单个原子可能因热噪声（布朗运动）或量子测不准原理而抖动，但在任何一点上的磁场都是
$10^{23}$ 个原子磁矩的矢量和。如此庞大的系综，其统计方差被无限稀释，几乎为零。 -
距离衰减： 微观的磁偶极子变化以
$1/r^3$ 的速率衰减。在导轨的工作距离（宏观间隙）下，原子级的噪声被完全“洗掉”，只留下纯净、平滑的场势能。
- 能达到物理极限吗？ 是的。磁场的精度在理论上可以逼近连续介质极限，其平整度将远远超过树脂材料本身的表面粗糙度。
- 最终壁垒： 唯一的限制不是磁场，而是树脂的流变学特性（分子大小和粘度）。然而，对于磁悬浮应用而言，相对于应用尺度，磁场平整度实际上可以达到“绝对零度”的粗糙度。
本文件介绍了一种非线性制造范式，利用“超植结构（HPA）”来解决“母机悖论”。通过综合丝瓜络、叶脉、硅藻及蒲公英等多种生物分形逻辑，我们构建了一个多尺度物理滤波器，能够将粗糙的原始磁场精炼为亚纳米级的平滑拓扑结构。
超植结构并非对自然的简单复制，而是四种不同生物优势的计算合成：
- 骨架（丝瓜络-树形拟合）： 主体采用丝瓜络网络，并结合树形生长模型进行计算拟合。结构从底部到表面呈现“由大到小、由粗到细”的梯度变化，产生“梯度阻抗”，逐层平复高幅值的磁通跳变。
- 排列（叶脉网络拟合）： 整体排列遵循叶脉形态发生学。这确保了磁能在表面能够均匀输运与消散，消除“边缘效应”和局部的磁场拥塞。
- 界面（硅藻微孔）： 整个结构表面覆盖有仿硅藻微孔阵列。这些亚微米级的孔隙作为最后的“高频滤波器”，抹平父代磁场最后残留的空间抖动。
- 内部阻尼（蒲公英种球）： 结构间隙填充有单独仿蒲公英种球的球体材料。这些轻质、各向同性的元件在树脂基质中充当“压力平衡器”，防止磁粉在固化过程中发生物理团聚。
- 生物结构获取： 对目标植物架构进行高分辨率 3D 扫描，建立基础几何库。
- 计算形态发生与多尺度拟合： 对丝瓜络骨架应用树形生长模拟。通过随机偏置旋转与模型重叠，在不丢失分形特性的前提下最大化利用空隙。
- 表面与间隙功能化： 在数字模型表面“生长”硅藻微孔，并计算内部蒲公英填充物的分布密度。
- 分层化处理（制造可行性）： 考虑到制造难度，可将超植结构解构为离散的层。每一层使用特定的单独或混合仿生结构（例如：底层侧重丝瓜络，表层侧重硅藻）。
- 增材制造： 通过多材料 3D 打印制作支架，允许在结构的不同位置调节磁导率。
超植支架为协议 III（随机均化法）提供了功能性环境。在此环境下，液态磁性树脂接受“随机抖动（全频振动）”。超植结构复杂的几何形状防止了驻波的产生，强迫磁性颗粒进入全局平衡态。分形结构的深度确保了父代的制造缺陷在数十亿个结构交点中被散射和平均化。
“超植结构”方案以拓扑复杂性取代了机械精度。通过迭代式的“自举演化”，磁场平整度将收敛至仅由场连续性定义的物理极限。该方法论使利用低成本开源工具制造纳米级参考基准成为可能。
- 场景设定： 我们没有母版，没有光刻机，也没有 MRI。只有一堆廉价、粗糙的普通磁铁阵列。
- Gen-0（粗糙阵列）： 使用普通磁铁阵列作为基底。
- 应用协议 III： 实施滴灌 + 全频震动。液态树脂对 Gen-0 的粗糙磁场进行物理平均。
- Gen-1（初代子模）： 固化后的 Gen-1 在磁场上比 Gen-0 略微平整。
- 迭代： 将 Gen-1 作为母版，生产 Gen-2。重复此过程 100 次。
奇迹： 通过递归卷积，初始的宏观误差被迭代平滑至消失。我们仅依靠廉价硬件和统计学平均原理，从“垃圾”中演化出了 PPB 级的“上帝模具”。
-
零创新风险： 这些方法不需要“新的”物理学；它们利用现有的最佳工业工具（光刻/MRI）作为一次性投资。
-
可扩展性： 通过将“精确制造”与“大规模生产”分离，单位成本大幅下降。
-
无变量添加： 这些协议侧重于被动复制， 这意味着它们不会在大规模生产线中引入复杂的主动反馈回路，从而显著提高产量和可靠性。
原理： 通过极低成本彻底消解关于耐用性和环境影响的质疑。
-
单次使用逻辑： 传统工程质疑胶水的长期稳定性。我们的回答是：既然这么便宜，为什么要长期稳定？
-
如果你花 10 万买导轨，你当然担心它第二年还在不在精度范围内。
-
如果你花 10 块钱买我们的“打印磁场条”，你完全可以把它当成耗材。
-
环境免疫： 如果环境温差导致磁场在 100 小时后发生了微米级漂移，解决办法不是花大价钱做温控，而是直接换一根新的。
-
结论： 我们不解决“维持精度”的难题，我们通过降低成本，让“获取新精度”变得像呼吸一样简单。
只要物理常数不变，本实验验证了从0到1，就证明了从1到100在原理上是一条康庄大道，后续的工程障碍是已知物理范畴内的常规挑战，而非原理性的“不可能”。
我的贡献在于 “发现了那条路” ，而大家需要做的是 “把路铺得更宽更平” 。
本文提出并实验验证了精密运动领域的一种颠覆性范式：从“确定性误差链”转向“统计性误差平均”。传统机械系统受限于精密公差的指数级成本增长，而本研究证明，通过被动磁场的离散调谐，系统误差随单元数量
-
方案 I：一阶统计平均乘区
无限精度计划的基石。利用
$1/\sqrt{N}$ 标度律实现精度的初始指数级提升，通过增加磁性调谐单元的数量，打破对物理实体公差的依赖。 - 方案 II：多维空间平均与过约束耦合 引入长度平均与宽度平均维度。通过限制上下左右及旋转翻滚等多自由度，构建“空间平均效应”。实现了伪钉扎效应与过约束耦合，使多个独立的指数级提升乘区在方案 I 的基础上进行乘积叠加。
- 方案 III：几何拓扑增益与采样密度扩张 通过几何尺寸比例放大（如 2:1 回形结构）以容纳更高密度的采样点。采用长条磁铁覆盖双排圆磁铁、且两排圆磁铁整体位移 5mm 相位差的交错布局，在大幅抑制间隙磁场突峰的同时实现三点支撑稳定性。总采样点提升至 480 个，从底层量级上完成了对前两代方案结果的指数级放大。
- 方案 IV：磁桥平滑与拓扑分形滤波 引入高导磁不锈钢条作为“磁桥”覆盖磁铁表面。这不仅物理性地平滑了间隙磁通突峰，更进一步过滤了磁铁制造偏差。通过多层叠加实现磁场高斯模糊化与磁场拓扑分形，在物理底层再次优化了各乘区的基数。
- 方案 V：主动逻辑纠偏与动态补偿 基于被动结构已抵消 80% 以上重力与稳定性贡献的前提，引入低成本控制系统。系统极大地降低了对控制带宽的要求，使万元级精度控制降至百元级成本。利用软件逻辑与调谐电路对残余物理不确定性进行最终坍缩。
-
方案 VI：模块化递归级联与全频段滤波
最终进化形态。将每一个回形模块视为一个独立的超强滤波器，通过刚性或差分连接进行多模块串联。基于非线性无摩擦特性，误差在模块传递过程中进行平方级独立运算。
亚原子精度结论解释：
之所以能达到亚原子级 (
$10^{-10}\text{m}$ )，是因为级联过程构成了误差分布的递归卷积。在级联系统中，每个模块的衰减系数是相乘关系 ($$E_{\text{终}} = E_0 \cdot \prod A_n$$ )。由于磁场是连续介质，不存在机械接触的原子颗粒感，多模块对 480 个采样点的递归过滤使得残余误差在数学与物理层面坍缩至原子尺度以下。即便在最恶劣的环境噪声下，级联滤波也保证了亚原子级的理论分辨率。
在 200 元极限预算下，系统通过**随机解耦（Stochastic Decoupling）**逻辑，将宏观几何形变、制造公差及热漂移视为统一的宽频噪声
随后，经由过约束空间耦合与磁桥高斯平滑，误差被进一步通过几何耦合系数
其中
- 疑问： 廉价磁铁的制造公差通常很大（>10%），如何实现纳米级精度？
- 逻辑： 在我们的初始“压力测试”中，我们故意使用了高度差达 1mm 的磁铁（相对于 2mm 基底，误差高达 50%），且偏转角超过 30°。即便如此，仅 20 个采样点的阵列依然成功过滤了误差。由于标准磁铁公差远低于 50%，它们在逻辑上被视为“随机噪声”。此外，通过多层调节片的高斯模糊效应，磁场在进入统计阶段前就已经在物理层面被平滑了。
- 疑问： 热胀冷缩和环境振动难道不会瞬间破坏纳米级的稳定性吗？
- 逻辑： 这是一个关于“尺度”与“信噪比”的问题。本系统旨在抑制 3mm 级的宏观误差。如果一套逻辑足以中和 3,000,000 纳米的物理偏差，那么微米级的环境扰动就会被完全“淹没”在系统的抑制带宽内。我们不是在对抗环境，而是让系统的鲁棒性远超环境噪声。
- 疑问： 如果基座整体变形或导轨不平行怎么办？
- 逻辑： 局部变形会被 480 点阵列自动过滤。整体宏观变形仅仅导致**“虚拟中心线”发生偏置**。这不需要百万级的控制系统，只需要几个电磁线圈和简单的电位器。通过旋转按钮调节电流，即可修正虚拟轴线——将机械对齐问题转化为简单的电路调谐问题。
- 疑问： 离散磁铁之间的间隙必然会导致力矩波动，如何保证平滑？
- 逻辑： 通过 海尔贝克阵列（Halbach Array） 及其变种解决。磁矢量旋转将磁通量集中并平滑化为一个连续的“超平面”。硬件只是表象，最终形成的磁场“灵魂”是一个连续、无摩擦的介质。
- 逻辑： 巨头追求的是**“能效比”和“极端动态响应”（如 10G 以上加速度）。这迫使它们使用昂贵的有源超导系统。而本项目追求的是“精度成本比”**。我们证明了：在非极高速场景下，用 1% 的成本即可实现 100% 的精度性能。
- 疑问： 传统工程学认为，机床加工不出比自己精度更高的东西。如果零件是低精度机床做的，凭什么输出高精度？
- 逻辑： 本项目打破了**“误差继承”的宿命。传统加工是“复制”机床的误差，而我们的系统将低精度硬件仅视为一个“随机种子（Stochastic Seed）”。最终的精度是磁场逻辑的“涌现属性（Emergent Property）”。就像粗糙生锈的铁管可以流出完美平滑的水流一样，磁场的“流体式”连续性可以忽略载体表面的微观粗糙度。我们不是在复制机床的精度，而是通过六阶递归级联**创造了一个全新的、独立的坐标系，其分辨率由磁场拓扑的数学收敛决定，而非母机的机械磨损。
-
实验材料: 两根木棍（筷子）、1mm厚度纳米胶带、502胶水、较硬的光滑塑料薄片、牙签、棉绳、102mm圆形钕磁铁、5020*2mm长方形钕磁铁
-
实验总花费: 35CNY（5USD）
-
大致安装方式: 木棍上贴上纳米胶，然后放上磁铁，圆形磁铁间距约5mm，将长方形磁铁中间隔开一些用牙签与胶水粘接，然后垂直按入只撕开一边的纳米胶上，或者说撕开另一边贴上塑料片，顶端粘上棉绳，然后两根木棍用斥力将长方形磁铁挤在中间。（注意，安装过程中要确定两根棍子都与长方形磁铁是相斥的）
-
选用两根木棍（筷子）作为安装基座: 表面粗糙度为正常木棍；木棍本身一头大一头小，约2mm平面误差；其本身为弯曲状态，中心点向下凹出从头到尾其最大点约3mm的圆弧形；另一根木棍情况相似，两根木棍本身不平行对齐，并且之间间距为大-小-大；木棍本身不固定，或者仅小面积使用1mm厚度纳米胶带固定在杯子上防止倒塌；
-
选用单元采用市场上购买的普通钕磁铁作为单元: 其本身制造误差约大于15%；10*2mm规格圆形磁铁通过1mm厚度纳米胶带随机间距与力度的安装在木棍离中心线距离约0~3mm的位置，其纳米胶带本身是软的会受力变形，并且由于手工安装导致形变误差；人为揉搓随机大小的纸团作为垫片将圆形磁铁一边垫高，产生了随机角度、随机方向的随机高度差与平行差；
-
使用牙签组成连接运动部件: 两个50202mm规格长磁铁组成的运动部件本身由牙签与胶水进行粘接，牙签显然不是一个常用的连接件；由于手工安装，两个磁铁本身XYZ轴并不平行；在塑料片上粘上纳米胶带，然后将连接好的磁铁按入纳米胶内来保持稳定；实际安装后并非垂直于表面，因两边磁场作用扭曲为约60~70度角；
-
使用手工拉线作为进给方式: 由于手工误差，其每次重复时力量、方向、距离、速度等并不一致；
-
在运动部件较为中心位置打孔安装铅笔芯以绘制曲线: 铅笔芯是直接插入孔中的，本身并不完全固定会一定摆动，底部伸出长度由手工控制；
-
使用0.1mm厚度430不锈钢片作为初级调整方式: 手工裁剪，总体形状约为1:2长方形，表面积约为2c㎡；调整方式为，凭肉眼观察与感觉往磁场高的区域放置；
video_20260110_0515506.1.mp4
video_20260112_1422185.1.mp4
-
第1根曲线表明了: 增加运动部件所覆盖单元数量可以在恶劣条件下的低精度基础上实现高精度；在大于3mm的各种综合误差基础上画出了平均误差约1mm的曲线。
-
第2根曲线表明了: 通过去除垫片以及其所带来的误差可以让精度提升，垫片带来的误差是磁场高度、角度、方向、平行误差，且这些误差本身大于磁铁制造误差15%，所以不仅证明了可以过滤制造误差还可以通过人为调整这些参数来提高精度；在减少垫片误差之后画出了平均误差约0.3mm的曲线。
-
第3根曲线表明了: 在第1根曲线的基础上通过使用调谐片进行磁场调节可以让精度提升；使用12片0.1mm厚度单个面积约2c㎡的430不锈钢薄片将平均误差约1mm的曲线调整为平均误差约0.5mm，一个调谐片约等于0.05mm调节精度。
-
第4根曲线表明了: 去除调谐片之后，精度还原为第1根曲线；每次基座之间的随机距离与摆放并不影响整体结果，只要在左右两边磁场的一定斥力之下，运动部件就会自动回归中心，并且前进方向由左右两边磁场组成的虚拟中心线决定。
使用没有人为添加纸团垫片的那一面，由于使用的是纳米软胶，仅仅使用平整的物体压平之后，就使得圆形磁铁的平面误差小于0.2mm。
经过镜子折射之后投射到5米的墙壁上的带有1mm刻度的十字标靶中心（经过光学杠杆100倍放大），因为只限制了左右自由度所以忽略上下抖动，激光左右跳动最大距离约等于3mm，平均跳动为2mm，除以光学杠杆之后，最大距离0.03mm，平均跳动0.02mm。
现在添加0.5c㎡调谐片，首先瞄准十字中心，然后移动一段距离后添加调谐片使激光回归中心，再移动一段距离继续添加，经过反复多次调整，最后最大误差约等于1mm与平均误差小于1mm，经经过换算之后实际结果约为0.01mm，然后使用一片长条形0.3mm厚度430不锈钢覆盖全部圆形磁铁表面搭建磁桥以平滑间隙磁场突峰之后，最大误差明显小于1mm，平均误差远远小于1mm，换算后最终精度为远小于0.01mm。
为什么还是将基准精度提高了10倍以上，因为纸团垫片本身增高了约1mm，而磁铁厚度2mm，等于一边的磁场比另外一边高1mm，1mm对于2mm是50%误差，远远大于磁铁的制造误差，所以其实制造误差本身就是可以被过滤的，而且由于纸团垫片的位置是随机的导致了每个圆形磁铁朝向不同方向偏转了二三十度以上，去掉之后因为角度偏转带来的误差也消失了，再加上磁桥缓解间隙过度带来的磁场突峰并且顺便平滑了一些磁铁制造误差带来的凹凸。
然而这仅仅是两个长磁铁覆盖20个圆形磁铁的情况，只触发了统计平均与长度平均，那么只要宽度20mm的长磁铁覆盖两排直径10mm的圆形磁铁，采样点就会增加到40个，不仅增强了统计平均而且引入了宽度平均，经过一层磁桥的过滤之后0.5c㎡调节片的调节精度约等于0.004mm，采样点从20增加为40之后，调节精度增加一倍约为0.002mm，单单这样增加一排圆形磁铁，就增强了长度平均与统计平均，并且引入了宽度平均，当宽度平均与长度平均混合之后变成平面平均就大幅提升了误差过滤效果，然而两排磁铁有了更好的组合空间，一排磁铁间隔5毫米，另一排磁铁同样间隔5mm但是整体向前移动5毫米，这样长条磁铁就能随时受到三点支撑大幅提升稳定并过滤误差，最后数量的增加使得调节片的调节精度增加，原理是采样点越多调节片产生的调节效果就越小，所以采样点增加一倍，调节精度增加一倍。
那么根据之前实验以及上面的推断，仅仅只是手工将磁铁用纳米胶带粘在两根木棍上并添加一些调节片，就让进度来到了0.01mm，现在加上上面的推断逻辑至少还能让精度提升10倍，也就是达到0.001mm。
你可能想质疑为什么调节片的调节精度是0.002mm我却说能达到0.001mm，首先目前磁场的误差根本不会来到0.002mm，这是40个磁铁平均出来的，实际上单个磁铁15%的误差至少可以通过调节片调节到1%以下，所以说可以达到0.001mm。
那就别管推理结果，只使用上面的实验数据，5美元做到0.01mm难道还觉得不够吗。
当然觉得不够也肯定是没有关系的，因为这是无限精度，上面的实验内容也只是在正常一点点的情况下，并且没有采用结构设计、磁场排列组合设计、模块化串并联拼装等无限方案之前的结果，虽然仅通过增加采样数也可以达到理论上的无限精度，但我的目的是低成本，所以让我们接下来继续探讨后续的无限方案。
那么，我们该如何继续前进呢？别担心，我已经规划好了直达终点的路线。
-
简单的方法: 将木头磨平然后抛光，再进行直线度校准，这是在基准面上提高磁场平整度。
-
困难一点: 如果你真的不喜欢木头，那么就把它换成花岗岩或者其他什么石头。（怎么会有人不爱木头呢？那可是由高性能低通阻尼滤波碳纤维材质组成的）
-
再困难一点: 使用塑料或者其他什么金属，但是导磁的金属会让磁场变形，这就需要计算机模拟计算，或者其他手段进行隔离。
-
简单的方法: 购买或者定制制造误差小于5%的磁铁，通过选配法在多个磁铁中分组选出误差小于1%的磁铁，这从制造根本上增加了磁场平整度。
-
困难一点: 在以上方法之后，通过测量然后使用脉冲、加热等退磁方法，人工或者自动校准局部或全部磁场，使之更加平整。
-
再困难一点: 从磁场的制造源头开始优化，或者参考一些现在有的解决方法，比如可以用电磁铁或者超导体等，但是它们大部分都需要算法与软件和硬件，量产化之前较为昂贵。
-
简单的方法: 使用硬胶或者软胶，一定的排列组合之后用笔在基座上画上线，然后直接把源粘在基座上面，经过以上的方法已经有一个较为平整的基准面，所以不用担心误差，物理与数学会原谅你。
-
困难一点: 挑选更合适的连接方式或者胶水，经过一定设计的排列组合，使用镊子或者其他手段保证安装精度，并且可以使用普通的垫片在磁源下方进行微量调整以保证整体平行度。
-
再困难一点: 筛选出最合适的连接方式，计算机模拟或者寻找现有最优排列方案，自动化以提升安装精度，使用复杂手段进行安装调优。
-
简单的方法: 用塑料片或者其他什么东西保持滑块稳定。
-
困难一点: 用某种能在网上查到的被动电路将滑块相对稳定在一个位置。
-
再困难一点: 直接换成超导体，又或者用精密的控制以及算法加上电磁铁或者其他方式，让滑块稳定。
-
简单的方法: 购买剪裁好的0.5c㎡或者你喜欢大小的调谐片，然后简单测量磁力或者仅凭结果反推出需要调整的地方，放上去进行调整，也可以使用胶水或者其他东西永久固定，这样从基准面到制造再到安装一套工序下来磁场本身就已经很平了，这个时候进行微量调节却还可以让它更平。
-
困难一点: 第1层建议使用0.2mm厚度以上，使用定制的使用十字网格划分的36分区调谐片，将一块圆形磁铁划分为36个相等方形或者其他形状开口区域，有条件进行测量，将磁场较强的区域封闭，没条件直接安装，第2层使用较大直径有序或者无序排列的圆孔或者方孔网格调谐片，第3层使用较小直径有序或者无序排列的圆孔或者方孔网格调谐片，建议厚度层层递减。
-
再困难一点: 使用计算机模拟后定制调谐片，或者直接使用调谐体，比如可以放上之后完美将磁场调节为超平面，又或者简单一点增加层数将磁场分层打碎为“流体”
这就结束了？不，最精彩的地方才刚刚开始！
-
一种经典结构: 假设基座使用宽高比2:1的长方体木头，再使用一个比它更短比它更大的长方体木头中间挖出贯穿长方形口，使之可以套入基座四边间隙保持4mm左右充当滑块，基座上表面中心对称左右各安放一排磁铁，下表面同样，左表面中心线安放一排磁铁，右表面同样，然后在滑块上挖出空缺或者干脆只剩中空结构支撑用来安放长方形磁铁，总共总共6排长方形磁铁对应六排圆形磁铁。
-
伪钉扎效应: 此结构特性，在加上物理支撑或者软件控制之后，限制了滑块上下左右旋转翻滚的自由度与超导体的钉扎效应极度相似，但是由于超导体的另一个效应导致可以在磁场表面前后移动，所以实际做到了功能基本相同。
- 精度提升拼装: 将以上经典结构视为一个模块，两个模块平行放置连接各自的滑块，然后可以继续提升数量来提升精度。
由于之前的原理验证，两个模块的精度高于一个，然后也可以继续一直增加数量提升精度直到收益某个极限。
- 大范围移动拼装: 将两个模块按照精度提升拼装连接作为X轴，然后基座首尾两端放置在两个垂直于这两个模块的另外两个模块作为Y轴，最后按照这个方式在X轴上增加小型化模块作为Z轴。
由于之前的原理验证，这种架构最大程度上利用了所有组成架构的空间平均大幅度提升了精度表现，使得中心点的Z轴进入整个架构的“零点”。
- 小范围移动超精度拼装: 将一个模块按照3×3点阵连接，使用8个模块来过滤误差使得中间模块最高精度得到质的飞跃。
-
全被动: 在滑块表面使用物理支撑的方式使之稳定，或者在左边，右边、左右两边连接上另一个模块，被连接的模块连接上固定物品、移动物品等，在动力传导时一定程度上受限于固定物品，但是由于固定物品仅支撑翻滚与旋转自由度所以影响度小于20%，80%以上靠磁场与结构自稳定，由于模块本身就是滤波器，经过一个模块的过滤之后到中心模块又能被再过滤一次最大程度上减少影响，此模式本身静止需要外力推动。
-
半被动: 使用某种有关电磁铁的电路特性可以在不需要算法的情况下使滑块维持稳定悬浮，此模式本身静止，可以增加控制装置人工调节推力。
-
半主动: 使用某种东西主动提供推力以及控制推力。
-
全主动: 使用某种方式主动提高推力以及控制推力，并且使用某种方式让滑块更加稳定并再次提升精度。
-
相位移动: 固定滑块，使基座充当移动部件。
“本项目定义的‘误差接纳范式’，在不同学科下可能被称为物理智能化或结构智能化，本质都是对物理规律的降维利用。”
- 本文章及延伸内容仅以世界和平、人人平等、共同富裕为原则发布，不得用于任何恐怖活动、军事等危害世界、国家、个人、环境、动物等以及会造成这些结果的技术。
- 本文章及延伸内容不得用于任何直接以及间接商业活动，公司禁止使用。
- 只要你基于、延伸、引用这篇文章，即代表你同意整篇文章的全部条款以及权利解释。本人（曾皓）拥有最高解释权。
为了彻底封死任何通过改变材料、形状或介质来规避本协议的行为，特此声明本项目涉及的技术范畴包含但不限于：
- 基座 (Base): 包含但不限于木材、石材（花岗岩、大理石等）、金属、塑料、复合材料、液体表面、气垫表面，或任何提供物理支撑的宏观物体。
- 磁源/磁场 (Magnetic Source/Field): 包含但不限于钕铁硼、铁氧体、钐钴、电磁铁、超导体（抗磁性）、准晶体磁性材料，以及一切能够产生静磁场或动态磁场的物质。
- 调谐单元 (Tuning Operator): 包含一切具有导磁、抗磁或顺磁特性的物质，无论其厚度、形状、加工工艺或物理状态。
- 运动范式 (Motion Paradigm): 包含一切利用被动场拓扑、伪钉扎效应、统计平均原理实现的线性、旋转或多轴向精密位移。
本声明之效力不仅限于物理学范畴，亦完全覆盖以下跨学科领域。严禁通过改变术语名词、学科分类或描述逻辑来规避本协议。本技术之原理在不同领域可能被称为以下名称（包含但不限于），均受本声明约束：
- 力学与制造领域: 运动学平均 (Kinematic Averaging)、弹性平均 (Elastic Averaging)、超约束定位 (Over-constrained Positioning)、结构智能化 (Structural Intelligence)。
- 物理与材料领域: 物理智能化 (Physical Intelligence)、被动场计算 (Passive Field Computing)、超材料拓扑 (Metamaterial Topology)、磁势阱自组装。
- 控制与算法领域: 硬件算法化 (Hardware-as-an-Algorithm)、无软件闭环 (Software-free Closed-loop)、模拟物理计算、前馈硬件矩阵。
- 测量与统计领域: 空间采样平均、统计精度增强、非确定性制造补偿。
- 新兴名词: 无论未来被称为“人工智能物理化”、“具身智能结构”或任何新创名词，只要其核心逻辑涉及“利用离散被动场的空间平均/统计分布来抵消宏观制造误差”，均视为本项目之延伸。
- 新颖性丧失声明: 本项目所有原理（统计平均、空间拓扑隔离、伪钉扎、场调谐算子等）自发布之刻起即进入全球公有领域 (Public Domain) 作为**“现有技术 (Prior Art)”**。
- 严禁抢注: 严禁任何个人、机构或公司以本项目之任何细节（包括但不限于特定的磁阵列排列、调谐方式、材料组合等）申请任何形式的专利、实用新型或外观设计。
- 无效化授权: 本人（曾皓）保留对任何基于本项目建立的“专利围墙”进行法律追诉及向全球专利局提起无效化申请的原始权利。
- 引用强制性: 任何基于、引用、参考或通过本项目获得灵感而撰写的学术论文、技术报告、白皮书等，必须在显著位置（摘要或引言部分）完整引用本项目链接并标注作者姓名（曾皓）。
- 禁止私有化成果: 严禁将本项目原理包装为个人或团体的独家科研成果。若未履行引用义务，视为恶意剽窃。
- 反击条款: 向我发送任何法律诉讼前，原告方必须先行证明其拥有该物理过程涉及的**“物理常数”、“宇宙规律”及“统计学概率定律”**的全球所有权，并拿出全球通用的证明。
- 法律责任: 任何钻空子绕过本声明的行为，其所产生的全部利益应自动归属于全球和平事业。
- 最终撤回权: 本人（曾皓）拥有随时撤回对特定对象授权的解释权。引用本项目即代表你承认：物理法则是全人类共有的，而非公司的私产。
如果你在学术论文、技术报告、开源项目或任何出版物中参考、引用或使用《无限精度计划》的原理，请使用以下标准格式。未按要求引用将被视为违反开源协议及潜在的剽窃行为。
Zeng, Hao. (2026). Infinite Precision Project: A New Paradigm for Precision Motion Based on Passive Field Computation and Statistical Averaging. GitHub Repository. Available at: [https://github.com/ZengHaohei/Infinite-Precision]
@misc{zeng2026infinite,
author = {Zeng, Hao},
title = {Infinite Precision Project: Achieving 1nm Precision via Passive Field Computation and Pseudo-Pinning Effects},
year = {2026},
publisher = {GitHub},
journal = {GitHub Repository},
howpublished = {\url{https://github.com/ZengHaohei/Infinite-Precision}},
note = {CC BY-NC-SA 4.0 License}
}
Project Name: Infinite Precision Project (Error Acceptance Paradigm) Author: Zeng Hao (曾皓) License: CC BY-NC-SA 4.0
请在操作前仔细阅读免责声明全文。 Please read the full Disclaimer before operation.
-
技术性质： 本项目（"无限精度"）中所包含的所有内容，包括但不限于设计逻辑、物理公式、工程图纸及商业模型，部分由大型语言模型 AI 辅助生成。尽管已进行逻辑审查，但 AI 生成的内容可能存在计算误差、物理局限性或未预见的工程风险。
-
风险自担： 本项目涉及超高速旋转（高 G 力）、高压容器及极端高温环境。任何个人或机构在尝试复现、制造或运行相关设备时，必须具备专业的工程知识与安全防护措施。
-
责任豁免： 作者（[曾皓]）及 AI 编写参与方不对应因使用、复现或改进本开源技术而导致的任何直接或间接后果负责，包括但不限于设备损坏、财产损失、人员伤亡或法律纠纷。
-
非医疗/军事用途： 本项目仅供科学研究与实验参考，严禁在未获得相关国家资质的情况下用于非法用途。
-
Technical Nature: All content within this project ("Infinite Precision"), including but not limited to design logic, physical formulas, engineering schematics, and business models, was partially generated with the assistance of Large Language Model (LLM) AI. While logically reviewed, AI-generated content may contain calculation errors, physical limitations, or unforeseen engineering risks.
-
Assumption of Risk: This project involves ultra-high-speed rotation (High G-force), high-pressure vessels, and extreme thermal environments. Any individual or organization attempting to replicate, manufacture, or operate such equipment must possess professional engineering expertise and strictly adhere to safety protocols.
-
Limitation of Liability: The author ([ZengHao]) and the AI contributors shall not be held liable for any direct or indirect consequences arising from the use, replication, or modification of this open-source technology, including but not limited to hardware failure, property damage, personal injury, or legal disputes.
-
Non-Regulated Use: This project is intended for scientific research and experimental reference only. Use for illegal purposes or in regulated sectors without proper national certification is strictly prohibited.