It is now the evening of April 20, 2026.

These past few days, I've been continuing to push forward the experimental work on the Three-Body Dynamics of Capital Markets. The main focus has been to first build a prototype in Pine Script that is visible, testable, and allows for rapid iteration.

The goal this time wasn't to immediately achieve a stellar strategy return, but to first answer some more fundamental questions: How exactly should the three market state variables $\delta$, $\mu$, and $\sigma$ be modeled? Are they truly independent of each other? And can I see even a hint of the previously conceived three-body gating mechanism working on the simplest possible strategy?

Let's start with the conclusion: This round of experiments was fruitful, and quite significantly so, but the gains were more in terms of validation and convergence. Some of the judgments proposed earlier in the Three-Body Dynamics were further validated in this Pine prototype. Additionally, some new implementation-level issues surfaced. It's the combination of these two parts that allowed me to converge on the directions truly worth exploring further.

1. First, Build a Three-Body Dynamics Prototype in Pine

I first built a Pine indicator prototype for the three variables + eight phases + gating mechanism. This way, I could at least visually see in TradingView what state the market is classified into during different phases.

The core of this prototype revolves around three things:

1. Estimating the three state variables: $\delta$, $\mu$, $\sigma$.
2. Standardizing them to form high/low states.
3. Mapping the ternary high/low states to the eight phases, and further mapping those to gates for momentum, value, and market-making strategies.

This step isn't particularly mysterious. The real difficulty lies not in plotting the eight-phase background colors, but in the first question: How exactly are these three quantities calculated, especially $\delta$.

2. First Important Validation: Defining $\delta$ via Moving Average Deviation is Experimentally Falsified Again

Initially, the most natural idea was to define the premium as the deviation of price from a slow-moving average acting as a central tendency. This is intuitive and easy to calculate.

To be more precise, this isn't a "discovery" but rather an experimental reconfirmation. I had already discussed this quite clearly in "Market State Variable Modeling Schemes for Three-Body Gating": If $\delta$ is defined using moving average deviation, it degenerates into a linearly correlated variant of $\mu$. More strictly, any linear slow filter used to define that so-called "central tendency" or "intrinsic value" will eventually cause $\delta$ to degenerate into a variant of momentum.

After actually implementing it in Pine this time, I saw the same problem again: The $\delta$ defined this way was highly correlated with $\mu$, almost identical. This isn't a parameter tuning issue; it's structurally wrong. I had theoretically argued this before; this time, it was just experimentally confirmed.

This issue is crucial.

For the Three-Body Dynamics to hold, the premise is that $\delta$, $\mu$, and $\sigma$ must be three relatively independent dimensions. If $\delta$ ends up being just $\mu$ in disguise, the entire system collapses from the start.

Therefore, I now believe this path can be clearly abandoned. At the very least, we can no longer call things like "slow moving average deviation" $\delta$. At best, it's a variant of some momentum filter, not the premium state variable I'm looking for here.

3. Second Important Convergence: I Now Lean Towards Interpreting $\delta$ as a Deviation Degree, Not a Direction

Next, I converged on another judgment: In my current framework, the core semantic of $\delta$ is not "whether the price is biased upward or downward," but rather "how far the price is from the consensus zone and how strong the pullback pressure is."

Thus, $\delta$ is more like a deviation intensity, not a directional variable.

Precisely because of this, I later changed many originally directional formulations, leaning towards understanding it in terms of absolute value, magnitude, or gradient intensity. Similar treatment was applied to $\mu$ and $\sigma$. At least in this prototype version, I didn't want these three quantities to inherently encode directional bias. I'm more interested in studying "state strength" first, rather than "directional judgment."

In other words, in this round of experiments:

• $\delta$ is more like deviation degree / pullback pressure intensity.
• $\mu$ is more like sustained movement intensity.
• $\sigma$ is more like volatility intensity.

After this adjustment, the semantics of the three variables became much clearer than before.

4. Third Important Convergence: Log Space is a More Suitable Coordinate System

Pushing further, one realizes that if the input is a price series, many things are better handled uniformly in log space.

Because returns are inherently log returns, and volatility is naturally more suitable to define on log returns. If $\delta$ remains in linear price space, the entire system feels a bit awkward.

So, I later switched the entire implementation to the coordinate system of log price / log returns. After this step, the internal dimensionality and interpretation of the entire model became much smoother.

I basically have no doubts about this now. If I continue to advance this work, I will default to thinking about it in log space.

5. Regarding $\delta$: The Quantile-Based Central Tendency Scheme is Useful, But I'm Not Satisfied

During the Pine prototyping phase, I also tried a scheme more substantial than the moving average: instead of a single moving average, using a fixed-window quantile band and taking its central tendency to depict the "consensus zone."

This scheme is indeed much better than moving average deviation. It's more stable and more akin to describing a price acceptance zone rather than a single line.

Visually, it appears more sensitive to some local reversal points.

However, I grew increasingly dissatisfied with this scheme. The reason is simple: Whether it's the median or a quantile band over a fixed window, it essentially performs a crude information compression. There might originally be multiple psychological anchors, multiple volume concentration zones, and multi-peak structures on the price axis, but you end up forcibly compressing them into a single "central tendency" or a "band," which actually destroys a lot of information.

This simplification might be acceptable during clear, single-peak trends. Once the environment becomes complex, ranging, or with multiple coexisting anchors, it appears very one-sided.

So, my current judgment is: The quantile-based central tendency scheme can serve as a good baseline and a very practical approximation in Pine, but it's not the $\delta$ I truly want.

6. The Direction I Now Favor More is the "Volume-Anchored Gravitational Field"

The understanding I now favor more is: Intrinsic value is not a point, but a field endogenously generated by market trading behavior.

Who traded at what price, how much volume was traded, how far those trades are from the present, and whether those anchors have expired—these factors collectively determine the pullback pressure the current price experiences.

Therefore, $\delta$ should not be understood as "how much the current price deviates from a single anchor point," but rather as "the magnitude of the net pullback pressure the current price experiences within the entire historical anchor network."

This is also why I later shifted towards the gravitational field scheme. Based on my earlier theoretical intuition, what is truly reasonable shouldn't be a single anchor point, but a field resulting from the combined action of multiple anchor points.

The intuition is actually quite simple:

1. Higher volume indicates stronger consensus in that price zone.
2. More recent historical trades should have a stronger anchoring effect.
3. Anchor points closer to the current price should contribute more to the pullback force.
4. What truly matters is not the field value itself, but the gradient of the field with respect to price, i.e., the "force pulling it back."

This intuition is much more natural than "taking a long-window median" and aligns better with my understanding of value capital behavior.

7. However, the First Implementation of the Gravitational Field Also Exposed a Practical Problem: Too Many Parameters and Prone to Explosion

I later also created an approximate implementation of this gravitational field scheme in Pine.

The result was immediate, extremely exaggerated numerical explosions, directly soaring above $10^{10}$. This isn't surprising because if you directly sum a bunch of gradient terms weighted by volume and then layer on a very aggressive bandwidth parameter, the dimensionality can easily get out of control.

Later, I added normalization and time decay, finally bringing the numerical values back under control.

But a new problem emerged: Although this scheme is theoretically more elegant, its perceived advantage at local reversal points wasn't as significant as I originally hoped. Especially compared to the quantile scheme, on similar time scales, the two ultimately showed relatively strong correlation.

This indicates two things.

First, the current implementation of the gravitational field isn't good enough; it's just a very rough Pine approximation prototype.

Second, the truly crucial aspect isn't blindly stacking more windows and parameters, but whether the behavioral assumptions embedded in the formula are correct.

If the mental model is wrong, tuning parameters beautifully is useless.

8. What's Truly Worth Further Research is Not the Window, But the Asymmetry in Behavioral Finance

As this round of experiments progressed, I increasingly felt that the truly worthwhile area to dig into for $\delta$ is not "whether the window should be 200 or 500," nor "what smoothing coefficient to use," but several more fundamental questions:

1. How exactly does the psychological anchoring effect decay?
2. Does the disposition effect make the kernel function inherently asymmetric?
3. When a long-side bias exists, are support and resistance levels inherently different in "hardness"?
4. Should the "survival probability" of a historical trade anchor point, as time passes, factor into its weight?

If these questions hold, then we shouldn't use a simple symmetric kernel to describe all anchoring effects.

I'm increasingly leaning towards this judgment: Residual anchoring in the market is not symmetric. Profitable positions tend to be closed faster, while losing positions are more likely to be held onto. After this layer of survivor filtering, the anchoring forces that truly remain in the market naturally skew towards the losing side.

If we further overlay the fact that most markets are naturally long-biased, then the phenomenon of support levels often being "harder" than resistance levels is not accidental but a natural outcome of this mechanism.

I believe this is very much worth pursuing further.

9. Preliminary Experimental Results for the Gated Strategy Did Not Satisfy Me

Besides the indicator, I also wrote a separate Pine strategy file. It used the simplest dual moving average crossover strategy as the base signal, then added a momentum_gate switch to see if this gating provided any improvement.

The result, so far, shows no significant improvement. At least under this most prototypical experimental setup, it hasn't delivered an answer I'm satisfied with.

This result isn't entirely unexpected, but it does highlight some issues.

I now believe the greater likelihood is not that "three-body gating is completely useless," but that my current experimental setup is too crude.

The two most probable problems are:

1. Large-scale state switching should gate small-scale signals, not self-gate within the same timeframe.
2. All parameters are still at the prototype level, far from being market-adapted.

Especially the first point, I now think is more critical. Because something like a regime filter is inherently more like a high-level state variable; it should operate on larger time scales rather than crowding and interfering with the underlying signals in the same frequency band.

So, while this round of gating experiments didn't yield particularly impressive results, it at least confirmed one thing for me: The next step is either to conduct genuine multi-timeframe experiments or to move to an offline data research framework. Otherwise, continuing with same-timeframe parameter tweaking in Pine will yield diminishing marginal returns.

10. The Most Important Takeaway from This Round of Experiments is Actually the Convergence of Research Direction

If judged solely by short-term strategy performance, this round of experiments can't be considered a great success.

But from a research perspective, I find it very valuable. Because it helped me separate many originally intertwined problems and distinguish "which were theoretical judgments from before" from "which were implementation issues newly exposed in this round of experiments."

My current understanding of this matter is now fairly clear:

1. The definitions of $\mu$ and $\sigma$ are relatively mature, with little controversy.
2. $\delta$ is the most difficult and valuable part of the entire Three-Body Dynamics.
3. $\delta$ can no longer follow the linear central tendency path, or it will inevitably degenerate.
4. The quantile-based central tendency scheme can serve as a baseline, but it's not the end goal.
5. The direction truly worth pursuing is the gravitational field model incorporating volume anchoring, time decay, and even left-right asymmetry.
6. The next step should continue from the perspectives of the disposition effect, psychological anchoring, and anchor survival probability to simplify and rewrite the formula for $\delta$.

In essence, the problem has been converged to a rather specific point:

What I'm looking for is not a "fancy-looking" premium formula, but a simplified model that can retain multi-anchor information without losing falsifiability due to too many parameters.

This is what's truly worth doing next.