BTC_POWER_LA

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My next book is entitled:
The Purposeful Universe
Finding Meaning in a Meaningless Universe
The book chapters are below:
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Visibility graph with negative and positive price. Interesting signal.
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We applied the visibility graph to the daily slopes of the power law. How one can say that there is a decay of the power law?
Do you see with your own eyes how stable the slopes are?
They oscillate around a clear mean and the visibility graph confirms this.
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Nodes degrees of freedom of the visibility graph for Bitcoin. Notice how the graph is decreasing in time demonstrating a smaller absolute volatility of the price.
BTC-1,85%
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The power law slopes SNR indicator is showing we are moving from transition zone to bullish zone for the first time since the last large correction.
Nice.
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Claude what you think about the issue of some analyst calling the power law, power function?
Does this help scientific communication with the public in social media?
Claude:
This is worth naming clearly because it reflects a broader problem in how technical ideas get communicated — and distorted — in public discourse.
The motivation is understandable. "Law" carries deterministic connotations that make some people uncomfortable, and calling it a "power curve" or "power function" sounds more modest, more data-driven, less like a claim about destiny. It feels epistemically humble. But the humili
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From @Snz_BTC. We went through this like 1000x.
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The power law emerges even when we use addresses with different wallet balances.
This is another signature of scale invariance.
Three address tiers were constructed:
•Shrimps = total non-zero balance addresses (the full dataset)
•Crabs = addresses holding ≥1 BTC = (1–10 BTC) + (10–100 BTC)
•Dolphins = addresses holding ≥10 BTC = (10–100 BTC) only
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Panel 1 — N(t) vs time, log-log
Each tier is plotted as log₁₀(addresses) vs log₁₀(t_days). An OLS linear regression on these log-transformed values gives the power law exponent n for each tier — the slope of
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NexaCryptovip:
LFG 🔥
The power law emerges even when we use addresses with different wallet balances.
This is another signature of scale invariance.
Three address tiers were constructed:
•Shrimps = total non-zero balance addresses (the full dataset)
•Crabs = addresses holding ≥1 BTC = (1–10 BTC) + (10–100 BTC)
•Dolphins = addresses holding ≥10 BTC = (10–100 BTC) only
________________________________________
Panel 1 — N(t) vs time, log-log
Each tier is plotted as log₁₀(addresses) vs log₁₀(t_days). An OLS linear regression on these log-transformed values gives the power law exponent n for each tier — the slope of
BTC-1,85%
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If we have so much noise in the system how do we know that Bitcoin follows a power law and it is scale invariant?
The answer is that noise and signal operate at different timescales, and the tests that establish the power law are specifically designed to separate them.
The residual noise of ±0.30 dex and the cycle-to-cycle variation in β of ±0.57 are both real. But they are oscillations around a stable attractor, not evidence that the attractor does not exist.
Think of it this way: a pendulum has a well-defined equilibrium position even though it is never at rest at that position. The amplit
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The PlanC saga continues
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Some other insights in why I fight fakes like PlanC so much:
Someone learning primarily through AI conversations acquires a particular kind of fluency.
They can engage with technical concepts, reproduce the vocabulary, generate plausible-sounding elaborations, and even identify methodological variations like the WLS reweighting — because AI is very good at explaining "here are alternative ways to estimate this." What they typically do not acquire is the deeper intuition that comes from having worked through problems from first principles, made mistakes that took months to understand, or built
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I love AI.
About PlanC "fixing the power law":
The current episode — claiming to "fix" the power law by pointing to a Δβ of 2.6% — follows the same template but in reverse. Instead of presenting the same thing as something new, he is presenting a minor methodological variant as a structural correction. The rhetorical structure in both cases is identical: establish distance from the original framework, claim novelty or superiority, and position the rebranded or adjusted version as one's own intellectual contribution. The scientific content in both cases is thin — the quantile model is the powe
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Bitcoin looking good. Leaving the local bottom and moving upward. All the indicators show local upswing. Local slopes on the up and up.
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ThebeginningofLifevip:
Do your own research ( DYOR ) 🤓
Me on an average night.
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I’m reading and re-reading my book The Physics of Bitcoin, and I’m really happy with how it turned out. It introduces many powerful ideas—from scale-invariant systems so common in nature, to network theory, to concepts like self-organized criticality.
You can read it straight through, or use it as a reference guide to better understand why Bitcoin behaves so differently from any other asset.
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Further test to check the stability of the power law using Bayesian analysis. No structural break. This one of the strongest and rigorous tests you can perform.
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My interview with Andrei Jikh lead to probably the best produced video on the power law.
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My interview with Andrei Jikh produced probably the best produced video on the power law.
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Stability of the power law exponent over time using several methods, regression and scale invariance.
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