Loop XXI · Research & Education
Understand what lasts.
Bitcoin, self-custody, AI, and monetary systems. Ideas for practical use.
The Series
Start here.
Power-law trends, cycles, and Sornette's bubble model, and why a good fit is not a forecast.
Read →Bitcoin payments and AI infrastructure.
Read →What agents do, where they fail, and why money matters.
Read →Forty-eight seconds on dollar purchasing power, pay, and Bitcoin's fixed supply.
Watch →The Bitcoin Power Law
Price history is loading. Model lines are illustrations, not price targets or floors. Power law model attributed to Giovanni Santostasi. Not investment advice.
Three ideas
Reading a model critically.
This illustration uses time raised to the 5.68 power. Its output is a model estimate, not fair value.
Drawn at 0.42 × the model line. This is a chosen multiplier, not a guaranteed price floor.
Inflation changes purchasing power. Compare historical data, assumptions, and measurement periods before drawing conclusions. BLS CPI Inflation Calculator, Jan 1971 → Jul 2026.
Lower line = 0.42 × model line
The time variable counts days from January 2009. A mathematical fit does not establish causation, future returns, or a reliable lower bound.
Power law model per Giovanni Santostasi — not investment advice.
Why it matters
Purchasing power over time.
1971–2026
Purchasing power, illustrated. Rounded estimates; not a live CPI feed.
For an official historical comparison, use the BLS CPI Inflation Calculator (Jan 1971 → Jul 2026) — not investment advice.
Learn by doing
See how a seed actually works.
A seed phrase is not a password. It is 12 or 24 words that encode random entropy, with a checksum on the final word. You can watch that happen without putting a single sat at risk.
Try the free, open-source Bitcoin Seed Tool. Roll dice into a seed, finish a partial phrase, derive BIP85 child seeds or test a forgotten passphrase, all in your browser. It is a learning tool only: never use it, or any online page, for a seed that protects real bitcoin. Independent of Loop XXI.