Physics of Bitcoin #30 Perrenod Santostasi.pdf
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In this edition of the Physics of Bitcoin show we covered Metcalfe's law applied to Bitcoin and explored why Bitcoin's adoption is growing with a cube law of time. We examined institutional adoption of Bitcoin and showed it is growing as a 4th power law of time. We presented a hypothesis as to why the adoption is growing as T^3 and therefore why price grows as T^6 as a consequence of Metcalfe's Law for network emergent behavior. We also looked at recent Bitcoin price history with log-periodic wave behavior as described by Sornette.
![PREMISE: FAT NODESTO POWER LAWTAILS
Investing in an ETF or BTC Treasury company
or having custody at an exchange is attaching to
a fat node
Fat nodes in a network support power law
behavior:
Airline hubs, Google, Bitcoin exchanges/ETFs
That is, of the form of preferential attachment
Pareto-style, with power law tails of index [2, 3]
typical
Studies of the Bitcoin graph have
found typical:
Attachment/connections index 2 to
2.5
Holdings fall off > 1.8
Holdings not same as connections
3](https://image.slidesharecdn.com/physicsofbitcoin30-250828045137-40d63046/85/Physics-of-Bitcoin-30-Perrenod-Santostasi-pdf-3-320.jpg)
Physics of Bitcoin #30 Perrenod Santostasi.pdf
- 1. PHYSICS OF BITCOIN #30 AUGUST 27, 2025 INSTITUTIONAL ADOPTION Stephen Perrenod @moneyordebt https://stephenperrenod.substack.com/ ROBERT METCALFE (1946- ) CO-INVENTED ETHERNET Wednesdays 11:15 PM EDT Live :YT & X 1
- 2. AGENDA: INSTITUTIONS AND INSIDE METCALFE’S LAW Institutions are network Fat Nodes Growth of Institutional holdings Power law, steep Why little to no holdings by Largest companies? Metcalfe’s Law:Why T3 for Adoption? Revisit Hurst with GPT-5 Bitcoin bubble 2025, Log periodic power law 2
- 3. PREMISE: FAT NODESTO POWER LAWTAILS Investing in an ETF or BTC Treasury company or having custody at an exchange is attaching to a fat node Fat nodes in a network support power law behavior: Airline hubs, Google, Bitcoin exchanges/ETFs That is, of the form of preferential attachment Pareto-style, with power law tails of index [2, 3] typical Studies of the Bitcoin graph have found typical: Attachment/connections index 2 to 2.5 Holdings fall off > 1.8 Holdings not same as connections 3
- 4. TREASURY COMPANIES PARETO CHART BTC Held vs. Rank as a power law Slope ~ -0.9 for largest companies Slope ~ -2.4 for bulk Many quite new, so this is evolving 4
- 5. GROWTH OF INSTITUTIONAL HOLDINGS Includes exchanges, public and private companies including miners, ETFs # BTC Increasing at ~ T4 or 4.5 R2 = 0.94 5 Institutional_btc_2017_2025 DATE (MONTH END) BTC PRICE USD CORPORATE BTC FUND TRUST BTC ETF BTC TOTAL INSTITUTIONAL LOG10 AGE PRICE LOG BTC HELD LOG 2017-12 14,156 140,000 175,839 0 315,839 0.954 4.151 5.499 2018-12 3,743 140,000 204,277 0 344,277 1.000 3.573 5.537 2019-12 7,194 140,000 261,192 0 401,192 1.041 3.857 5.603 2020-12 29,002 210,470 607,039 0 817509 1.079 4.462 5.912 2021-12 46,306 264,391 644,810 54,300 963501 1.114 4.666 5.984 2022-12 16,548 264,391 644,810 34,318 943519 1.146 4.219 5.975 2023-12 42,265 1,204,800 619,000 42,500 1,866,300 1.176 4.626 6.271 2024-12 93,429 1,508,400 0 1,160,000 2,668,400 1.204 4.970 6.426 2025-07 117,833 1,865,600 0 1,475,000 3,340,600 1.220 5.071 6.524 Except 1st Price vs. age Holdings vs. age Except 1st Slope vs age 6.036 4.422 3.980 4.468 Holdings vs. price 0.652 0.696 R2 (price vs age) 0.823 0.676 0.938
- 6. GROWTH OF INSTITUTIONAL HOLDINGS Includes exchanges, public and private companies including miners, ETFs Increasing at T4.5 (or 4.0) R2 = 0.95 6 10 16 13
- 7. GROWTH OF INSTITUTIONAL HOLDINGS BTC Held vs. BTC price Increasing as Price0.7 (or 0.65) R2 = 0.83 7
- 8. GROWTH OF INSTITUTIONAL HOLDINGS BTC Held vs. BTC price Adoption (buying, Quantity) is Increasing as ~ Price0.7 (prior slide) But retail quantity is decreasing; ownership diffusion Whales selling to custodians for many holders ? Market Cap ~ Price, as supply nearly fi xed Inference: Price ~ Institutional Adoption1.4 to the extent institutions are dominating net purchases, price trend And that is consistent with Price ~T5.8 and Institutional holdings H ~T4 8 ✅ Contextual Percentages (2025 YTD net buying ~225k BTC total) • Public Companies: 70% • ETFs: 22% • Governments: 8% • Private Companies: ≈0% net, possibly slightly negative (due to Mt. Gox out fl ows). • Retail: –247,000 BTC (large net sellers). Slope 1.2 R2 = 0.83 Price Holdings
- 9. $TRILLION CAP CO. HOLDINGS ~ ZILCH Institutions adopt iff Price is High They need large capital store Thus, Magni fi cent 7 are late to the party The price is too low for them 9 COMPANY NVDA 0 MSFT 0 APPL 0 GOOGL 0 AMZN 0 META 0 TSLA 12K BTC
- 10. EFFECT ON PRICE IF LARGEST CORPORATIONS BUY Even only 1% allocation relative to market cap? (Of order $20 B) Cash holdings range between $27B and $110B for top 6 companies Annual cash fl ows range from $50B to $120B Suppose they put 10% of their cash into Bitcoin to start: $3B to $11B For the top 6 it would be 360K BTC aggregate, $42B If they did it within one year, it would be $106B market cap increase (~5% now) assuming market multiple 2.5 (typical MVRV) What they are facing is Bitcoin is rising much faster (40% p.a.) than their cash balances (13% p.a.) Necessity being the mother of invention, they don’t see the necessity yet 10
- 11. INSIDE METCALFE’S LAW Price ~ Market cap ~ Value ~ Nm, with m ~ 2, N users Adoption ~ Ν ~ Τλ , observe λ ~ 3 Price ~ Tλ*m ; λ*m ~ 6 , is general thesis Why* is λ ~ 3? Internet history: Power law of index: 4.6 overall, R2 0.97; until 2020 saturation First half > 5, second half 2.8 index 11 Web ₿ 2020 *There is a ‘why’ in physics, but not in economics
- 12. WHY IS LAMBDA (Λ) 3? Adoption: Ν ~ Τλ , observe λ ~ 3 Three mutually reinforcing factors: Lifetime, awareness More on-ramps, easier to buy Capital commitment grows Retail, then institutions (custodians) Actively and passively 12
- 13. WHY IS LAMBDA (Λ) 3? CONJECTURE 13
- 14. WHY IS LAMBDA (Λ) 3? CONJECTURE 14 Institutions 10 Institutions 10 10 Awareness Channels
- 15. WHY IS LAMBDA (Λ) ~3? CONJECTURE N users ~ f (awareness, opportunity) Awareness: know enough about BTC Opportunity: channels for investment (exchanges, regulatory environment, futures, ETFs, stable coin gateways, treasury companies…) Commitment: level of investment Active, stacking Passive, simply because price rises over time faster than stocks, real estate etc. 15 Awareness Opportunity Commitment GPT5 guesstimates Adoption = Users * Commitment
- 16. HURST EXPONENT REVISITED H measures trend persistence, reversion R/S = range/standard deviation ~ NH is a function of window size N and measure H: H = 0.5 random walk H < 0.5 mean-reverting H > 0.5 trend persistence 16 “There’s no evidence” ? 15 K views, 125 likes
- 17. EASY HURST EXPONENT GPT-5: MONTHLY DATA, 4 SENTENCE PROMPT <10 MINUTE EXERCISE 17
- 18. EASY HURST EXPONENT W/GPT-5: MONTHLY DATA, 4 SENTENCE PROMPT 10 MINUTE EXERCISE 18
- 19. EASY HURST EXPONENT GPT-5, CORE AND BUBBLE 19 Bubble Core
- 20. LATEST LOG PERIODIC FITS 8/26 20 • Two years, daily Long-term Daily LPPL fi t: A = 12.009 B = -0.001781 C = -0.000350 m = 0.990 w = 12.29 phi = -1.38 Tc = 885.98 days since 2023-09-07 -> 2026-02-08 R^2 = 0.963 σ = $9070 (width band $18K) Price at Tc-3 days: $163,262 40/20/40 split 163K 99K 60K 36K
- 21. LATEST LOG PERIODIC FITS 21 • One year, daily Tc = 370.0 days since 2024-08-27 -> 2025-09-01 R^2 = 0.945 σ = $5500 (width of band $11K) Price at Tc-3: $120,348 • 4 months (4h data) Tc = 157.1 days since 2025-04-28 -> 2025-10-3 R^2 = 0.828 σ = $2970 (width of band $6K) Price at Tc-3: $126,677 $109K $109K $121K
- 22. ONTHE OTHER SIDE? 22 Short-term 1h LPPL fi t: Tc = 74.153 days since 2025-07-28 -> 2025-10-10 R^2 = 0.7095 σ = $1430 Price at Tc-3: $107,237.88 Price at Tc-1: $106,797.31 • 1 month (one hour data) LPPL TIMESCALE TC R^2 PRICE K$ AT TC - 3 D PRICE UNCERTAINY K$ 2 years 2026-02-08 0.96 163.3 9.1 1 year 2025-09-01 0.95 120.3 5.5 4 months UP: 2025-10-3 0.83 126.7 3.0 1 month DOWN: 2025-10-10 0.71 107.2 1.4
- 23. ALL IS NOT LOST, YET: SEASONALITY 23
- 24. NVIDIA LPPL, ONEYEAR 24 X Best- fi t parameters • A = 8.538 • B = -2.094 • C = 0.1015 • m = 0.100 (at the lower bound) • ω = 9.576 • φ = 0.3886 • Tc = 417.9 (≈ 168 trading days after the last sample day) 2026-03-26 Fit quality: R^2 = 0.861 Dec. 2025 (last business day) $198 End-Jan 2026 (last business day) $232 One week before t_c (5 bdays) 2026-03-19 $422 Tc (model limit): 2026-03-26
- 25. PHYSICS OF BITCOIN #30 AUGUST 27, 2025 Stephen Perrenod @moneyordebt https://stephenperrenod.substack.com/ 25 Bubbles? We don’t need no stinkin’ bubbles. We have the Power Law. Froth, Decay vs. Clarity