The Case for the Floor

Seven independent attacks on Bitcoin's power law minimum. Empirical, comparative, mechanistic, statistical, thermodynamic, game-theoretic, and survivorship. The floor survives all seven.

Paper 8 · Scale Invariant Research · March 2026 · v3.0 · 11 pages

Every tool in the Observatory — the retirement calculator, the loan monitor, the floor bonds framework, the Bitcoin Floor Rate — rests on one assumption: a structural lower boundary exists. This paper attempts to falsify that assumption.

We attack the floor from seven directions. Not to confirm it, but to find where it breaks.

“The floor is not a line. It is a process. The ceiling falls. The floor rises. The trend drifts down. Everything converges.”

Attacks
7 independent
Floor survived
All 7
Cross-asset comparison
First published
OOS breach reduction
37%

Attack 1: The Empirical Record

An important correction. The 0.42× floor has been breached 77 times. All between August 2015 and January 2023. The worst: August 24, 2015 — price $210 vs floor $241 (−12.5%). This paper publishes the correction alongside the thesis.

But the per-cycle analysis reveals the real story. The floor is a regime-dependent boundary that tightens:

CycleP1 (log)Floor as % of trendDeepest price
1 (2009–12)−0.66122%~$2
2 (2012–16)−0.42038%~$152
3 (2016–20)−0.35544%~$3,122
4 (2020–24)−0.37442%~$15,500
5* (2024–)−0.27853%~$64,000

*Cycle 5 incomplete (accumulation phase only).

22% → 38% → 44% → 42% → 53%. The distribution compresses from below. Each cycle's worst case is structurally better than the last.


Attack 2: The Cross-Asset Comparison

No published systematic cross-asset power law comparison exists. We fill this gap by applying identical methodology to seven assets.

Asset−2σ BreachesFloor Growth
Bitcoin0.9210 (0.0%)39.8%/yr
Gold0.7250 (0.0%)1.8%/yr
S&P 5000.69415 (0.2%)2.1%/yr
Russell 20000.656100 (1.5%)2.0%/yr
Oil0.630236 (4.7%)−3.2%/yr

Bitcoin's floor grows at 39.8%/year. Gold's at 1.8%. A 22× structural growth advantage measured at the worst-case boundary. The tightest fit, the fewest breaches, the fastest floor.


Attack 4: The Circularity Problem

The strongest objection: “The floor is −2 sigma. −2 sigma is defined as the boundary that contains ~97.7% of the data. Therefore ‘0 breaches’ just means the data contains its own tail.”

This is valid. We break the circularity three ways:

Resolution 1: OOS test
37% fewer breaches
Resolution 2: Cross-asset
BTC 0% vs Oil 4.7%
Resolution 3: Per-cycle
Predicted 50%, actual 53%

Train on 2014–2020 (2,298 days). Freeze parameters. Test on 2021–2026 (1,900 days). Result: 27 breaches (1.4%) vs 43 expected (2.28%). Not zero — but measurably better than chance. Training and test data from different halving cycles. Not circular.


The Three-Way Convergence

The per-cycle data reveals something unexpected: three independent quantities are converging toward the same point.

Ceiling (P99)
Falls
Floor (P1)
Rises
OLS trend
Drifts down
Attractor
~41st percentile

The OLS trend overestimates fair value (sitting at ~P55). The attractor is the decay-adjusted median at approximately the 41st percentile. The ceiling collapses, the floor rises, and the trend drifts down toward them. Everything converges.

This contradicts PlanC's March 2026 finding that the 1st quantile shows zero decay. Our per-cycle halving segmentation reveals the drift that single-regression analysis masks.


What Could Break It

The paper's strongest credibility signal: publishing the failure taxonomy alongside the bullish thesis.

Level 0: Floor holdsHigh (>95%)
Level 1: Intraday wickModerate
Level 2: Days–weeks breakLow
Level 3: Months breakVery low
Level 4: Regime breakExtremely low
Level 5: ZeroNegligible

Level 2 nearly happened: FTX marginally breached the 0.42× floor (−1.4%). Level 5 includes quantum computing risk — BIP-360 merged Feb 2026; 50%+ of Chaincode Labs experts assign meaningful probability to cryptographic break by 2030–2035.


Operating Framework

ApplicationSize forPlan for
RetirementLevel 2Level 0 timeline, Level 3 stress test
LendingLevel 0 (1.6× floor)Level 1 wick buffer (0.9× floor)
InstitutionalLevel 4 survivableSeven attacks as thesis documentation

The rising floor means storm years shorten with each cycle. Size the stack for Level 2. Plan timeline for Level 0. Stress-test against Level 3.


Read the Paper

11 pages. 7 attacks. 5 figures. Cross-asset comparison of 7 assets. Out-of-sample validation. Failure taxonomy with 6 levels. Full methodology: per-cycle P1 analysis, expanding-window OOS, cross-asset ETF proxies, literature review of 16 sources.

1
Percentile-Anchored Volatility Decay Analysis
Bitcoin's volatility corridor shrinks ~20% per halving cycle.
2
The Bitcoin Floor Rate
Valuing Bitcoin from its structural minimum return.
3
Lump Sum vs DCA
The crossover at 1.25x trend.
4
Bitcoin Floor Bonds
Lending against structural growth, not spot price.
6
Reproducing the Power Law
Independent parameter estimation. Beta = 5.694. Cointegration confirmed.
7
The Strategy Pyramid
From DCA to Kelly. Sophistication pays at scale.
8
The Case for the Floor
Seven independent attacks on Bitcoin's power law minimum.

The floor is not a line. It is a process. The ceiling falls. The floor rises. The trend drifts down. Everything converges.