The Nikkei, The ACWI, The SPX , the QQQ, et. al. – are all undergoing deterministic self-ordering terminal fractal growth to a blow-off peak valuation on 19-22 September 2025 with an expected crash low on 3-6 October 2025. The central banks of the world will rapidly lower federal interest rates to near zero over the ensuing months with final lower lower high of composite equities in about 125-126 trading days after the 3-6 October 2025 low. A final crash then will be spectacularly fast (like 1987) and devastating.

The fiscal year 2025 2 trillion dollar deficit spending which provided unneeded greater wealth to the wealthiest and bonuses and employment for those gathering illegal aliens made ubiquitous by the bad policies of the preceding administration, will do little to promote job creation for American service workers now paying considerable import taxes to support that deficit.

At the end of the 1982-2026 13//33 year :: x/2.5x 1st and 2nd fractal series, the world will become a much more dangerous place as many citizens become unable to service personal debt.

21 Sept 2025 Post-script update: (19 Sept high equity valuation confirmed)

An hourly blow-off peak occurred on 19 Sept for the QQQ, ACWI, and SPX. The 14 day 3rd fractal ending on 19 Sept of the 2 Sept 7/16/14 day fractal growth series was composed of a 2/5/5/2 day :: x/2.5x/2.5x/1.5x 4 phase fractal series followed by a 17 Sept 3-phase 3/7/8 hour :: x/2.5x/2.5x fractal blow-off growth series. A nonlinear blow-off gap upward can be observed between the closing on 17 Sept and the 930AM 18 Sept opening between the 2nd and 3rd hour of the 1st 3 hour fractal of the 3/7/8 hour fractal series and ending in the 8th hour with a high during the last 5 minutes of trading on 19 Sept.

It is mathematically fractally possible that a self assembly 7 April 2025 52/104-105/104-105 day :: x/2x/2x :: y/2y/2y fractal series will conclude the 2008 35/88/86-88 monthly x/2.5x/2.5x equity valuation peak growth and nonlinear collapse concluding a 1982-2026 13/33 year :: x/2.5x first and second fractal series. Deficit spending in the recent past has been spent on elements that promote economic growth at the base of the population pyramid. This year that deficit spending has been redirected for tax advantages for the super wealthy with little stimulus for employment of the base. That is a qualitative identifiable sharp prick.

The recent monthly US job creation and the 4.3 % unemployment rate are consistent with an incipient serious recession made worse by the sudden disruption of globalization, world trade, and international interdependent manufacturing . The US 80% service sector economy is at the edge of a 1982 13/32 of 33 year 1st and 2nd fractal series with expected nonlinear devaluation of asset prices in the terminal portion of the 33 year 2nd fractal.

The 2020 Covid dead horse macroeconomy was re-animated by repetitive annual quasi-WW2 US % GDP deficit spending and AI, crypto, real estate, software, and social media exuberant malinvestment. The PE ratio’s for palantir stood at 508.84 on 5 September 2025

The final lower high fractal growth series from the 27 Oct 2023 ACWI low appears to be a 120/252/251-252 day :: x/2-2.5x/2-2.5x growth series. The 252 day 3rd fractal appears to be composed two 126 day fractal series, the 1st ending 6 October 2025.

Fractal groupings are determined by the underlying trendline from the first time unit to the last time unit of the grouping whereby all interim valuations are above that trendline.

From the 7 April 2025 low there are three identifiable fractal groupings consistent with this definition.

1: a 3-phase 10/25/20 day :: x/2.5x/2x growth fractal grouping

2: a 3-phase 6/12/13 day :: x/2x/2-2.5x growth fractal grouping and

3: a potential 4-phase 7/13 of 14/14/9- 10 day :: x/2x/2x/1.5x or 1.5xi growth and crash decay fractal grouping ending 29 or 30 September 2025.

A peak global equity composite valuation day on 5 Sept 2025 represents day105 from the 7 April low composed of two 53 day sequences 10/25/20 days and {6/12/13 and 7/14/6 of 14 days}

A Primer on Quantitative Time-based Self-Assembly Lammert Fractal Growth and Decay of Valuations of The Asset-Debt Macroeconomic System’s Composite Equities

Qualitatively …on the longest time-unit cycles (years) (e.g. 1807 36/90/90/54-57 years :: x/2.5x/2.5x/1.5-1.6x and 1982 13/32 of 33/32-33/20 years x/2.5x/2.5x/1.5-1.6x credit expands via governmental, corporate, and citizen debt; assets are produced and over-produced , overvalued and over-consumed; consumers reach maximum debt loads; the population of possible traders/invested are fully invested and composite equity asset valuations reach a singular fractal time-unit (minute, hour, day, week, month) peak valuation and thereafter undergo decay; recessions occur with weakening demand, interest rates fall; excess debt undergoes default and restructuring; individual and corporate bankruptcies occur; and composite equity (and commodity) asset valuations eventually reach a singular fractal time-unit nadir. The cycle thereafter repeats itself.

On smaller time-unit fractal cycles (quarters, months, weeks, days, hours, 15-minute/ 5 and 1-minute) : trader/investor population saturation of asset buying occurs ending in a transient peak valuation .. followed by trader/investor population saturation end selling resulting in a transient nadir valuation. These peaks and nadirs occur in one of the two quantitative fractal patterns as above.

Empirically composite equity asset valuation growth and decay cycles occur in 2 modes(laws) of mathematical self-organizing, self-assembly time-based fractal series:

a 4-phase fractal series: x/2-2.5x/2-2.5x/1.5-1.6x and
a 3-phase fractal series: x/2-2.5x/1.5-2.5x

In the 4-phase fractal series sequential elements are termed: the 1st, 2nd, 3rd, and 4th fractals and in the 3-phase fractal series: the 1st, 2nd, and 3rd fractals.

The 2nd fractal is characterized by terminal gapped nonlinear lower lows between the 2nd fractal’s terminal 2x and 2.5x time period. (These gapped nonlinear lower lows can be observed in weekly valuation units for the DJIA between 1929 and 1932, the terminal portion of the US 90 year 2nd fractal; within the last three day before the terminal 5 August 2024 139 day 2nd fractal low occurring in an interpolated ACWI/SPX 27 October 2023 55/139/135-136 day (SPX-ACWI respectively) :: x/2.5x/2.5x valuation maximum growth series ending 18/19 February 2025: and can be expected within the last months on a daily and weekly basis of the current 32 of 33 year 2nd fractal of the interpolated 1982 13/32 of 33 year 1st and 2nd fractal series. (The 27 October 2023 dominant fractal series appears to have a 119 first fractal base, whereas the 55/139/136 day 3 phase growth series was a secondary interpolated series).

With the exception of the 3rd fractal in the 4-phase series whose fractal grouping is determined by its terminal high or final lower high peak valuation, fractals (fractal groupings) are determined by the nadirs of the first and last time unit in the grouping with all intervening valuations above the connecting nadir trend-line.