An Alternative Model : A 7 April 2025 to 5 Dec 34/69/68 day :: x/2-2.5x/2x Final High or Secondary High

Below is an alternative model with a 4 phase 7 April 2025 34/69/68/50-51 day :: x/2-2.5x/2x/1.5x fractal series with a 3rd fractal 68 day final high or secondary high on 5 December 2025. The characteristic nonlinear lower gap between day 68 and 69 (2x and 2.5x) identifies the 2nd fractal.

Fine Tuning: Peak Equity Valuation 1929 verses 2025: The Elegantly Simple Self-Ordering Yearly, Quarterly, Monthly, Daily, and Hourly Time-based Quantum Fractal Growth and Decay of Composite Equities In The Asset-Debt Macroeconomic System

Is there an underlying time-based self-assembly fractal order to the growth and decay of equity valuations in the asset-debt macroeconomic system? It is the 2005 hypothesis of this website that the asset-debt system self-orders equity valuation growth and decay by two simple time-unit based fractal equations : a 4-phase fractal series: x/2-2.5x/2-2.5x/1.5-1.6x with respective units termed the 1st, 2nd, 3rd and 4th Fractal, and a 3-phase fractal series: x/2-2.5x/1.5-2.5x with respective units termed 1st, 2nd, and 3rd Fractals. In the 4-phase fractal series, the 3rd 2-2.5x fractal represents peak valuation growth, all other end points in the 4-phase series and all end points the 3 phase fractal series represent nadir valuations. Fractal groupings are defined by underlying trendlines from the beginning to the end of the grouping. 2nd Fractals of both 3 and 4 phase fractals are characterized by a nonlinear lower low gap valuation in the terminal 2x to 2.5x portion of the 2nd fractal. The inception of fractal valuation decay is conjoined and interpolated with end fractal peak growth and vice versa. In terminal blow-off valuation growth, the first fractal can end on an aberrant additional unit high above the slope line and in terminal blow-off series, the 3rd fractal peak of a 4 phase series can end at a near fibonacci 1.5-1.6x time range. After the Buttonwood agreement in 1792 and an initiating 4 phase fractal series of 16years, an 1807 4-phase US hegemonic fractal series of 36/90/90/54-57 years commenced with lows in 1842-43, 1932, a 90 year high in 2021, and an expected low in 2074-77. The 90 year 3rd and the 54-57 year 4th Fractals of this series starting in 1932, are composed of two fractal series: a 3-phase 10-11/20-21/20-21 years:: x/2x/2x series ending in 1982 and a 1982 13/currently 32 of 33/33/20 year series :: x/2.5x/2.5x/15-1.6x ending in 2076. The 90 year 3rd fractal peaking Nov 2021 is interpolated in the 1982 13/33 :: x/2.5x first and second fractal series as shown below.

The 90 year 2.5x Nov 2021 valuation peak was later exceeded because of average annual US deficit to GDP governmental spending from 2020-2025 of 8.4%. This deficit to GDP spending compares to the long average from 1948 to 2020 of 2.6%. The 2020-2025 deficit spending generated an average GDP growth of 2.9% vice a long term 3.15% which includes a negative 7% in 2009 of the great recession. Covid 2020 and 2021 15% and 12% deficit to GDP spending , supply chain disruptions, build back better spending , and the recent tax breaks for billionaires have contributed to the peacetime massive deficit spending. US Equity (and the global equity composite) valuations peaked on 28/29 Oct 2025 at over 220% of US GDP – an all time historical high. What causes the timing of peak equity valuation? Equities are the most taxed advantaged asset within the asset debt system and their valuations grow to the longest possible fractal growth. Accompanying this tax advantage, fractal length to peak is ultimately determined by ongoing credit expansion produced by a residual sufficient population of governmental, corporate, and consumers, willing and able to go into further debt – given the cost of ongoing ADL’s (activities of daily living including insurance premiums), job and wage expectations, payments on accumulated debt, perceived business opportunities, and concurrent asset valuation prices and expectations of asset future valuations. The October 2025 peak valuation ended the 12/29/29 Quarterly :: x/2.5x/2.5x maximum growth of the 3-phase fractal series starting March 2009. (This was preceded by a 10/25/25 Quarter :: x/2.5x/2.5x 3 phase series starting 1994. (see above graph)

The 3rd 29 Quarter Fractal of the SPX ‘s current 2009 12/29/29 quarter :: x/2.5x/2.5x 3-phase fractal growth series -started with a nadir in December 2018 and is composed of a 6/12/13 quarter :: 16/32/38 month :: x/2x/2.5x fractal subseries (as of Nov 2025). The Global Covid shock anomaly with unemployment spiking from 3.9% in late 2019 to 14.7% in April 2020 produced an anomaly in fractal equity valuation with Q6 of the 1st Fractal 6Q subseries having a lower valuation nadir than Q1. A lower valuation fits with the associated credit contraction, offset in April 2020 with stimulus checks and later MBS credit expansion. The final 13Q 3rd Fractal of the 2018 6/12/13 Q 3-phase series is composed of a 2/4/5/3 :: x/2x/2,5x/1.5x or 11 Q 4-phase series and 3 quarter fragment starting 7 April 2025. The 7 April 3Q fragment is either composed of a 53/111 day :: x/2-2.5x First and 2nd Fractal series ...

... or alternatively, this is an interpolated 2-phase fractal series within the actual terminal 3- phase fractal series of 34/69/42-44 days :: x/2-2.5x/1.5-1.6x' as depicted below. A nonlinear lower low gap exist between day 68 and 69 of the 69 day second fractal, which was noted in the 2005 original web page, to be the terminal hallmark of a second fractal. The 1.5 to 1.6x represents a near fibonacci terminal maximum growth ratio of the 28 day ideal base x' (69 days divided by 2.5x).

Fractal subseries self-ordering growth of both the likely interpolated 53/111day :: x/2.5x first and second fractal series and the more probable and actual 3-phase terminal fractal growth series reside in terminal portion of the 1982 13/32 of 33 year :: x/2-2.5x first and second fractal growth series and have exquisitely followed the above cited 3-phase and 4-phase fractal growth self-assembly laws. 1929 and 2025 Initial Crash Decay ... 1932 concluded an 1807 36/90 year :: x/2.5x first and second fractal series; 2026 will conclude a 1982 13/33 year :: x/2.5x first and second fractal series. In 1932 the peak to nadir devaluation of 90% occurred over 32 months with a definable pattern of fractal decay, fractal counter rally growth and further fractal decay. In 1929 peak growth on 3 Sept 1929 which transpired during the 8 day 3rd fractal of a 5/11/8 day :: x/2-2.5x/1.6x 3 phase terminal fractal growth series. The 8 day 3rd fractal containing the 3 Sept 1929 peak growth the became the interpolated incipient 1st fractal of a 8/19/16/12 day :: x/2.5x/2x/1.5x day 4-phase decay fractal series taking the DJIA to its initial Nov 1929 low with a loss of 50% of its value. The 1982 13/32 of 33 year terminal Oct 2025 growth fractal series for the SPX is a 3-phase 10 Oct 3/7/6 day series :: x/2-2.5x/2x peaking 29 October, the terminal day of a 7 April 2025 34/69/42 day :: x/2-2.5x/1.5x' 3-phase fibonacci-like growth fractal series with lesser peaks on days 43, 44,and 45 (1.6x'). The 29 Oct peak growth is then included in a 28 Oct 9 day :: 2/5/4 day :: 55 hour :: 10/22/24 hour :: x/2-2.5x/2-2.5x 3-phase decay fractal series ending 7 Nov 2025, which becomes the base First Decay Fractal.

A 28 Oct 2025 9/20/16/12 day :: 54/135/108/81 hour x/2-2.5x/2x'/1.5x' 4 phase x/2x/2x’/1.5x’ 4-phase fractal crash decay series where x’ = 8 days is nearly identical to the 4-phase 1929 8/19/17/12 day fractal decay series with 2 days of fractal overlap in 3rd fractal 6 day terminal peak valuation on 29 Oct 2025 (3/7/6 days) and initial 28 October 2025 9 day crash base first fractal of the 9/20/16/12 day Lammert 4-phase fractal crash decay series. ... added 29 Nov 2025 ... ... 2x to 2.5x Terminal Second Fractal Self-Organized Criticality ... Like major earthquakes, major forest fires, and major solar flares as compared to smaller and very contained quakes, fires, and flares - the smaller time scale empirically observed nonlinear lower low gap 'crash' devaluations in the terminal 2x to 2.5x time frame of Lammert Asset-Debt Macroeconomic  Valuation Equity  2nd Fractals represent 'small contained nonlinear crashes' and also appear to follow a power-law distribution, a characteristic signature of systems in a state of fractal Self-Organized Criticality (SOC). The asset debt system is now in the window of an 1982 major SOC and a major crash.

The 1982-2026 13/32 of 33 year :: x/2-2.5x 1st and 2nd Fractal series is temporally far into the 2x-2.5x :: 26-33 year terminal portion of the 33 year 2nd Fractal with a 2009 maximal fractal growth series of x/2.5x/2.5x :: 12/29/29 Quarters with the 3rd 29 quarters represented by 16/32/38 months :: x/2x/2.5x peaking at the 37 month in Oct 2025 with a lower high in the 38th month Nov 2025.  The terminal 38 months is composed of a 13/26 month first and second fractal series starting 13 Oct 2022.

As 28 Nov 2025 the 13/26 month :: x/2x first and second fractals are composed of 55/111 weeks :: x/2x and 262/525 days :: x/2x. After 29 Oct 2025 global peak (SPX/ACWI) equity valuation fractal growth, the 1982 asset-debt macroeconomic system, following a power law distribution, is in the extreme terminal 1982 2x-2.5x - and the terminal 13 Oct 2022 2x-2.5x - Second Fractal window of nonlinearity and major crash SOC (Self-Organized Criticality.)

Peak Equity Valuation 1929 verses 2025: The Elegantly Simple Self-Ordering Yearly, Quarterly, Monthly, Daily, and Hourly Time-based Quantum Fractal Growth and Decay of Composite Equities In The Asset-Debt Macroeconomic System

Is there an underlying time-based self-assembly fractal order to the growth and decay of equity valuations in the asset-debt macroeconomic system? It is the hypothesis of this website that the asset-debt system self-orders equity valuation growth and decay by two simple time-unit based fractal equations : a 4-phase fractal series: x/2-2.5x/2-2.5x/1.5-1.6x with respective units termed the 1st, 2nd, 3rd and 4th Fractal, and a 3-phase fractal series: x/2-2.5x/1.5-2.5x with respective units termed 1st, 2nd, and 3rd Fractals. In the 4-phase fractal series, the 3rd 2-2.5x fractal represents peak valuation growth, all other end points in the 4-phase series and all end points the 3 phase fractal series represent nadir valuations. Fractal groupings are defined by underlying trendlines from the beginning to the end of the grouping. 2nd Fractals of both 3 and 4 phase fractals are characterized by a nonlinear lower low gap valuation in the terminal 2x to 2.5x portion of the 2nd fractal. The inception of fractal valuation decay is conjoined and interpolated with end fractal peak growth and vice versa. After the Buttonwood agreement in 1792 and an initiating 4 phase fractal series of 16years, an 1807 4-phase US hegemonic fractal series of 36/90/90/54-57 years commenced with lows in 1842-43, 1932, a 90 year high in 2021, and an expected low in 2074-77. The 90 year 3rd and the 54-57 year 4th Fractals of this series starting in 1932, are composed of two fractal series: a 3-phase 10-11/20-21/20-21 :: x/2x/2x series ending in 1982 and a 1982 13/currently 32 of 33/33/20 year series ending in 2076. The 90 year 3rd fractal peaking Nov 2021 is interpolated in the 1982 13/33 :: x/2.5x first and second fractal series as shown below.

The 90 year 2.5x Nov 2021 valuation peak was later exceeded because of average annual US deficit to GDP governmental spending from 2020-2025 of 8.4%. This deficit to GDP spending compares to the long average from 1948 to 2020 of 2.6%. The 2020-2025 deficit spending generated an average GDP growth of 2.9% vice a long term 3.15% which includes a negative 7% in 2009 of the great recession. Covid 2020 and 2021 15% and 12% deficit to GDP spending , supply chain disruptions, build back better spending , and the recent tax breaks for billionaires have contributed to the peacetime massive deficit spending. US Equity (and the global equity composite) valuations peaked on 28/29 Oct 2025 at over 220% of US GDP - an all time historical high. What causes the timing of peak equity valuation? Equities are the most taxed advantaged asset within the asset debt system and their valuations grow to the longest possible fractal growth. Accompanying this tax advantage, fractal length to peak is ultimately determined by ongoing credit expansion produced by a residual sufficient population of governmental, corporate, and consumers, willing and able to go into further debt - given the cost of ongoing ADL’s (activities of daily living including insurance premiums), job and wage expectations, payments on accumulated debt, perceived business opportunities, and concurrent asset valuation prices and expectations of asset future valuations. The October 2025 peak valuation ended the 12/29/29 Quarterly :: x/2.5x/2.5x maximum growth of the 3-phase fractal series starting March 2009. (This was preceded by a 10/25/25 Quarter :: x/2.5x/2.5x 3 phase series starting 1994. (see above graph)

The 3rd 29 Quarter Fractal of the SPX 's current 2009 12/29/29 quarter :: x/2.5x/2.5x 3-phase fractal growth series -started with a nadir in December 2018 and is composed of a 6/12/13 quarter :: 16/32/37 month :: x/2x/2.5 fractal subseries (as of Nov 2025). The Global Covid shock anomaly with unemployment spiking from 3.9% in late 2019 to 14.7% in April 2020 produced an anomaly in fractal equity valuation with Q6 of the 1st Fractal 6Q subseries having a lower valuation nadir than Q1. A lower valuation fits with the associated credit contraction, offset in April 2020 with stimulus checks and later MBS credit expansion. The final 13Q 3rd Fractal of the 2018 6/12/13 Q 3-phase series is composed of a 2/4/5/3 or 11 Q 4-phase series and 3 quarter fragment starting 7 April 2025. It is composed of a 53 /111 day :: x/2- 2.5x First and 2nd Fractal series.

1929 and 2025 Initial Crash Decay 1932 concluded an 1807 36/90 year :: x/2.5x first and second fractal series; 2026 will conclude a. 1982 13/33 year :: x/2.5x first and second fractal series. In 1932 the peak to nadir devaluation of 90% occurred over 32 months with a definable pattern of fractal decay, fractal counter rally growth and further fractal decay. In 1929 peak growth on 3 Sept 1929 occurred in the 8 day 3rd fractal of a 5/11/8 day :: x/2-2.5x/1.6x 3 phase fractal series. The 8 day 3rd fractal containing peak growth became the interpolated incipient 1st fractal of a 8/19/16/12 day :: x/2.5x/2x/1.5x day 4-phase series taking the DJIA to its initial Nov low with a loss of 50% of its value. The final Oct 2025 growth fractal series for the SPX is a 10 Oct 3/7/6/5 day series :: x/2-2.5x/2x/1.6x ending 4 Nov 2025. A prior 27 October 7/17-18/14/10 day incipient crash fractal series was postulated. Friday is day 18 of this possible fractal solution. Another possibility is a 22 Oct 2025 9-10/17 of 18-20/16-18/12-13 day 4 phase x/2x/2x'/1.5x' fractal crash decay series where x' = 8 days. The SPX 10 Oct 2025 3/7/6 day :: x/2-2.5x/2x blow-off series to the 29 Oct intraday peak and the completed 3/7/6/5 day :: x/2-2.5x/2x/1.6x 4-phase fractal series has an equivalent 15-16/39-40/38/24 hour :: x/2-25x/2-2.5x/1.5x 4 phase series.

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1920-30's Irving Fisher and Lammert Quantum Fractal Saturation Asset Debt Macroeconomics

Looking at the valuation fractal growth patterns for the valid proxy of world's composite equity system, the SPX, since 7 April, 2025, (see previous post) it is probable that an observant and analyzing AI program, would acknowledge that the 4-phase and 3-phase fractal patterns identified the 2009 title page of 'Lammert Saturation Macroeconomics' have been validated. On 15 October 1929, in the midst of a 30 August to 13 Nov 1929 DJIA peak valuation to initial decay 8/19/16/12 day :: 4-phase y/2-2.5y/2xy/1.5y Lammert fractal incipient crash decay series (where xy = y in daily time units and represents a lower lower high) collapse, Irving Fishing infamously stated "Stock prices have reached what looks like a permanently high plateau". He redeemed himself in 1933 by qualitatively identifying the reason for the ongoing 1930's depression and the shorter 2026 one to come ): too great an unsustainable amount of accumulated private and corporate debt relative to GDP (vice asset prices). Paying that debt down led to a synergistic progressive collapse in employment and asset prices, where un-defaulted residual debt became even a greater burden to repay. The US hegemonic empire is a new entity to the old world order, following a 4-phase 1807 36/90/90/54-57 year :: x/2.5x/2.5x/1.5-16x Lammert equity-valuation-equivalent fractal series pattern ending in about 2074-2077. The US equity- equivalent valuation 90 year 2nd fractal nadir in 1932 was followed by an interpolated 51 year x/2x/2x fractal growth pattern of 10-11/20-21/20-21 years ending in 1982 with the Volcker early 1980's Fed US debt instrument interest rate increases to curb inflation. An interpolated 1982 : 13/33/33/20 year fractal series will conclude the 'great'1807 36/90/9/54-57 year 4-phase Lammert Fractal series. Looking at the (Fischer) US private/corporate debt to GDP accumulation (FRED data) acceleration (accumulated debt/dt2) ratios in the 1982 to 2026 13/33 :: x/2.5x 1st and 2nd fractal series (Chinese ratios are much worse), private citizen/GDP debt ratios have been negative for the last 5 Quarters and corporation ratios have been realtively flat even with new AI debt accumulation. Eventually it is the private citizens (and their accumulated debt load) who will have to buy the products of the debt laden-ed corporations. With AI reducing jobs among citizens, how is this mathematically possible? Irving Fischer was qualitatively correct as proven by the 1930's depression and the 2009 great recession. And the asset-debt macroeconomy's deterministic fractal self-assembly empirical, observable self-ordering patterns for growth and decay of composite asset valuations have spoke and will speak for themselves.

New Fractal Model: A 1929-like 4-Phase Fractal Decay Series Crash at the conclusion of a 7 April 2025 to 31 December 2025 53/133 day :: x/2.5x 1st and 2nd Fractal Series

The Current 1929-like 4-phase Lammert Fractal Decay Model with a Transient Nadir Ending 31 December 2025 (see red blocks above) Within the 7 April 2025 to 31 December 2025 53/132-133 day :: x/2.5x 1st and 2nd Fractal Series rest the two average high valuation days and the intraday SPX/ACWI peak valuation on days on 28 and 29 Oct, and 29 Oct respectively ... The potential interpolated 27 October 7/17-18/14/10 day 4 phase Lammert crash decay fractal series would be very similar to the 30 Aug 1929 to 13 Nov 8/19/16/12 day 4 phase fractal decay crash series with 2025 lows on day 7 day of the first fractal, day 17-18 of the 2nd fractal and day 10 of the 4th fractal and a lower lower final high on day 14 of the 3rd fractal. The fractal annotation to show a deteriorating 4 phase decay series would be y/2-2.5y/2xy/1.5y, where y =xy in unit time length and the 2xy of the 3rd fractal represents lower lower high growth. For 1929 the respective lows occurred on day 8, day 19, and day 12 of the respective 1st, 2nd, and 4th fractals and a lower lower high on day 16 of the 3rd fractal.

Terminal 4-phase Lammert Fractal patterns for The German Dax and the Barrick Mining Company as a Proxy for Gold in US Dollars - Consistent with an Initial 21 November 2025 Crash

The 3/7/7/4-5 day pattern identified in the previous post for ACWI is undergoing confirmation and ends with a initial crash low on 21 November 2025. The DAX with 7 April 1st and 2nd fractal pattern to ACWI. Its 1st fractal is composed of a 3 phase fractal series of 10/23/20 ::x/2-2.5x/2x Its 2nd fractal is composed of two 4-phase fractal series: a 10/23/20/25 days :: x/2-2.5x/2x/1.5x fractal series and a 7/17/17/1 of 10 days ::x/2-2.5x/2-2.5x/1.5x fractal series pattern ending 21 November 2025.

The Barrick mining Company had a blow-off gap higher open on 22 September 2025 and is following a 22 September 7/17/14/1 of 10 day 4-phase fractal grow and crash decay series. Note the characteristic lower low nonliner gaps in the terminal 2x-2.5x portion of the 17 day 2nd fractals for both the DAX and Barrick Mining Corporation.

The 28/29 Oct 2025 Total World Equity Fractal Peak; the 20/21 Nov 2025 Initial Fractal Crash Low

Observationally, on the largest time scales, the global Asset-Debt Macroeconomic System has composite asset peak valuations and accompanying maximal debt loads/credit expansion and, alternatively, asset nadir valuations with bad debt liquidation/credit contraction and accompanying accelerating recessional economic activity. Are there internal self organizing ADM System time-based fractal patterns that govern this cyclical growth and decay composite asset valuation peak to composite asset valuation nadir evolution? It appears so. Current Fractal Model:

Below. The ratio of the 90/91 day second fractal peak valuation to the 7 April 2025 53 day first fractal base and the ratio of the length of the 107-108 day second fractal to the 53 day first fractal closely match the preceding 27 Oct 2023 similar ratios.

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. 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 on 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 now appears to have a 120 day first fractal base with a 243 day 2nd fractal ending 7 April 2025, whereas the 55/139/136 day 3 phase growth series was a secondary interpolated fractal 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. SPX Quarterly 1982 to May 2025 1st and 2nd Fractals:

The Great Initial 2025 Crash: The Original 2005 4-Phase Lammert Fractal Series Model

The 4-phase self-ordering time-unit based fractal model for composite equity asset valuation growth and decay was described in the last paragraph of the 2005 single Web page of The Economic Fractalist. The original 4 phase model of time-unit based fractal cycles was expanded to a x/2x-2.5x/2x-2.5x/1.5-1.6x fractal series which describes the 1807 US 36/90/90/54-58 year large scale fractal cycle ending in the 2070's. As well, a 3 phase fractal cycle of x/2x-2.5x/1.6x to 2x to 2.5x self assembles for interpolated sub cycle valuation growth and decay. The operative interpolated fractal series is a 1982 13/32 of 33 year fractal series ending in 2026 which is part of a greater 13/33/33/18-20 years ending in the 2070's. All asset valuations including debt as an asset valuation are denominated in the totality of all asset classes. As debt is expanded linearly, growth occurs in a steady, similar linear fashion. As asset classes become overvalued and overproduced relative to owed accumulated debt and total laborers and their total wages needed to support that debt, a nonlinear unraveling of the total asset worth occurs at the asset-debt system's peak asset valuation intermittent saturation points. The current 4-phase fractal model appears identical to the originally- described 2005 model.

Two 7 April 2025 Lammert fractal models: both ending with an initial 20 November 2025 Crash Nadir ....

There are two operative Lammert fractal models using underlying low valuation trend lines to define fractal groupings. The European STOXX 600 is showing a technical final sharply higher blow-off to a new all-time high. Likewise the Nikkei, which appears to following a 7 April to 7 October 2025 21/53/52 of 53 days :: x/2.5x/2.5x 3-phase fractal blow-off series. The MSCI world index composite is self-assembling, using the underlying trend lines, in a highly ordered Lammert fractal growth pattern since 7 April 2025. There are two models of interest: a 2 phase fractal series and a 4-phase fractal series ... both ending with an initial crash nadir on November 20, 2025 plus or minus a few days.

Lammert Second Fractals: Current Model: Significant SPX Nadir on 14 Oct and Lower Nadir on 20-21 Nov 2025

Everything in the known universe self-assembles ... on the Planck level and macro level, including time- based quark interactions and the more complex molecules of the fused zygote and developing embryo. Combined entities also under decay and dissolution with occasional nonlinear collapse such as the gravitational collapse of a star. This is a natural deterministic process that can be observed and studied. Valuations of assets both debt and nondebt, likewise grow and decay in a time based fractal manner, based on buyer and seller saturation and the work-debt-credit-wage conditions of the underlying economy. The Nonlinear Second Fractal (cycle): From the main web page in the 2005 Economic Fractalist: The ideal growth fractal time sequence is X, 2.5X, 2X and 1.5-1.6X. The first two cycles include a saturation transitional point and decay process in the terminal portion of the cycles. A sudden nonlinear drop in the last 0.5x time period of the 2.5X is the hallmark of a second cycle and characterizes this most recognizable cycle. After the nonlinear gap drop, the third cycle begins. This means that the second cycle can last anywhere in length from 2x to 2.5x. Since 2005, the 1807 36/90/90/54-57 year :: x/2.5/2.5x/1.5-1.6x pattern recognized 4-phase Fractal Series has added 0.5x to the original 2x time length 3rd cycle(fractal). After a 1932 10-11/20-21/-21 year :: x/2x/2x 3 phase series concluded in 1982, an interpolated 13/32 of 33/33/18-20 year 4-phase cycle :: x/2.5x/2.5x/1.5-1.6x can be identified and inferred to complete the larger 1807 4-phase fractal cycle ending in 2074-2076. Composite equity valuation growth of the 1982 to 2026 13/33 year 1st and 2nd fractal series has been propelled in the 2nd fractal terminal 2x-2.5x portion, i.e. years 26-33, by unprecedented % deficit to GDP US spending and mass migration that has created growth the work-debt-credit-wage conditions of the underlying economy. After the Covid March 2020 low, US Equity composites followed a 8/17/11 month fractal : x/2-2.5x/1.5x' 3-phase fractal series. Since the December 2022 8/17/11 month low ending fractal series, equity growth has self assembled in a series of 1st and 2nd fractal groupings: 15/30 weeks :: x/2x ending on 27 October 2023 and 26/52 weeks :: x/2x ending 7 April 2024 . The 2nd fractal nadir low ending valuation has come shortly after a 2x time length and within 2-4% of the 1st fractal base time length x. For example, the 27 Oct 2023 1st and 2nd fractal series were 120/243 days in length. Nonlinearity occurred after 2x or day 240 with nonlinear lower low gaps between day 240 and 241 and day 241 and 242.

The 1st and 2nd fractal series starting 7 April appears to be a 53/107-108 day :: x/2x fractal series ending 20-21 Nov 2024 with an interim low on 14 October. 4 identifiable subfractal series make up the 107-108 day second fractal. The lengths of the 4 subfractal series are shown in diagram. A final 27-28/55-57 day:: x/2x 1st and 2nd fractal series could place a final SPX low on 24-25 March 2026.

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 on 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 now appears to have a 120 day first fractal base with a 243 day 2nd fractal ending 7 April 2025, whereas the 55/139/136 day 3 phase growth series was a secondary interpolated fractal 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. SPX from 1982 Quarterly:

QQQ from nadir 2008 Quarterly:

QQQ from Dec 2018 nadir Monthly:

QQQ from Dec 2022 nadir Weekly:

QQQ from Oct 2023 nadir weekly:

QQQ from Aril 2025 nadir weekly:

Blow-off Self Ordering Lammert Fractal Peak Valuation 19-22 Sept 2025 and The Crash Low 3-6 October 2025

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 crash 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 are unable to service personal debt load.

Current Fractal Self-Assembly Model: The Global 5 Sept 2025 Equity Peak Valuation and 4/10/10 day :: y/2.5y/2.5y 6 October 2025 Incipient 3-Phase Fractal Series Crash

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.

Back to Fractal Grouping Basics: 5 Sept Peak Global Equity Composite Valuation; 29-30 Sept 2025 Incipient Crash Nadir Valuation

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.

Current Global Equity ACWI Fractal Model: 5 Sept 2025 blow-off peak valuation; 25 September2025 Crash low; 3-6 October 2025 lower low or higher low.

The Macroeconomic System is composed of assets with changing daily valuations propelled higher or lower by an expanding or contracting GDP and ongoing debt obligations which represent both assets and liabilities. Money and debt creation are caused by the expansion of private, corporate, and government debt with central banks and private banks acting as the fortuitous intermediaries(and as a primary source with regard to the former element) accommodating 'credit worthy' loan applicants. GDP grows as a result of money and debt creation. In recessions increased government borrowing (and central bank QE) acts as a counter-cyclical measure. Governments backed by nuclear-deliverable and capable military assets offer the greatest reassurance of loan repayment. With an accommodating central bank and ongoing and future social contract promises to the 99% of private citizens, the US government will, per force, create more debt and money expansion than corporations(the billionaire class proxies) and the private sector combined. The end of prominent of major economic cycles and recessions occur for the pleurality of private citizens when the valuation of assets are too high, the personal debt load is collectively too great, the liabilities of held and sought after assets, e.g., property taxes, new home and car loans, and the cost ongoing assets of daily living exceed the ability to pay or to further expand private debt. After lofty overvaluation of asset prices, these devaluations occur periodically and in a nonlinear fractal manner. The major self-ordering US fractal cycle is an 1807 36/90/90/54-57 year :: x/2.5x/2.5x/1.5-1.6x cycle with nadir commodity/equity prices in 1807, 1842-32, 1932, and expected in 2074-2077 with a 90 year 3rd fractal peak in November 2020 extended to higher highs by 7-15% annual US deficit to GDP spending in 2020 -2025. After a 1932 10-11/21-22/21-22 :: x/2x/2x fractal growth cycle ending in 1982, the dominant interpolated fractal cycle from 1982 is 13/32 of 33/33/20 years ending in 2077. A March 2020 9/23/14 month :: x/2.5x/1.5x fractal cycle was followed by a 27 Oct 2023 119/ 243 day cycle ending 7 April 2025. Nonlinearity in the 2nd 243 day 2nd fractal is seen between days 240 and 241 and days 241 and 242 with a final low on day 243 7 April 2025. From the 7 April 2025 nadir an ACWI 105 day 53/53 day peak is expected to occur on 5 September 2025 composed of two sequential fractal growth series of 10/25/20 days and 10/20/25 days. A 5 Spet 2025 15-22 day crash series of 5/11/7 days will take the ACWI to a 11 day 2nd fractal low on 25 September 2020 with a lower low or higher low on day 7/8 of the 3rd fractal on 3-6 October 2025. With the market (and the fed following) creating lower interest rates, a 119 day rebound is expected with a final crash of 15-21/22 days with a low in March/April of 2026.

The ACWI 22 Aug 2025 Peak Valuation and the Initial 25-26 September 2025 Crash Nadir.

In the asset-debt macroeconomic system there is an underlying self-ordering mathematical fractal pattern in composite asset valuation growth to composite asset peak valuation and thereafter decay to composite asset nadir valuation. Governments and central banks can expand credit and the money supply but are constrained by inflation of assets affecting the pyramid base population of the system. Overvaluation of assets represents a limiting barrier to further consumption in the face of constrained base population job availability and the nonlinear limiting factor of ongoing financial stress of debt servicing and further debt expansion. The mathematical self-assembly deterministic fractal process in the tradeable markets represents the optimal growth and decay investment pathway in the global asset debt macroeconomic system - just as does the steady state of the self-assembly process of the growth and decay of galaxies and black holes occur in the infinite universe. In the current system, 40 years of billionaire-led. corporation-led, both US political party led globalization, lowest wage highest corporation profit led, and resulting international production, transport supply chains, and assembly ... are being suddenly rent apart by US tariffs politically intended to bolster American internal product line manufacturing. This populist political anomaly is coincident with the timing of the 1982 credit cycle began by Volcker's 13-15.5% 3 month interest rates which has been fueled by gradually declining interest rates and extraordinary US peacetime percentage GDP-deficit spending. A 1982- 2026 13/33 year x/2.5x fractal credit cycle is an interpolated part of a greater US 1807 36/90/90/54-57 year x/2.5x/2.5x/1.5-1.6x. The 2020 15% US deficit to GDP COVID money expansion economy began with a nadir in the global composite ACWI equity index in March 2020. It is hard to imagine how a president whose name was at the bottom of the treasury checks sent to unemployed individuals resting at home and now making more than their usual salary, lost the Nov 2020 election. The current fractal projection from the 27 Oct 2023 low is: 118-119 //243//119-120 and 124 = 243//147 days :: x/2x+/2x+/1.5x'. An ACWI peak is predicted on 22 Aug 2025 followed by a 5/10-11/10-11 day 3 phase crash decay fractal series ending near 25-26 September 2025. From the April 2025 low a 10/25/20 day :: x/2.5x/2x growth fractal series is followed by a x/2x/2x' growth fractal series of 10/20/16 days with x' = 8 days for the observable 20 day 2nd fractal and the 3rd fractal 2x' or 16 days, reaching a peak on 22 Aug 2025. A growth fractal of 119-122 days is expected with falling US fed funds rates and lowered US interest rates with the US 3 month rate reaching near zero. The following ACWI 119-122 high will not exceed the 22 Aug 2025 high. A nonlinear collapse will the result in a sequential 124 day or total 2x+ 243 day nadir. The 147 day 1.5 x' 4th fractal double low nadir will occur near the 2026 midterms. Tariffs will be perceived as the post hoc ergo propter hoc etiology of an otherwise natural nadir valuation fractal progression.

Two Sequential Self Ordering Lammert Fractal Series From the 7 April 2025 ACWI Global Equity Nadir to a 26 August 2025 Peak Valuation and thereafter to the 11 September 2025 Initial Crash Nadir.

What is the correct and observable self assembly fractal pathway to the 1982 13/33 year global equity peak valuation and thereafter to the incipient crash low? The gapped nonlinear lower low on 1 August 2025 identifies the preceding 20 day fractal grouping as a 2nd fractal. The ideal base for a 20 day 2nd fractal is 8 days = x'. The observable base is 10 days starting on 23 June, the same nadir day that concluded a 7 April 2025 10/25/20 day :: x/2.5x/2x fractal growth series. The peak range of a 3rd fractal with an 8 day base is 2-2.5x' or 16-20 days with a 4th fractal of 1.5x' or 12 days. The 3rd fractal appears to be a 1 August 2025 4/7 of 8/8 day fractal growth series with a peak on day 18 or 26 August 2025. A 12 day 4th fractal crash decay would place the crash nadir on 11 September 2025.

On 3 Sept 1929, the DJIA average reached a peak valuation of 381.17. Ninety-six years later (97 by fractal count) on 23 July 2025, the DJIA reached a peak valuation of 45073.63, about 118 times the previous century’s earlier peak valuation. The average US house in 1929 was about 6000 US dollars and in 2025 about 515000, a comparable 85.5 times fold increase in valuation. The DJIA valuation peak in 1929 was near the close of a US 1807 to 1932 :: 36/90 year first and second fractal series … and the peak valuation in 2025 near the close of a US 1982 to 2026 13/33 year first and second fractal interpolated series, part of the greater US 1807 36/90/90/54 year :: x.2.5x/2.5x/1.5x 4-phase fractal series with a 90 year third fractal peak in Nov 2021.

Going into a population-overdebt-burdened-related, asset-highest-ever-valuation-related, highest-consumer-product-cost(except vehicle fuel), tariff-and-US consumer-paid-for-related … recession … Nvidia’s PE ratio is currently about 59 and Microsoft’s 38, both perfectly valued on a daily basis, but grossly overvalued in the long term credit cycle basis. From the 27 Oct 2023 low the Global Equity ACWI propelled by historical deficit to GDP annual credit/money expansion followed a 3 phase x/2.5x/2.5x maximum valuation growth fractal progression of 55/139/136 days followed by a 4 phase 5/13/11/7 day decay fractal series ending 7 April 2025.

The Deterministic Self-ordering 7 April 2025 17/37/37/22-23 day :: x/2-2.5x/2-2.5x/1.5x' 4-phase Lammert Growth and Decay Fractal series Pathway to the 12 Aug 2025 Global Equity Peak Valuation and the 4th Crash Fractal to the Initial 10-11 Sept 2025 Crash Nadir Low

On 3 Sept 1929, the DJIA average reached a peak valuation of 381.17. Ninety-six years later (97 by fractal count) on 23 July 2025, the DJIA reached a peak valuation of 45073.63, about 118 times the previous century's earlier peak valuation. The average US house in 1929 was about 6000 US dollars and in 2025 about 515000, a comparable 85.5 times fold increase in valuation. The DJIA valuation peak in 1929 was near the close of a US 1807 to 1932 :: 36/90 year first and second fractal series ... and the peak valuation in 2025 near the close of a US 1982 to 2026 13/33 year first and second fractal interpolated series, part of the greater US 1807 36/90/90/54 year :: x.2.5x/2.5x/1.5x 4-phase fractal series with a 90 year third fractal peak in Nov 2021.

This was propelled yet higher in valuation in 2024 and 2025 by unprecedented US peacetime deficit to GDP Covid spending of about 15% and 12%, respectively, in 2020 and 2021. Global equity peak valuation, represented by ACWI, which includes Nvidia, the latter now the #1 market cap company at 4.46 trillion, about 15% higher than #2 Microsoft, reached an intraday peak valuation (similar to Nvidia's ending daily close) on 8 August 2025. The Nikkei reached its blow-off top on 12 Aug 2025 at 42999.71, some 11% higher than its 1989 near 39000 peak occurring some 36 years ago carrying the Global Equity index ACWI likewise to its all time peak valuation on 12 August 2025. Going into a population-overdebt-burdened-related, asset-highest-ever-valuation-related, highest-consumer-product-cost(except vehicle fuel), tariff-and-US consumer-paid-for-related ... recession ... Nvidia's PE ratio is currently about 59 and Microsoft's 38, both perfectly valued on a daily basis, but grossly overvalued in the long term credit cycle basis. From the 27 Oct 2023 low the Global Equity ACWI propelled by historical deficit to GDP annual credit/money expansion followed a 3 phase x/2.5x/2.5x maximum valuation growth fractal progression of 55/139/136 days followed by a 4 phase 5/13/11/7 day decay fractal series ending 7 April 2025.

Since 7 April 2025, ACWI valuation growth has occurred in a 17/37/37 day 12 August 2025 peak valuation with a 21-22 day crash decay series ending 10-11 September 2025.

The ACWI 12 August peak valuation to a 10-11 September 2025 initial crash nadir is congruent with a Chinese property crash represented by the Shanghai property index of a April 2025 nadir 4 phase fractal series of 16/36/36-37/22-23 days. The 55 trillion Chinese property bubble is the defining element of the 2025 global equity crash akin to the US 1929 grossly overvalued US equity market.

The Deterministic Self-ordering Fractal Growth Pathway to the 11 Aug 2025 Global Equity Peak Valuation and the Crash Fractal Pathway to the Initial 10 Sept 2025 Crash Nadir Low

On 3 Sept 1929, the DJIA average reached a peak valuation of 381.17. Ninety-six years later (97 by fractal count) on 23 July 2025, the DJIA reached a peak valuation of 45073.63, about 118 times the previous century’s earlier peak valuation. The average US house in 1929 was about 6000 US dollars and in 2025 about 515000, a comparable 85.5 times fold increase in valuation. The DJIA valuation peak in 1929 was near the close of a US 1807 to 1932 :: 36/90 year first and second fractal series … and the peak valuation in 2025 near the close of a US 1982 to 2026 13/33 year first and second fractal interpolated series, part of the greater US 1807 36/90/90/54 year :: x.2.5x/2.5x/1.5x 4-phase fractal series with a 90 year third fractal peak in Nov 2021, propelled yet higher in valuation in 2024 and 2025 by unprecedented US peacetime deficit to GDP Covid spending of about 15% and 12%, respectively, in 2020 and 2021. Global equity peak valuation, represented by ACWI, which includes Nvidia, the latter now the #1 market cap company at 4.46 trillion, about 15% higher than #2 Microsoft, reached an intraday peak valuation (similar to Nvidia’s ending daily close) on 8 August 2025 with an expected final minutely and hourly gapped peak blow-off valuation on 11 August 2025 for both ACWI and Nvidia. Going into a population-overdebt-burdened-related, asset-highest-ever-valuation-related, highest-consumer-product-cost(except vehicle fuel), tariff-and-US consumer-paid-for-related … recession … Nvidia’s PE ratio is currently about 59 and Microsoft’s 38, both perfectly valued on a daily basis, but grossly overvalued in the long term credit cycle basis. From the 27 Oct 2023 low the Global Equity ACWI propelled by historical deficit to GDP annual credit/money expansion followed a 3 phase x/2.5x/2.5x maximum valuation growth fractal progression of 55/139/136 days followed by a 4 phase 5/13/11/7 day decay fractal series ending 7 April 2025. Since 7 April 2025, valuation growth has occurred in two 3-phase fractal series: a 10/25/20 day :: x/2.5x/2x series ending 23 June 2025. And from this 23 June relative nadir a 7/15/14 of 15 day 3-phase growth fractal series has taken the ACWI to a double top peak valuation on 8 August 2025. The 2nd 15 day 2nd fractal subseries is a curvilinear blow-off of 4/8/5 days :: x/2x/1.5x’. The final 14 of 15 day 3rd fractal subseries was self-assembled into a 3/7/6 of 7 day fractal subseries with a characteristic nonlinear lower low gap between day 6 and 7 of the 7 day 2nd subfractal and starting 1 Aug 2025 a self-ordered 6 day growth series to 8 August ensued. A final 7 day 3rd subfractal blow-off peak valuation on 11 August 2025 will result in a 23 June 2025 to 11 August 7/15/15 day :: x/2-2.5x/2-2.5x 3-phase growth final blow-off fractal series. From Friday 1 August 2025 ACWI has self-ordered into a 6/15/15 hour 3 phase growth series and is followed by a self-assembly 3/7/1 of 5-7 hour blow-off series. A gap higher at the opening on 11 August 2025 with a possible close near the low of the day would confirm this final self-assembly peak series. From the 11 August peak a 4/8/8/5 day 4-phase fractal decay series would take the ACWI to a 10 September 2025 initial crash nadir congruent with a Chinese property crash represented by the Shanghai property index of a April 2025 nadir 4 phase fractal series of 16/36/36-37/22-23 days. Fractal Charts to follow …

25 July 2025 was the 1982 13/32 of 33 year :: x/2.5x Global Equity Peak Valuation ... Now the Initial Nonlinear Crash with an Interim Nadir on 4 Sept 2025 ...

The 60 trillion dollar equivalent Chinese Property market, the total value of crypto proxies, AI proxies, and the ACWI Global index have all reached their maximum valuations for this global macroeconomic asset-debt credit cycle starting in 1982. After the nonlinear crash devaluation of all asset class valuations(except long term debt instruments), the US central bank will rapidly lower interest rates, causing one final lower lower high valuation with a final collapse in Sept to November of 2026. ACWI peak valuation 25 July 2025 with expected nadir 4 Sept 2025.

Chinese Property Fractal Monthly and Daily Decay:

Bitcoin Proxy GBTC Monthly and Daily:

From the 7 April 2025 nadir valuation,the 26 July 2025 Current Lammert Fractal Self-0rdering Observed Progression, the predicted progression, the predicted peak valuation August 2025 date and the predicted Oct 2025 crash valuation low date.

The Asset-Debt macroeconomic grows and decays it assets' valuation in a self-assembly well defined fractal manner. From the 1807 low the US hegemony macroeconomic asset-debt system has self-ordered the growth and decay of its asset valuations in a time ordered fractal manner of x/2.5x/2.5x with nadirs in 1842-43 and 1932 and a peak valuation in Nov 2021 following a 36/90/90 year fractal proportionality. The conclusion of a x/2.5x/2.5x/1.5-1.6x 4-phase Lammert fractal series would terminate in 2074-2077. Valuation growth has extended beyond the Nov 2021 90 year 2.5x 3rd fractal peak because of the historical debt-GDP % government peacetime spending secondary to Covid. After a 32 year crash low in October 2025, an interpolated 1982 13/33 year :: x/2.5x US fractal series is expected to conclude in 2026 with 1987-like 1-2 day collapse (%-wise worse than 1987) in asset valuation.