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: