Fractal self-assembly and self ordering of asset valuations, traded daily (or five times a week), occur in combinations of three and four phase mathematical fractal series: x/2-2.5x/2-2.5x/1.5-1.6x and x/2-2.5x/1.5x-2.5x, where x denote a fractal time unit in days, weeks, months, and years.

An alternative 149-150 day DAX 17 January 2024 second fractal decay model of the 23 October 2023 60/125 day of 126 to 150 day first and second fractal series has no flash crash, rather a 14 July 2024 6/12/9-10 day :: x/2x/1.5-1.6x decay series ending 15-16 August 2024.

The current model for the DAX and western equity composites from the March 2020 covid low is an averaged 8-9/23-24/23/1 of 12-15 month :: x/2.5x/2.5x/1.4-1.6x four phase growth and decay fractal series.

The expected June- Sept 2025 low for global equities represents the end of a major consumer-citizen 1982 13/32-33 year debt-dependent credit cycle, where asset prices in the terminal 32nd/33rd year of he second fractal particularly, global residential asset and equity prices will fall precipitously and debt default and restructuring will occur, forming the basis for another 30-33 year inflationary credit expansion.

The expected incipient August September 2024 Fed fund rate cuts and mid August 2024 149-150 day second fractal nadir valuation saturation selling would provide two explanations for rebound valuation growth beyond the incidental US November 2024 election cycle.

The 1982 -2024 German DAX 13-14/30-31 year First and Second Fractals

Within the 4-phase 267 year 1807 to 2074 US hegemonic x/2.5x/2.5x/1.5x :: 36/90/90/54 year fractal series, rests an interpolated 1982 German DAX 13-14/30-31 year series. The 30 year second fractal nonlinearity could as an incipient feature have an initial shocking flash crash (with a sharp rebound beyond the November 2024 election.

The self-assembly fractal mathematical architecture of the 23 October 2023 to 5 July 2024 x/2x :: 13(-)/25-26 week :: 60/120 day fractal series is observable. Rather than 28 October 2023, the Incipient day for the 13-/25-26 week first and second fractal series is 23 October 2023 consistent with the fractal maxim that fractal valuation growth begins in terminal fractal decay. Objectively, a 13(-)/25 week first and second fractal series can be identified from 23 October 2023 to 5 July 2024. The first 13 week fractal occurs as a 3/7/5 week fractal series(x/2-2.5x/1.6x) and the second fractal, a 5/10/12 of 12-13 week fractal series x/2x/2.4x-2.5x. Next trading week, the 23 Oct 2023 x/2x series with a base (x) of slightly less than 13 weeks will be in the window (2x to 2.5x)of 26-32 week second fractal nonlinearity.

As of 5 July 2024, a 23 October 2023 60/120 day :: x/2x first and second fractal series is observable. The terminal fractal window begins next week  between day 121 and day 150.

The Dax is at/near its March 2020 third fractal apogee with a three phase fractal growth series of 8/24/23 months as of 5 July 2023. (see below.)

The extended second fractal of 24 months or 4/9/8/6 months :: x/2-2.5x/2x/1.5x is beyond the expected 2.5x or 20 months of the 8 March 2020 base fractal because of the extraordinary QE in 2020-2021 with the Fed adding 10-11 trillion dollars to their balance sheet or a historical 30 % increase in the GDP/national debt ratio in just two years. The last 5/10/10 month third fractal takes the DAX to its July 2024 lower high with a potential high next week completing a 4/10/6-10 day:: x/2.5x/1.5-2.5x 3-phase growth fractal series.(see the final green/yellow/orange 4/10/4 of 4-10 day growth series above).

For the SPX Friday 28 June 2024 meets the criteria for a peak (bearish) Key Reversal Day:
‘Key Reversal Day: In a bearish key reversal the market OPENS above the prior close, often leaving a gap, sets a new high, and then closes the day lower than the prior day’s close.’

A two day chart from 27 and 28 June 2024 is shown for the SPX below.

28 June 2024 for the SPX represents year 31 of a 13/31-33 year 1982 first and second fractal series. As an update from the second picture below 28 June represents the 121 quarter of a 49-50/123-125 quarter first and second fractal series

For the SPX 28 June 2024 represents day 114 of a 55/112-140 day 27 October 2023 first and second fractal series. The SPX is in the terminal 2x to 2.5x portion of the 112-140 second fractal window where nonlinear occurs.

US total market cap to GDP ratio was at 193.3 % on 27 June 2024, still more than 6% below its 2021 199.5% peak.

Second Fractal Nonlinearity:

From the 2005 website page of TEF regarding first and second fractals (cycles) of a 4 phase fractal (cycle) (x/2x-2.5x/2x(to 2.5x)/1.5-1.6x series.

…. “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 (fractal)and characterizes this most recognizable (fractal) cycle.”