Dominik Collapse–Di e gence Law
Au ho : Ma hew Dominik (Hollis Black)
Dominik Resea ch Ins i u e • Cle eland, Ohio
P ep in o Zenodo
Abs ac
This pape o malizes he Dominik Collapse–Di e gence Law, a uni e sal op imiza ion p inciple
desc ibing how na u al, physical, biological, elec ical, and economic sys ems al e na e be ween
collapse (ene gy minimiza ion) and di e gence (ene gy expansion). The law p o ides a uni ying
s uc u e ac oss complexi y physics, he Colla z dynamical map, plane a y p ocesses, and ma ke -like
sys ems.
1. Fo mal S a emen
All na u al sys ems op imize ene gy low by al e na ing be ween wo undamen al modes:
1. Collapse Mode (1- ule): con ac ion owa d minimum-ene gy, low-en opy con igu a ions.
2. Di e gence Mode (3- ule): expansion in o highe -ene gy, b anching, high-en opy con igu a ions.
A sys em e ol es e icien ly when i ansi ions be ween hese wo modes in a way ha minimizes
oppo uni y cos and maximizes a ailable u u e pa hways. Sys ems ha esis o dis o his al e na ion
exhibi s agna ion, ins abili y, o explosi e ailu e.
2. Ma hema ical Fo m
Le S e ol e h ough disc e e s eps n:
- C(n): collapse ope a o
- D(n): di e gence ope a o
S(n+1) =
C(S(n)) i local ene gy g adien is nega i e
D(S(n)) i local ene gy g adien is posi i e
Wi h he uni e sal condi ion:
Minimize immedia e ene ge ic cos .
P ese e maximum long- e m op ionali y.
3. Physical In e p e a ion
Collapse Mode:
- pa h sho ening
- cha ge concen a ion
- lamina low s abiliza ion
- g a i a ional con ac ion
- ma ke clea ing
- pheno ype s abiliza ion
Di e gence Mode:
- b anching ins abili y
- elec ical a cing
- u bulence
- specula i e expansion
- mu a ion bu s s
- mul i-pa hway explo a ion
4. Rela ion o Colla z
The Colla z map al e na es be ween he collapse ule n → n/2 and he di e gence ule n → 3n+1.
The Dominik Law in e p e s his as he minimal compu a ional model o uni e sal ene gy al e na ion.
5. Uni e sal Implica ions
Sys ems ha mi o he uni e se’s op imiza ion logic ou pe o m sys ems ha oppose i . This applies o:
- plane a y clima e eedback
- neu al lea ning sys ems
- ma ke economies
- biosphe ic e olu ion
- elec ical discha ge phenomena
- ci iliza ion g ow h cycles
Conclusion
The Dominik Collapse–Di e gence Law p o ides a uni ying s uc u e o unde s anding ene gy low,
sys em e iciency, and pa e n o ma ion om ma hema ics o physics o ci iliza ion dynamics. I may
ep esen a ounda ional op imiza ion g amma embedded in na u al law.
