What must survive a return?
Preparation-Return Holonomy and Equilibrium Uniqueness in Engineered Interacting Networks
Exact state-return protocols single out Born equilibrium among all Borel laws at an engineered preparation.
Jeremy Rodgers · Independent Researcher · 4 October 2026
Publication revision of the 7 September 2026 manuscript
The complete paper
Follow the full argument.
Every section, proof and appendix, with linked equations and the complete bibliography.
- OpeningAbstract and publication identity
- Section 1Introduction
Publication relationship. · Main result and scope · Relation to previous work
- Section 2Hamiltonians and exact return maps
- Section 3Exact nonlinear returns on a plane
A weighted inverse with global estimates · Physical density rectangles · Curvature and arbitrary invariant measures
- Section 4Exact Gaussian returns with fixed interactions
Symplectic endpoint correction · The actual Gaussian configuration curvature · From return curves to the exact group
- Section 5Engineering the holding network
- Section 6Equilibrium uniqueness and an explicit witness
A finite smooth loop detecting a non-Born radial law
- Section 7Preparation transport and operational consequences
Reversibly reachable preparations · Linear readouts using the fixed network
- Section 8Randomized returns and finite preparation
A countable determining library and controller · Actual kernel and asymptotic behavior · Finite rounds and independent random completion · Retained memory and a reversible echo
- Section 9Discussion
- Appendix AGaussian holonomy beyond engineered weak couplings
An exact recurrent auxiliary seed · Transport back to the original preparation
- Appendix BExact moment bound for the nonlinear witness
- OpeningDeclarations
Funding. · AI assistance and responsibility. · Independent review and collaboration.
- OpeningBibliography