Mathematical foundations
Observable Quotients and Exact Projected Dynamics: Closure, Memory, Minimal Dynamical Completion, and Effective Field Operators
Autonomous projected laws, memory, and minimal dynamical completion.
Jeremy Rodgers · Independent Researcher · 2026-07-15
The complete argument.
Read every section on site, including the mathematics, proofs, examples and references. Each section has its own address for citation and navigation.
- 01Abstract
- 02Introduction
- 03The exact observable quotient
- 04Descent of observable functionals
- 05Compact observation and controlled reduction
- 06Descent of source dynamics
- 07The exact projected-dynamics identity
- 08Minimal dynamical completion
- 09Nonlinear dynamical descent
- 10Elimination of a source sector: Schur-complement effective operators
- 11Effective metric response
- 12Exact versus approximate reduction
- 13Consequences for Shadow Theory and conclusion
- 14References
Publication and computational material.
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