Mathematical foundations
Target-Relative Necessity of Completion: When Readout Loss Obstructs, and What a Sufficient Extension Must Retain
When missing distinctions obstruct a target and what any sufficient repair must retain.
Jeremy Rodgers · Independent Researcher · 2026-07-15
The complete argument.
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- 01Abstract
- 02Introduction
- 03Reduced source, readout, and target
- 04Exact target solvability and its obstruction
- 05Active and inactive information loss
- 06Minimal sound uncertainty without completion
- 07Readout extensions and target sufficiency
- 08What every sufficient extension must retain
- 09The joint target image and universal minimality
- 10Flat U(1) connections on the circle
- 11The charged covariant Laplacian and the curvature obstruction
- 12The minimal completion for the spectral target
- 13Finite-time dynamical descent
- 14Discussion and scope
- 15Conclusion
- 16References
Publication and computational material.
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