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Shadow Theory

Mathematical foundations

Source–Readout Non-Equivalence: Descent and Equivariant Reconstruction Obstructions

Exact quotients, source relations, and symmetry-compatible reconstruction.

Jeremy Rodgers · Independent Researcher · 2026-07-15

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  1. 01Abstract
  2. 02Introduction
  3. 03Realization states, physical equivalence, and readout
  4. 04Quotient exactness and source equivalence
  5. 05Descent of source relations
  6. 06Representative selection is not reconstruction
  7. 07Equivariant reconstruction
  8. 08A finite marked-carrier occupation model
  9. 09Invariant ensembles versus deterministic selection
  10. 10A continuous obstruction: the Hopf fibration
  11. 11The source–readout non-equivalence theorem
  12. 12Interpretation and scope
  13. 13Discussion
  14. 14Conclusion
  15. 15References

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The seven mathematical foundations →Constructive sources and readers →The Everything Equation’s development →Original publication record →