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Shadow Theory

How does a record last?

Autonomous Quantum Measurement Chains with Faithful Equilibrium Records

A finite autonomous apparatus produces and preserves its own measurement records under complete initial quantum equilibrium.

Jeremy Rodgers · Independent Researcher · 4 October 2026

Consolidated revision of the version 2 massive-configuration preprint

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15 reading sections15 statements11 proofs98 mathematical displays

The complete paper

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Every section, proof and appendix, with linked equations and the complete bibliography.

  1. OpeningAbstract and publication identity
  2. Section 1Introduction and scope

    Relation to established work and the earlier version · The result in outline

  3. Section 2The model and its statistical assumptions

    Self-adjointness, domains and nodes · The law on complete histories

  4. Section 3An exact massive detector in physical time

    Actual timing, false-ready tails and null continuation · Energy and force resources

  5. Section 4A finite coherent source and resource module

    Physical null, capture and loss · Finite stock and exhaustion

  6. Section 5Physical records that remain true about their past

    A genuine copy and its classification error · Reset with the receiving system retained · Feedback from a literal spatial record

  7. Section 6Protected coherent transport in the same inventory
  8. Section 7An autonomous massive clock and archive current bounds

    The complete autonomous Hamiltonian · Derivative control uniform in clock resources · Why the same estimate controls actual archive history · Choosing the archive comparator.

  9. Section 8Complete instruments, references and finite histories

    The exact finite pointer output and a strong comparator · Noncommuting continuation without a fresh probability postulate · Conditioning and returning branches. · Preparation information is retained.

  10. Section 9A complete finite example and reproducible calculations

    Null followed by an incompatible measurement · Captured copy, reset, spatial feedback and a second record · A complete reversal remains a different experiment · Finite numerical values

  11. Section 10Why reliable records do not uniquely select guidance

    Same local net current, mutually singular paths

  12. Section 11Scope and remaining physical questions
  13. Appendix AA compact proof of complete output and conditioning bounds
  14. OpeningDeclarations

    Funding. · AI assistance and responsibility. · Independent review and collaboration.

  15. OpeningBibliography