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Shadow Theory

How are whole histories selected?

A Deterministic Hybrid Medium for Bell Jump Paths and Autonomous Records

A deterministic hybrid medium approaches the complete Bell path law in physical time and carries faithful autonomous records.

Jeremy Rodgers · Independent Researcher · 4 October 2026

Research manuscript and revision of the September 2026 pilot-medium paper

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17 reading sections21 statements20 proofs115 mathematical displays

The complete paper

Follow the full argument.

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

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

    What the convergence statement includes · Relation to earlier work and contribution · Fixed domain and physical premises.

  3. Section 2Microscopic state and model assumptions

    Complete state and interaction catalogue · Energy, reversibility and finite resources

  4. Section 3Canonical edge ownership and conservative export
  5. Section 4Binary species and contact geometry

    Routing from a declared charge spectrum · Deterministic candidate contacts

  6. Section 5A finite spatial ensemble and its Poisson comparison

    Which contact marks are compared.

  7. Section 6Recombination and the removal of surplus
  8. Section 7Mass-action tracking and convergence through nodes

    The complete tagged path and the nodal boundary

  9. Section 8The complete physical-time Bell-path limit

    Complete configurations and projections.

  10. Section 9An autonomous clock and faithful copying cuts

    Exact autonomous propagation · A faithful archive is created at a monomial clock cut

  11. Section 10An explicit retained-resource measurement and continuation

    Finite production, fuel, capture, pending and loss states · Nine exact gates with every receiving system retained · A null result with a reference-sensitive continuation · Basis-ready preparation and transfer to finite resources · Exact time scope.

  12. Section 11Countermodels and limits of inference

    A stationary coherent cycle tests individual edge ownership · The finite-recombination rival really has dark traffic · The spatial ensemble selects timing beyond mean flux · Recombination does not conceal a readable pilot ledger · Fine and coarse paths remain distinct

  13. Section 12Conclusions and remaining obligations
  14. OpeningResearch transparency

    Funding. · Independent review and collaboration.

  15. Appendix AInitial calibration and fixed-circuit resource rates

    Initial independent equilibrium and uniformity · An explicit fixed-circuit resource rate

  16. Appendix BA smooth autonomous realization of the finite contact module

    Register cells and an explicit permutation compiler · Positive kinetic coupling and exact passage time · Present-state logical decoding and path topology · Smooth channel plates and the projected history bound

  17. OpeningBibliography