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Recovering Yang–Mills through Shadow Theory.

Shadow Theory constructs a connected realization of the Wilson Yang–Mills argument: its configurations, measures, effective quantities, physical fields and operator correlations, with explicit recovery maps and compatible operations throughout.

Shadow Theory and the Wilson Yang–Mills Construction: A Source–Readout Reconstruction

Shadow Theory constructs a connected realization of the Wilson Yang–Mills argument: its configurations, measures, effective quantities, physical fields and operator correlations, with explicit recovery maps and compatible operations throughout.

A configuration, an effective action and a physical field are different readouts. Recovering the final expression is only part of the task. Shadow Theory makes their relationship explicit: sections show which target objects are covered, fibres identify what is discarded, and operation identities establish how the construction passes through each layer.

Jeremy Rodgers originated Shadow Theory, the source–readout architecture and the Source Lift protocol, and directed this reconstruction with AI assistance. The mathematical input is the expanded translation of OpenAI’s underlying Lean Yang–Mills work. The chapters develop the complete realization and recovery argument alongside its Yang–Mills derivations.

The gauge group, faithful representation, four-dimensional Wilson law and stated analytic hypotheses are inputs. The full fixed-period mesh limit precedes the permitted outer volume extraction. The centered trace and comparison exclusions retain their own hypotheses; a positive mass gap is not a conclusion of these editions.

The Einstein reconstruction develops the same discipline in classical gravity →

The argument in full

  1. The contribution and the reading path

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  2. Introduction

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  3. Source–readout and reflective mathematics: the objects and the task

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  4. Provenance and mathematical contract

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  5. The supplied public conclusion and its recovery target

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  6. Inherited analytic conventions

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  7. Native admission, literal preparation and the realized sector

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  8. Finite-lattice realization and exact recovery

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  9. The source support of the realized family, its lift groupoid and its interfaces

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  10. Activity domains, ordered derivatives and absolute budgets

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  11. Finite reflection positivity and rooted bounds

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  12. Quadratic ultraviolet kernels and comparison

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  13. Quadratic ultraviolet kernels and comparison · Part 2

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  14. Quadratic ultraviolet kernels and comparison · Part 3

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  15. Local nonlinear geometry and Haar realization

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  16. Local nonlinear geometry and Haar realization · Part 2

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  17. Local nonlinear geometry and Haar realization · Part 3

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  18. Local nonlinear geometry and Haar realization · Part 4

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  19. Local nonlinear geometry and Haar realization · Part 5

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  20. Local nonlinear geometry and Haar realization · Part 6

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  21. Local nonlinear geometry and Haar realization · Part 7

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  22. Marked integration and coupling reset

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  23. Marked integration and coupling reset · Part 2

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  24. Marked integration and coupling reset · Part 3

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  25. Marked integration and coupling reset · Part 4

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  26. Marked integration and coupling reset · Part 5

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  27. Marked integration and coupling reset · Part 6

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  28. 14 The analytic stationary graph, loop moments and the cali- brated coupling history

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  29. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 2

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  30. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 3

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  31. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 4

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  32. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 5

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  33. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 6

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  34. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 7

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  35. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 8

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  36. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 9

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  37. 14 The analytic stationary graph, loop moments and the cali- brated coupling history · Part 10

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  38. Convergence of interacting scale histories

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  39. Convergence of interacting scale histories · Part 2

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  40. Convergence of interacting scale histories · Part 3

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  41. Convergence of interacting scale histories · Part 4

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  42. Radial jets, calibrated labels and the free Maxwell comparison hierarchy

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  43. Radial jets, calibrated labels and the free Maxwell comparison hierarchy · Part 2

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  44. Radial jets, calibrated labels and the free Maxwell comparison hierarchy · Part 3

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  45. Radial jets, calibrated labels and the free Maxwell comparison hierarchy · Part 4

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  46. Physical labels and their detection

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  47. Physical labels and their detection · Part 2

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  48. The common continuum hierarchy

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  49. The common continuum hierarchy · Part 2

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  50. Phase decomposition and Wightman reconstruction

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  51. Phase decomposition and Wightman reconstruction · Part 2

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  52. Phase decomposition and Wightman reconstruction · Part 3

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  53. Phase decomposition and Wightman reconstruction · Part 4

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  54. Phase decomposition and Wightman reconstruction · Part 5

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  55. Phase decomposition and Wightman reconstruction · Part 6

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  56. Phase decomposition and Wightman reconstruction · Part 7

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  57. Phase decomposition and Wightman reconstruction · Part 8

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  58. Separated and nested operator products

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  59. Separated and nested operator products · Part 2

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  60. Separated and nested operator products · Part 3

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  61. Extension across collision sets

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  62. Extension across collision sets · Part 2

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  63. Extension across collision sets · Part 3

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  64. Gaussian short-distance comparison

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  65. Gaussian short-distance comparison · Part 2

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  66. Gaussian short-distance comparison · Part 3

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  67. Finite stress, scaling maps and shell charges

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  68. Finite stress, scaling maps and shell charges · Part 2

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  69. Finite stress, scaling maps and shell charges · Part 3

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  70. The centered trace and its comparison exclusions

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  71. The centered trace and its comparison exclusions · Part 2

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  72. The centered trace and its comparison exclusions · Part 3

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  73. Exact stress correction and local quantitative estimates

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  74. Exact stress correction and local quantitative estimates · Part 2

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  75. Exact stress correction and local quantitative estimates · Part 3

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  76. Position coupling, real remainders and equation markers

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  77. Position coupling, real remainders and equation markers · Part 2

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  78. Common-family assembly of the supplied conclusion

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  79. Conclusion

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  80. Attribution of the source and mathematical background

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  81. Tangent coverage, forms and horizontal operations

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  82. Integral, residual and limit transport

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  83. Reflection quotients and field recovery

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  84. Compression algebras and phase recovery

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  85. Operator-product readers and collision extensions

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  86. Gaussian and ordered inverse operations

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  87. Assumptions, dependency chain and source–readout contracts

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  88. Claim-status register

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  89. Correspondence with the supplied text

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  90. Verification, limitations and reproducibility

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  91. References

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Source: Shadow Theory and the Wilson Yang–Mills Construction: A Source–Readout Reconstruction. Both papers belong to one Zenodo record. No external funding.