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Shadow Theory

Source Lift / The complete argument

Marked integration and coupling reset · Part 6

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

Jeremy Rodgers · Independent Researcher · 2026-11-12
Shared publication DOI: 10.5281/zenodo.24173681

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sΘ3 ≤1, sΘ4 ≤1 and 2P(s)vΘ2 ≤1 uniformly for v ≤1. Substitution gives lk(2s) ≤4Ck + 1, with δk, κk ≤1 and sbg2 k = 1. Therefore
Source page 146.
Searchable transcription
sΘ3 ≤1, sΘ4 ≤1 and 2P(s)vΘ2 ≤1 uniformly for v ≤1. Substitution gives lk(2s) ≤4Ck + 1,
with δk, κk ≤1 and sbg2
k = 1. Therefore
τk ≤2{1 + (4Ck + 1)} + 1 + |P|(Cdir,k + C2 k) + 4dM{log 16 + 1 2 log bβk}.
Source page 146.
Searchable transcription
τk ≤2{1 + (4Ck + 1)} + 1 + |P|(Cdir,k + C2
k)
+ 4dM{log 16 + 1
2 log bβk}.

Stage parameters remain explicit; logarithmic reference-coupling growth is asserted after fixing them. The lift retains the same normalized numerator, denominator and history parameters. Exact probability readout and the recovered denominator bound preserve the cancellation and volume coefficient, without absorbing volume into a vanishing error.

The normalized mode reader is recovered as a ratio of two exact integrals. For the realized prior and insertion XZ = L X,

R [XZ]A dμZ R RZ dμZ = tw(A)| R [X]A dμ| ZR . tw(A)
Source page 146.
Searchable transcription

R [XZ]A dμZ

R RZ dμZ
= tw(A)|
R [X]A dμ|
ZR
.
tw(A)
The denominator is strictly positive by the recovered shelter estimate. Its vacuum factor ev0 is the same one present in the numerator majorant, so cancellation leaves precisely the displayed extensive bill. All history choices entering τk are recorded scalar data; readout retains bgk, the band β ≤2 bβk, and the fixed stage constants. Consequently its monotonicity substitution and stagewise logarithmic bound recover with the same quantifier order and site factor |Λk|. Section recovery returns the original full-law mode integral and treasury estimate.
Source page 146.
Searchable transcription
The denominator is strictly positive by the recovered shelter estimate. Its vacuum factor ev0 is
the same one present in the numerator majorant, so cancellation leaves precisely the displayed
extensive bill. All history choices entering τk are recorded scalar data; readout retains bgk, the band
β ≤2 bβk, and the fixed stage constants. Consequently its monotonicity substitution and stagewise
logarithmic bound recover with the same quantifier order and site factor |Λk|. Section recovery
returns the original full-law mode integral and treasury estimate.

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