Manuscript X-F-ST@1 · X-F-ST.tex · section · e71f03ef
F6: VII-C audit and the separate analytic boundaries
F6: VII-C audit and the separate analytic boundaries · lines 2137–2231
VII-C concerns a specified sharp mixed insertion, a fixed Wick matrix, a specified normal-topology approximating family, and continuous extraction of the fully contracted coefficient of
Its logarithmic obstruction retains that joint hypothesis package VIIC.
{}1.12
| Item | VII-C requires | X-F-ST constructs |
|---|---|---|
| (E1) | Its exact de Donder multiplet and fixed Wick matrix | A declared flat free tensor carrier with block ; background gauge enters , not a new free product |
| (E2) | Its unchanged sharp zero-Cauchy mixed insertion | Completed ramp insertions at fixed positive width |
| (E3) | Admission continuous on its specified normal-topology approximating stages | Three fixed-width coefficient kernels; no such approximating family |
| (E4) | The required triple word and continuous field-independent extraction | Three isolated trees; no required word or extraction |
The theorem therefore does not apply and is not contradicted. The presence of a self tree does not identify its field content, kernel, or contraction with that word.
The omitted mixed quantum contractions are a possible later comparison point, but even there VII-C would require an actual hypothesis match. Its obstruction is not automatically a theorem about every mixed loop.
product-hierarchy inference. The earlier scalar one-contraction boundary does not construct a general , and the three trees do not construct one either XBST,XCST. No loop kernel square, extension prescription, contact catalogue, or subtraction is selected.
transmission and boundary domains. VII-I's finite-width free algebra and changed sharp transmission data are not this prescription. IX-A-ST's boundary-sensitive carrier and IX-D-ST's causal-support interface do not supply a time-ordered lift for these kernels, and these trees do not solve the IX-E problem ComparisonRecords.
is not convergence. Em01-B's polynomial smoothing growth is not a characteristic limit or a rate for the present kernels. Em01-C's aligned-null scalar family is different. Em02-D's raw-family nonconvergence is a contrast, not a repair EmRecords.
multiplication is not subtraction. For fixed smooth , . This fact does not construct an undefined product, choose a finite part, or supply uniform estimates for arbitrary scale-dependent multipliers Hormander,XVIA.
-map boundary. The present sum-zero calculation is for the explicitly constructed internal trees. It does not compose their kernels with the separate characteristic quantum cross-lines. Historical H2 and the full I3/J2 obligations are not discharged here; XIV-I's narrower internal-amplitude construction is not withdrawn BoundaryRecords.
Displayed formulas in this passage
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