Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb
Verification checklist and limits
Verification checklist and limits · lines 1879–1957
| Item | Status and locator |
|---|---|
| Ambient normalization | Proved: , ; Lemma lem:families |
| Full-Hessian structure | Analytically proved from the finite density: Proposition prop:hess |
| General numerical coefficient list | Supplied exact-arithmetic verification record: Appendix app:script |
| Dual-basis contraction | Derived from the inverse fiber pairing: Lemma lem:dual |
| Derivative sign and numerical products | Proved using the off-diagonal Feynman relation: Lemma lem:sign |
| Scaling and subtraction orders | Numerical degrees , declared orders : Proposition prop:sd |
| Finite extension coherence | Constructed on , preserving constant relations: Proposition prop:RK |
| Differentiation defects | Contact formulas proved; values not evaluated: Lemma lem:defect |
| Root attachment | Conditional on imported (R1)–(R3): Lemma lem:attachK |
| Switch counting | One factor in , none in : (eq:apq), (eq:T) |
| Properness and continuity | Root compactness plus compact interaction switch: Theorem thm:main |
| XVI-J regression | Exact, including the selected contact part: Proposition prop:regression |
| Propagated ambiguity | Proved with coherent-family constraints distinguished: Proposition prop:localambiguity, Lemma lem:amb |
Nonvanishing is separated by level:
The numerical graded spaces are nonzero by Lemma lem:grading.
The supplied output records nonzero algebraic/background decorated tensors, described below.
Nonvanishing after the switch, root attachment, or final smearing is not inferred from either statement.
The plateau source, the source, and other contraction types remain outside this selected sector. The final coefficient has not been evaluated on explicit preparation, switch, root, and scalar data. The derivative-defect values, sharp distributional orders, and locality of the propagated ambiguity are not established.
No state, expectation, retarded interacting observable, BRST/BV closure, Ward identity, all-orders time-ordered family, or ultraviolet completion is claimed. No limit is taken. The inherited root bound is not re-proved, and no predecessor free-shell obstruction is repaired or transferred by this construction.