Special Functions

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

Read this chapter with formatted equations

1 \section*{Checks accompanying the proofread edition}
2 The complete manuscript was reviewed for prose, definitions, hypotheses,
3 notation, cross-references and agreement between chapter summaries and proof
4 appendices. Corrections include the Hankel order convention, zero-orbit
5 notation, the real-polynomial domain of signed quadratic forms and several
6 missing definitions. The chapter text now includes both finite-test
7 nonconvexity examples proved in Appendix~C.
8 
9 Fresh execution covered all ten foundational check scripts and the three
10 coupled and resolution scripts. The foundational scripts passed
11 \textbf{19,871 exact and 5,576 numerical assertion statements}. The coupled
12 scripts passed \textbf{5,272 exact and 26 numerical assertion statements},
13 with 13 separate operational guards. All 14 coupled and resolution figure
14 pairs were regenerated. Counts describe executed finite assertions, not
15 independent theorems or exhaustive parameter coverage.
16 
17 The first foundational orchestration attempt reached the execution time
18 limit after nine scripts had recorded passing results. The final script was
19 then run separately against the same isolated input snapshot and passed.
20 The retained logs distinguish this recovered execution failure from a
21 mathematical or numerical assertion failure.
22 
23 The editorial change log, exact source diff and fresh execution records are
24 included in the package. No Lean build was performed. Analytic conclusions
25 continue to rest on the written proofs and their stated hypotheses.
26 

Back to source controls

Back to Special Functions