Evidence and access grades

ANALYTIC

A result proved by the displayed argument, with cited analytical inputs identified.

SUPPLIED_ NUMERIC

An execution statement inherited from one of the supplied records. It has not been rerun in preparing this consolidated text.

UNCERTIFIED

A computation lacking the artifacts and rigorous error enclosure needed for a certified numerical interpretation.

All numerical reports in the appendices are simultaneously SUPPLIED_ NUMERIC{} by provenance and UNCERTIFIED{} as total-error bounds. An inherited symbolic execution report is not a newly executed symbolic proof.

The bibliography's marks preserve the predecessor access ledger: {$\ast$}{} means the source reported reading the full paper; {$‡$}{} means metadata, sometimes an abstract, or citations in a read paper were consulted without reading that full paper; {$†$}{} means recalled from memory. These are archival access grades, not claims that the present consolidation re-read every marked work in full. The formula-level comparisons identify the passages actually relevant to the mathematics.

verification gate. A reproducible numerical package should record

A relative residual is inapplicable when its denominator is zero or unreliable. A successful retention of a known discrepancy does not remove that discrepancy.

Agreement at a shared rounded binary input is not equal accuracy at an intended irrational parameter. For example,

gives a separate input-error estimate from a parameter enclosure.

For a generic-angle diffraction tail with $|{\Phi }_{\beta }|\le C{e}^{-\delta u}$, $u\ge U$,

A certified run must supply $C,\delta ,U$, and differentiated bounds for stress or current; merely invoking exponential decay is not a certificate.

and build status. The source files name scripts and logs, but their contents were not supplied with the manuscripts. No independent numerical run, interval verification, proof-assistant check, or successful pdflatex run is asserted here. This manuscript is self-contained as a LaTeX source, not as a reproduction archive for those computations.