Integrity of numerical comparisons

The existence, support, and kernel identities above are analytical statements. Their proofs do not use the numerical discrepancies reported in the supplied draft.

The supplied draft refers to scripts and logs that are not contained in this single-file source. Accordingly:

1. the inherited discrepancies are retained as reported numerical data, not as newly verified error bounds;

2. no execution, independent rebuild, interval certification, or code availability is asserted;

3. a submission using those values as reproducible computational evidence should provide the scripts, versions, truncations, precision settings, raw values, and residuals;

4. no reported finite agreement is used as a proof of causal support or distributional equality.

This values-plus-residual discipline is consistent with the integrity-aware reporting of XVI-O1-ST CheungXVIOOneST. Its unrelated algebraic or quantum statuses are not imported.

A useful record for a new comparison is

When the denominator is zero or unreliable, a relative residual should be marked inapplicable. Appendix app:numerics preserves the principal supplied numbers, including the high-frequency cancellation failure. Theorem thm:speed, not that table, proves support.