docs(paper): drop the negative-results section and repair what cited it - #54
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Section 8 reported two experiments that were pursued and abandoned: leaving the
orthogonal factor implicit through geqrf/ormqr, and a Numba port. Removed --
126 lines, and the paper goes from fifteen pages to twelve.
The section was not self-contained. Seven passages referred to it, and five of
those leaned on it for a quantitative claim, so each has been rewritten to stand
on its own rather than to cite evidence the paper no longer carries:
* the abstract's promise of "two negative results in full", with the figures it
quoted, is gone;
* the contributions list loses its fourth item;
* "we quantify it in S8", on updating versus recomputing the factor, now states
the O(n^3) against O(n^4) consequence directly;
* "S8 shows why that costs a factor of 57", after the least-squares remark, now
says plainly that the quantities are already available in factored form and
that recomputing them each iteration is the more expensive route;
* the remark on folding R_G^{-1} and Q into J loses its forward reference;
* "a floor set by the language implementation ... and S8 confirms it by removing
it" now stops at the claim itself;
* Limitations said S8 "establishes" that closing the small-n gap requires leaving
pure NumPy; it now says this "appears to" be so, since the experiment that
established it is no longer reported.
That last hedge is deliberate rather than cosmetic. It is the one claim in the
paper whose only support was the removed section, and overstating it without the
measurement would be worse than weakening it.
The numba2015 entry is left in the bibliography, now uncited. It is not orphaned
for long if the optional accelerator lands.
Compiles clean under tectonic with no unresolved references.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Pull request overview
This PR updates the LaTeX paper to remove the “Two negative results” section and revises all passages that previously relied on that section so the paper remains internally consistent (including removing/rewriting claims that previously cited §8).
Changes:
- Deletes the “Two negative results” section entirely.
- Removes or rewrites references in the abstract, contributions list, and multiple sections that previously cited the removed section for support.
- Softens one previously-measured claim in Limitations (“establishes” → “appears to require”) to avoid overstating without the removed evidence.
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| method. Small problems remain slower than the compiled reference by up to | ||
| 13 times, and \S\ref{sec:negative} establishes that closing that gap | ||
| requires leaving pure NumPy. The structure detection of \S\ref{sec:structure} | ||
| 13 times, and closing that gap appears to require leaving pure NumPy. The structure detection of \S\ref{sec:structure} | ||
| recognises single-nonzero columns and general sparsity in the slack product but |
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Summary
Removes §8, "Two negative results" — the implicit-
Qexperiment (geqrf/ormqr) and theNumba port. 126 lines out; the paper goes from fifteen pages to twelve.
The section was not self-contained
Seven passages referred to it and five leaned on it for a quantitative claim, so
deleting it alone would have left those claims citing evidence the paper no longer carries.
Each is rewritten to stand on its own:
O(n³)vsO(n⁴)consequence directlyThat last hedge is deliberate. It is the one claim whose only support was the removed
section, and asserting it without the measurement would be worse than weakening it. If the
optional Numba accelerator lands, that sentence should become a forward reference to it
rather than a hedge.
Note
numba2015is now uncited. I left the entry in the bibliography rather than deleting it,since adopting Numba as an optional extra would need it back.
Testing
make paper-tectonic— compiles clean, 0 unresolved referencesmake fmtdocs/paper/quadprog.texonly.🤖 Generated with Claude Code