Related work: fix three stale cells, and cover all four families in the README - #38
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The comparison table still listed the odd-characteristic doubling and both
characteristic-2 formulas as unbuilt, with "*none*" in our column and "Future work,
PR6 / PR7 / PR8" beside it. All three were derived and merged in those very PRs. The
arb doubling figure was stale too, quoted at 61 M+S / 3C / 92A where it has measured
58 / 4C / 80A since the PR36 sweep.
That is the worst kind of stale for this file, because it is the document a reader
consults to find out where the work stands against the literature -- and it said we
had no entry in three of the four cells that have competition, when in fact we are
ahead on both axes in all four:
cell previous best ours margin
odd ADD 67 M+S, 105A Nyukai 56 M+S, 0C, 59A -11, -46
odd DBL 68 M+S, 93A Nyukai 58 M+S, 0C, 61A -10, -32
ch2 ADD 67 M+S, 100A GKP 54 M+S, 0C, 62A -13, -38
ch2 DBL 69 M+S, 107A GKP 55 M+S, 2C, 55A -14, -52
The two lane sections carried the same staleness in prose -- "the doubling comparison
still cannot be made until nch2_ramifiedG3_DBL.mag exists" and "we have no entry in
this lane yet" -- and the Birkner reconciliation was still written as something
PR7/PR8 would do, where it was decided on 2026-08-24 to be a publication task rather
than a repository one. All corrected.
README GAINS A "RELATED WORK" SECTION carrying that table, because the comparison
against prior art is the first thing a reader wants and it was previously reachable
only by opening a second file. Four caveats travel with it rather than being left to
the reader to discover: the A counts for prior work are DERIVED by us and marked, no
author in this area publishes additions; C is zero in every previous-best cell
because those normal forms leave nothing to multiply by, so our arb rows' 1C and 4C
are the price of generality; three of the four cells did not exist when this work
started; and the char-2 rows are quoted at deg h = 3, since cheaper numbers at other
h-shapes are not comparable.
The Operation counts section keeps what is about provenance -- every row measured,
and the 168 published cells the counter reproduces -- and hands the comparison
material to the new section. Every margin was re-derived from the measured figures
rather than carried across.
…"This work" row
The section covered genus-3 ramified only, because that is the family the thesis
defers and therefore the only one whose comparison had to be compiled here. The
other three already have published comparisons -- in the thesis itself, the split
model and genus-2 ramified being its own contribution -- so the repository was
telling a quarter of the story in the place a reader looks first.
Now all four are there:
genus 2 ramified vs Lange 2005 (4-coordinate affine)
genus 2 split vs Erickson, Jacobson and Stein 2011
genus 3 split vs Rezai Rad et al. 2019 and Sutherland 2019
genus 3 ramified vs Nyukai 2006, GKP 2004 -- compiled here, no thesis coverage
EVERY "THIS WORK" ROW WAS RE-DERIVED FROM opcount.py AND MATCHES. Thirteen rows
checked across the three thesis comparison tables -- five genus-2 ramified, four
genus-3 split, four genus-2 split -- and every one reproduces exactly. That is not a
redundant check against PR41's: the COST tables and the COMPARISON tables are
separate transcriptions of the same quantities, and a transcription is precisely
where a copy error hides. It found none, which is worth recording as a fact rather
than assumed.
The genus-2 split comparison is the one where the summary omits more than it shows:
two cells tie exactly, and the larger gains are in the adjustment operations, where
EJS need two inversions for several that this work does in one. The thesis table
carries those in full.
ONE LIMITATION STATED RATHER THAN GLOSSED: the three thesis comparisons are as
published in 2020 and no search for work appearing since has been done. Only the
genus-3 ramified survey is current, having been compiled in 2026. So those three
rows are re-verified against our own measurements, not independently re-surveyed --
which is a different and weaker claim, and the section says so.
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Documentation only —
git diff --name-only master -- '*.mag'is empty.The staleness
RELATED_WORK.md's comparison table still listed three of the six genus-3 ramified cells as unbuilt,with
*none*in our column and "Future work, PR6 / PR7 / PR8" beside them. All three were derivedand merged in those very PRs — the odd-characteristic doubling in #30, both characteristic-2 formulas
in #32. The arb doubling figure was stale too, quoted at 61 M+S / 3C / 92A where it has measured
58 / 4C / 80A since the PR36 sweep.
That is the worst kind of stale for this particular file, because it is the one a reader opens to find
out where the work stands against the literature — and it said we had no entry in three of the four
cells that have competition. In fact we are ahead on both axes in all four:
The same staleness appeared in prose in both lane sections — "the doubling comparison still cannot be
made until
nch2_ramifiedG3_DBL.magexists" and "we have no entry in this lane yet" — and theBirkner reconciliation was still written as something PR7/PR8 would do, where it was decided on
2026-08-24 to be a publication task rather than a repository one. All corrected.
The README gains a "Related work" section
The comparison against prior art is the first thing a reader wants, and it was previously reachable
only by opening a second file. It now sits in the README with the table above, and four caveats travel
with it rather than being left to be discovered:
†marks A counts we derived, not figures the authors published — no prior work in this areareports additions at all.
Cis zero in every previous-best cell, because those normal forms leave no coefficient tomultiply by. It is non-zero only for us and only in
arb, which cannot normalise — so that row's 1Cand 4C are the price of generality.
addition was inherited.
deg h = 3. Cheaper numbers exist at otherh-shapes and are notcomparable — Birkner's
h = 1doubling is 21 M+S, but a constanthcollapses most of the work.The harder target is quoted in every row: GKP is 70 M+S for both odd-characteristic operations against
Nyukai's 67 and 68, and their alternative char-2 variants are 68 and 72 against the 67 and 69 shown.
What moved, and what did not
Operation counts keeps what is about provenance — every row measured, and the 168 published cells
the counter reproduces — and hands the comparison material to the new section. The
arbfamily'scomparison against the thesis's own split Degree-3 rows moved with it: 12 better on M+S, 11 on C and
16 on A for the addition, 18 / 15 / 21 for the doubling, which is what "ramified has strictly less to
do than split" predicts and which was not true when this work started.
Every margin was re-derived from the measured figures rather than carried across, and checked
arithmetically. The underlying counts come from
verification/opcount.py, which executes the formulasrather than reading a table.
Verification
Docs only, so the gates that apply are the static ones:
check_paths --strict(259 references),readme-paths(91 paths across 6 READMEs), andruff. No formula, tester or tool is touched.Update: all four families, not just genus-3 ramified
The section originally covered genus-3 ramified only, since that is the family the thesis defers. The
other three already have published comparisons — in the thesis itself — so the README was telling a
quarter of the story in the place a reader looks first. All four are now there:
Every "This work" row was re-derived from
verification/opcount.pyand matches. Thirteen rowsacross the three thesis comparison tables — five genus-2 ramified, four genus-3 split, four genus-2
split — every one exact. This is not redundant with PR41's check: the cost tables and the comparison
tables are separate transcriptions of the same quantities, and a transcription is where a copy error
hides. It found none.
One limitation stated rather than glossed: those three comparisons are as published in 2020, and no
search for work appearing since has been done. Only the genus-3 ramified survey is current, having been
compiled in 2026. So the three thesis rows are re-verified against our own measurements, not
independently re-surveyed — a weaker claim, and the section says so.