372 Math Papers, Zero Engine Features

A model screen of 372 one-line OpenAI math index rows found four candidates for mojo-baro's engine and none survived, and the checks that exist came earlier, from claims built out of single papers and tested against oracles, not from the screen.

Four candidates came out of 372 OpenAI math result families. All four were rejected. The corpus gave mojo-baro no engine feature. It gave newera checks, but those came before the screen and by a different method. This post records the screen, the rejections, and the dates that stop us crediting the screen with checks it did not produce.

The screen was wide and shallow

The corpus is an index file in openai-math-checks, docs/papers-index.tsv (commit cf93bef), with one line per result family: 372 families. Three model passes read the rows in blocks of 124. Each pass was told not to open any paper, to skip nine families already ruled out (017, 110, 111, 122, 124, 125, 238, 107, 128), and to flag a row only if it could give mojo-baro an implementable algorithm, a usable explicit number, or a cheap certificate. The brief is .work/speed/briefs/paper-screen.md, and the three outputs sit beside it in .work/speed/out/paper-screen-*.md.

A model screen over one-line summaries is cheap and wide. It is also shallow, and most of the work in this post was finding out how shallow.

The passes returned three, none and one candidate. The middle block, rows 125 to 248, flagged nothing, but its output lists near misses with explicit numbers and no home: an exact DFT below n log n with a delta of 10^-13 (family 130, galactic, and mojo-baro has no FFT), an Ising threshold of tanh(beta) at most (d-1)^(-1/2) (236, no sampler uses it), and a switch chain bound of O(n^8) (131). An empty list did not mean an empty block.

Four candidates, four rejections

Family	Result	Why it died
090	Triangular lattice minimizes energy per particle for completely monotone potentials	A density-limit statement, not a finite-n constant. The hexagonal lattice is already the optimal 2D quantizer, and weights and KV caches are high-dimensional. No gain we can quantify.
116	Deterministic polynomial-size matrix tuple detecting nonzero noncommutative formulas	"Polynomial-dimensional" and "polynomial bit time" with no exponent. Freivalds already covers our matmul checks. Galactic for a check run on every matmul.
118	Bin-packing round-up conjecture disproved	A negative result with no algorithm. It is a warning: an LP round-up bound cannot promise a small gap for expert packing.
325	Complete Crouzeix inequality, constant 2	The constant is explicit. No inference operator in mojo-baro is a matrix polynomial, so the bound has no caller.

Family 325 is the cleanest case: it has a number and no home. One honest limit on the table. The screen's brief forbade opening papers, and we hold no receipt of a full read for these four. Each rejection rests on the index description and on what the engine runs.

The closest miss was read in full

Family 125 was the one we wanted, and it was one of the nine skipped in advance. The Brain vault needs clusters, and a metric k-median approximation looks like a tool for that. We read its two preprints on 2026-10-21. The main result is a (1+2/e+eps) approximation. Its LP rounding yields k + c_eps facilities, and removing the surplus needs a Li-Svensson enumeration of n^{O(c/eta)} candidates (preliminaries.tex, lines 58 to 63). Delta and c depend on eps only through existence.

The companion result is randomized and runs local search over O(N^10) swap pairs (local.tex, line 39), with constant C_0 = 10 + 60000 * 2^3999 (line 388). Solving the LP alone on Brain vectors needs |F| * |J| variables, which is 4e8 for 20,000 notes. Family 125 adds a threshold proof and no algorithm. Brain clustering stays with k-means++ and swap local search, the methods we already had. It was the sixth of six round-two "daily use" papers to die at the read step.

Screen wide for a reading list, and decide only after the full read.

What the corpus did give: checks, earlier

It is tempting to say the screen's real yield was a Float64 log reference and a set of vero claims. The dates rule that out. The screen ran on 2026-10-21. flog landed in newera on 2026-10-14 (4a726f7), and the four vero claims landed on 2026-10-17. Neither came from the screen.

flog came from a difftest. A vero golden claim sat a constant 2.6e-10 below its Python oracle, and the cause was Mojo 1.1's std.math.log. Against a correctly rounded oracle (Python decimal, 40 digits) over 40,315 inputs, it is correctly rounded on 14.4%, off by up to 2.1e7 ulp on normal numbers, and wrong on all 5,008 subnormals: log(5e-324) returns -709.09, not -744.44. The replacement is the fdlibm algorithm as kept in musl, correctly rounded on 98.2% of log inputs and never more than 1 ulp off. tests/check_flog.sh plants two bugs, a dropped k * ln2_lo term and a skipped subnormal rescale, and requires both to fail. Scope note: our record from 2026-10-15 says the nightly 1.2.0.dev2026101405 fixed log (within 0.67 ulp) and not log2 (22.4M ulp). We did not rerun that today.

The four vero claims, heavylight, saturate, packing and hill, each take a lemma from one paper, the planar Schrodinger endpoint-convergence paper dated 2026-09-24. All pass the gate in interpreted and compiled modes (9287d44, 751845e, 35b8836, f6fa6cb). heavylight has 3 named mutants and 36 generated ones killed by value, with 24 equivalent.

Two of the claims had gate lies on the way. The saturate grid killed four generated mutants by division by zero, which proved nothing about the check. Shifting every coordinate by +100 fixed it, and d08fa3d reports 4 named and 38 generated killed by value. The dense AG(2, 5) check in packing used the constants s = 5 and o = 1 instead of measuring them, so a broken plane() passed unnoticed. 1b0f032 measures them, and generated kills rose from 70 to 85. A loose_overlap mutant for packing was dropped because it changed the experiment and not the decoder.

What counts:

An explicit constant at a finite size the engine runs, with an operator that calls it.
A full read of the paper body before the verdict.
A check that fails on a planted bug, and a mutant that dies by value.

What does not count:

An existence or asymptotic statement with no constant.
A model pass that flags nothing, read as proof that nothing is there.
A candidate with a number and no caller.

What it cost

The screen cost three passes, and it bought a list of four rejections and a retraction. The checks that exist cost a paper's lemmas each, written as claims and run against mutants. That is the trade the title hides: width found nothing, and depth (claims written from one paper's lemmas and tested against an oracle) found four claims and a library bug, and we cannot say how many families a deeper pass over the other 368 would also yield.

The screen's reach is small. The four rejections rest on index text. The three passes skipped nine families that earlier reads had ruled out, and the screen never saw them. A family rejected on its index line may hold a usable result deeper in, and we have not measured how often that happens. No GPU was used.

How to prove this wrong

The verdict covers this index and mojo-baro's current operators. It does not say that no math result helps LLM inference. To defeat it, open the papers behind the four rejected rows and the 368 unflagged ones, and look for a family whose paper gives an explicit constant at a finite size this engine runs, plus an operator that would call it. Send us the family number and the line in the paper. Until that read is done, the verdict is narrower than the title: nothing usable in this index, judged by its index lines.

Provenance

Screen of 2026-10-21 (outputs in .work/speed/out/paper-screen-*.md). Index commit cf93bef in openai-math-checks. Newera commits: 4a726f7 (flog), 9287d44, 751845e, d08fa3d, 35b8836, 1b0f032, f6fa6cb (vero claims). Toolchain for flog figures: Mojo 1.1.0. Paper for the vero claims: planar Schrodinger equation endpoint convergence, OpenAI, 2026-09-24.