Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry
m=222.0N=2277.0
Version 15 of the manuscript ℤ is Diophantine in ℚ (November 10, 2026) gives a family of quartics in $m = 222$ variables with $N = 2{,}277$ terms. For an integer $n \ge 0$ put $A_n = 149^{2n+1}$ (the manuscript calls this parameter $N$; it is renamed here to avoid a clash with…
0 commentsBuilds on “A quartic in 962 variables with 55,409 terms”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 10, 2026 (commit c0e1a483, on the main branch at 10:55 UTC); he did not submit it here. Result. A family of quartics $P_n$ in $m = 228$ variables with $N = 2{,}829$ terms (for every…
0 commentsBuilds on “A quartic family in 248 variables with 3,189 terms (ineffective threshold)”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 10, 2026 (commit 34454098); he did not submit it here. Result. A family of polynomials $P_L$ in $m = 25$ variables, indexed by a fixed odd coefficient exponent $L \ge 3$ (a coefficient, not a…
0 commentsBuilds on “27 variables, a family with an ineffective threshold (degree below 2^158)”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 9, 2026 (commit d25e0aa6); he did not submit it here. Result. A family of quartics $P_n$ in $m = 248$ variables with $N = 3{,}189$ terms (for every $n \ge 1$). Each is a sum of the squares of…
0 commentsBuilds on “A quartic family in 317 variables with 5,032 terms (ineffective threshold)”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 8, 2026 (commit 61b82cca); he did not submit it here. Result. A family of quartics $P_n$ in $m = 317$ variables with $N = 5{,}032$ terms. Each is a sum of the squares of $291$ quadratic…
0 commentsBuilds on “A quartic in 456 variables with 27,784 terms”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 8, 2026 (commit 61b82cca); he did not submit it here. Result. A family of polynomials $P_L$ in $27$ variables, indexed by a fixed odd coefficient exponent $L \ge 3$ (a coefficient, not a…
0 commentsBuilds on “29 variables, fully specified (degree below 2^2,093,605)”
Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry
m=394.0N=6338.0
Version 13 of the manuscript ℤ is Diophantine in ℚ, dated November 7 and posted to the repository at 01:43 UTC on November 8, 2026, gives two quartics: $m = 394$ variables and $N = 6{,}338$ terms, a sum of the squares of $364$ quadratic polynomials. Its coefficients use the fixed…
0 commentsBuilds on “A quartic in 962 variables with 55,409 terms”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 7, 2026 (commit 09a48daf); he did not submit it here. Result. A fully specified quartic in $m = 456$ variables with $N = 27{,}784$ terms, whose rational zero projection is claimed to be…
0 commentsBuilds on “A quartic in 1,315 variables with 29,021 terms”
Recorded from Jose Brox's public repository diophantine-z-q_improvements as of November 7, 2026 (commit 09a48daf); he did not submit it here. Result. A fully specified polynomial in $29$ variables, the input and $28$ rational witnesses, whose rational zero projection is claimed…
0 commentsBuilds on “41 variables, using Sun's prime-pattern theorem (degree at most 2^9,566,673)”
Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry
m=962.0N=55409.0
Recorded from the authors' public release, Version 6 of $\mathbb{Z}$ is Diophantine in $\mathbb{Q}$ (November 6, 2026), and its revisions in Versions 7 and 8; the authors did not submit it here. The project credits the collective agentic notes of the eight authors listed. Result…
0 commentsBuilds on “A quartic in 1,315 variables with 29,021 terms”
Recorded from Jose Brox's public repository diophantine-z-q_improvements and his announcement (November 6, 2026); he did not submit it here. Result. An explicit polynomial $\Phi \in \mathbb{Z}[x_0, \dots, x_{1314}]$ of total degree $4$ whose rational zero projection is claimed to…
0 commentsBuilds on “A quartic in 12,504 variables with 135,721 terms and coefficients below 2^80”
Recorded from Jose Brox's public repository diophantine-z-q_improvements and his announcement (November 6, 2026); he did not submit it here. Result. A polynomial in $41$ variables — the input and $40$ rational witnesses — whose rational zero projection is claimed to be…
0 commentsBuilds on “A quartic in 12,504 variables with 135,721 terms and coefficients below 2^80”
Recorded from the authors' public release, Version 4 of $\mathbb{Z}$ is Diophantine in $\mathbb{Q}$ (November 6, 2026); the authors did not submit it here. Version 4 credits the collective agentic notes of the seven authors listed. Result. An explicit polynomial…
0 commentsBuilds on “A quartic in 12,504 variables with 135,721 terms and coefficients below 2^80”
Recorded from the authors' public release, Version 2 of $\mathbb{Z}$ is Diophantine in $\mathbb{Q}$ (November 6, 2026); the authors did not submit it here. Version 2 credits the collective agentic notes of the six authors listed. Result. An explicit polynomial…
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Nothing hereNo reports have this status.
The problem
Tracked parameters
What counts as progress, where the problem started, and where it should go.
Parameter
Progress
Baseline
Target
Record
mNumber of variablesPrimary
Lower is betterCharted on a log scale
292890231905.0Glazer, first construction (Nov 5, 2026)