ℤ is Diophantine in ℚ

Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry2026-11-10

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…

Jose Brox2026-11-10

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…

Jose Brox2026-11-10

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…

Jose Brox2026-11-09

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…

Jose Brox2026-11-08

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…

Jose Brox2026-11-08

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…

Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry2026-11-08

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…

Jose Brox2026-11-07

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…

Jose Brox2026-11-07

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…

Stefan Baranczuk, Jose Brox, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jennifer Park, Caroline Terry2026-11-06

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…

Jose Brox2026-11-06

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…

Jose Brox2026-11-06

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…

Stefan Baranczuk, Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jenn Park, Caroline Terry2026-11-06

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…

Gabe Conant, Sohail Farhangi, James Freitag, Elliot Glazer, Jenn Park, Caroline Terry2026-11-06

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…