carlok

Solved 50

• A logarithm off the axes lies on no algebraic generalized lineProved

  Sep 2026

• The value $e^{\gamma/(i\pi)}$ is never a root of unity, for algebraic $\gamma \neq 0$Proved

  Sep 2026

• Strong four exponentials implies Diaz's modulus conjectureProved

  Sep 2026

• The real-axis half implies $\pi^2$ is transcendentalProved

  Sep 2026

• Strong four exponentials implies that no algebraic multiple of $1/(i\pi)$ is a logarithmProved

  Sep 2026

• An algebraic $\pi\,\operatorname{Im} u$ forces an algebraic multiple of $1/(i\pi)$ into $\mathcal{L}$Proved

  Sep 2026

• At a candidate, $e^{u^{2}/\bar{u}}$ is transcendentalProved

  Sep 2026

• A candidate has a four-point orbit and its rational conjugate-plane meets the modulus condition only on the axesProved

  Sep 2026

• On the torsion branch the second point of a fibre is the conjugate and the common value is realProved

  Sep 2026

• Adding the period to a point of the period plane returns to the locus only in two casesProved

  Sep 2026

• In the plane spanned by a torsion-branch candidate and its conjugate only the two axes have algebraic modulusProved

  Sep 2026

• Over the whole rational orbit the quantisation bound says exactly that Re u is non-zeroProved

  Sep 2026

• The real-generic case is equivalent to one relation: t² + π² is transcendentalProved

  Sep 2026

• A rational multiple of a failure of the one-relation form is a failure only for the multiplier plus or minus oneProved

  Sep 2026

• Two failures of the one-relation form give two real logarithms of algebraic numbers with algebraic productProved

  Sep 2026

• The unimodular part of an exponential has order dividing m exactly when m·Im v lies in πℤProved

  Sep 2026

• π² is transcendentalProved

  Sep 2026

• A period-aligned candidate makes an algebraic multiple of 1/(iπ) a logarithmProved

  Sep 2026

• A candidate is Q-bar-independent from 1 and its own conjugateProved

  Sep 2026

• Diaz's conjecture on the real and imaginary axes, given Hermite--LindemannProved

  Sep 2026

• A candidate is exactly a point of the Diaz locusProved

  Sep 2026

• $1$, $\nu$ and $p$ are $K$-independent when $p\nu$ is a non-zero element of $K$Proved

  Sep 2026

• No holomorphic stabilizer: a Möbius map over $K$ fixing a transcendental point is the identityProved

  Sep 2026

• Normalizing to the unit circle is not an arithmetic invarianceProved

  Sep 2026

• Matrix coefficients transfer along a ring hom fixing the base, and vanish togetherProved

  Sep 2026

• A logarithmic modulus forces independence, from the master dichotomyProved

  Sep 2026

• The independence upgrade at the Diaz-locus quadricProved

  Sep 2026

• Four exponentials in transcendence degree one, from the master dichotomyProved

  Sep 2026

• The candidate locus is stable under conjugation and under non-zero rational scalingProved

  Sep 2026

• Two independent candidates have a ℚ-independent conjugate quadrupleProved

  Sep 2026

• Determinantal descent in dimension two: the pencil determinant is a multiple of $x_1x_2-\rho x_0^2$Proved

  Sep 2026

• A conjugation-stable rational line has a real or imaginary generatorProved

  Sep 2026

• $1$, $u$ and $\bar u$ are linearly independent over the base fieldProved

  Sep 2026

• Balanced jets: $u^j\bar u^{\,k}\alpha$ is algebraic exactly when $j=k$Proved

  Sep 2026

• No vanishing statement over $\bar{\mathbb{Q}}$ separates a Diaz candidate from an ordinary point of its circleProved

  Sep 2026

• On either axis, an algebraic modulus forces the point itself to be algebraicProved

  Sep 2026

• Complex conjugation does not commute with multiplication by $i$Proved

  Sep 2026

• Quantisation of the real branch: a candidate with real exponential has $|u|^2 > \pi^2$Proved

  Sep 2026

• $G_u/(2r)$ is a rank-one projection: $\det G_u=0$, $\operatorname{tr}G_u=2r$, $P_u^2=P_u$Proved

  Sep 2026

• An axis-parallel pair of unequal modulus has independent coordinatesProved

  Sep 2026

• At most two points of an exponential fibre have algebraic modulusProved

  Sep 2026

• The four-point orbit of a candidate on its circleProved

  Sep 2026

• Non-real two-point fibres force $e^{\pi^2}$ transcendentalProved

  Sep 2026

• Algebraic squared distance forces an algebraic ratioProved

  Sep 2026

• Three algebraic norms force the mixed product algebraicProved

  Sep 2026

• Homogeneous exhaustion of the forced conjugation plane of a candidateProved

  Sep 2026

• The two conjugate planes meet only in the base fieldProved

  Sep 2026

• $t$ and $\bar t$ are $\mathbb{Q}$-linearly independentProved

  Sep 2026

• Coordinate ratios on a rational subspace of the quadric z1 z2 = z3 z4Proved

  Sep 2026

• Diaz 2007, Corollaire 2 (P)(1), from Roy's strong six exponentialsProved

  Sep 2026

Posted 50

• A logarithm off the axes lies on no algebraic generalized lineProved

  Sep 2026

• The value $e^{\gamma/(i\pi)}$ is never a root of unity, for algebraic $\gamma \neq 0$Proved

  Sep 2026

• Strong four exponentials implies Diaz's modulus conjectureProved

  Sep 2026

• The real-axis half implies $\pi^2$ is transcendentalProved

  Sep 2026

• Strong four exponentials implies that no algebraic multiple of $1/(i\pi)$ is a logarithmProved

  Sep 2026

• $e^{\beta/\pi}$ is transcendental for every non-zero real algebraic $\beta$Open

  Sep 2026

• No real algebraic multiple of $1/(i\pi)$ is a logarithm of an algebraic numberOpen

  Sep 2026

• Period-aligned, norm-free: no four-exponentials matrix over the certified logarithm spanOpen

  Sep 2026

• Four exponentials in transcendence degree one (Brownawell; Waldschmidt)Open

  Sep 2026

• Period-aligned, norm not a rational multiple of the aligned datum: the residual halfOpen

  Sep 2026

• Period-aligned, norm a rational multiple of the aligned datum: the four-exponentials-reachable halfOpen

  Sep 2026

• No algebraic multiple of $1/(i\pi)$ is a logarithm of an algebraic numberOpen

  Sep 2026

• An algebraic $\pi\,\operatorname{Im} u$ forces an algebraic multiple of $1/(i\pi)$ into $\mathcal{L}$Proved

  Sep 2026

• A candidate has a four-point orbit and its rational conjugate-plane meets the modulus condition only on the axesProved

  Sep 2026

• Cubic collapsibility when $a^2/3-b$ is represented by $x^2+xy+y^2$Proved

  Sep 2026

• Cubic collapsibility when every collapsing polynomial has degree $\ge 4$Open

  Sep 2026

• Irrational angle, no period translate but $\pi\,\Im u$ algebraicOpen

  Sep 2026

• Irrational angle, $\pi\,\Im u\notin\overline{\mathbb Q}+\pi^{2}\mathbb Q$: the residualOpen

  Sep 2026

• Rational rays force algebraic dependence: exclusivity in the pair dichotomyProved

  Sep 2026

• A rational combination $au+b\bar u$ lies off both rational raysProved

  Sep 2026

• The real-generic case is equivalent to one relation: t² + π² is transcendentalProved

  Sep 2026

• π² is transcendentalProved

  Sep 2026

• A rational multiple of a failure of the one-relation form is a failure only for the multiplier plus or minus oneProved

  Sep 2026

• Over the whole rational orbit the quantisation bound says exactly that Re u is non-zeroProved

  Sep 2026

• Adding the period to a point of the period plane returns to the locus only in two casesProved

  Sep 2026

• On the torsion branch the second point of a fibre is the conjugate and the common value is realProved

  Sep 2026

• In the plane spanned by a torsion-branch candidate and its conjugate only the two axes have algebraic modulusProved

  Sep 2026

• The unimodular part of an exponential has order dividing m exactly when m·Im v lies in πℤProved

  Sep 2026

• Two failures of the one-relation form give two real logarithms of algebraic numbers with algebraic productProved

  Sep 2026

• A period-aligned candidate makes an algebraic multiple of 1/(iπ) a logarithmProved

  Sep 2026

• Irrational angle, period-free: every exponential fibre meets the locus onceOpen

  Sep 2026

• Irrational angle, period-aligned: a rational multiple of u has a two-point algebraic fibreOpen

  Sep 2026

• A candidate is exactly a point of the Diaz locusProved

  Sep 2026

• A logarithmic modulus forces independence, from the master dichotomyProved

  Sep 2026

• The independence upgrade at the Diaz-locus quadricProved

  Sep 2026

• Four exponentials in transcendence degree one, from the master dichotomyProved

  Sep 2026

• Non-real two-point fibres force $e^{\pi^2}$ transcendentalProved

  Sep 2026

• Coordinate ratios on a rational subspace of the quadric z1 z2 = z3 z4Proved

  Sep 2026

• Diaz 2007, Corollaire 2 (P)(1), from Roy's strong six exponentialsProved

  Sep 2026

• A six-exponentials rank bound admits no rank-one witnessProved

  Sep 2026

• Equal-modulus chords land in the norm-one group of the coefficient fieldProved

  Sep 2026

• A distance-rigid locus has no collinear tripleProved

  Sep 2026

• The multiplier set of a point of one conjugate plane is exactly the opposite planeProved

  Sep 2026

• A conjugation-aligned transcendental admits no algebraic multiple of algebraic normProved

  Sep 2026

• An algebraic norm forbids any algebraic alignment with the conjugateProved

  Sep 2026

• Rational subspaces of singular 2x2 complex matricesProved

  Sep 2026

• Opposite conjugate planes multiply into the span of 1, u and its conjugateProved

  Sep 2026

• The two conjugate planes meet only in the base fieldProved

  Sep 2026

• A set with at most two representations of each difference is sparseProved

  Sep 2026

• A conjugation-stable rational line has a real or imaginary generatorProved

  Sep 2026