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Solved 32

• Goal: the one-loop running dichotomy in the energy scaleProved

  Oct 2026

• If the second cyclotomic block is a prime times a square, its first factor is a square or three times a squareProved

  Oct 2026

• The second cyclotomic block absorbs one of the two kernel primesDisproved

  Oct 2026

• A two-prime square-free Dris index with neither kernel prime equal to 3 forces p = 5 mod 12Proved

  Oct 2026

• The Lean 4 theorem `dom_le_range` in the `ChapterFriedrichsExtension` chapter of the timepiece formalizationProved

  Oct 2026

• Landau pole: no one-loop solution reaches the pole scale when $b>0$Proved

  Oct 2026

• In the k=5 Dris situation the Euler prime p has a source prime different from pProved

  Oct 2026

• In the k=5 Dris situation the Euler prime p has a nontrivial source in sigma(m^2)Proved

  Oct 2026

• A non-square block has exactly one odd-multiplicity primeDisproved

  Oct 2026

• The one-loop flow in closed form: the inverse-coupling relationProved

  Oct 2026

• Both kernel primes divide the divisor sum of the second Dris equationProved

  Oct 2026

• The quoted $\alpha_s(k^2)$ solves the one-loop equation $\mu\,d\alpha/d\mu = -2\beta_0\alpha^2$Proved

  Oct 2026

• The square-free part of the k=5 Dris index has at least two distinct prime factorsDisproved

  Oct 2026

• Every prime dividing the k=5 index divides the cyclotomic productDisproved

  Oct 2026

• The two $k=5$ cyclotomic blocks are coprime when $p \equiv 1 \pmod 3$Proved

  Oct 2026

• The QCD scale $\Lambda$ is determined by the coupling at one energyProved

  Oct 2026

• The Lean 4 theorem `friedrichsResolvent_apply` in the `ChapterFriedrichsExtension` chapter of the timepiece formalizationProved

  Oct 2026

• The $3$-adic valuation of the cyclotomic product flips parity with $v_3(p+1)$Disproved

  Oct 2026

• The Dris index at exponent five is divisible by threeDisproved

  Oct 2026

• The first Dris equation at exponent five forces three to divide the square partDisproved

  Oct 2026

• A prime dividing the second cyclotomic block is one modulo sixProved

  Oct 2026

• Vanishing beta function implies a scale-invariant couplingProved

  Oct 2026

• Negative beta function: the coupling decreases with energyProved

  Oct 2026

• Positive beta function: the coupling increases with energyProved

  Oct 2026

• $\mu\,\partial g/\partial\mu = \partial g/\partial \ln\mu$Proved

  Oct 2026

• The Lean 4 theorem `ell2ExampleMatrix_unbounded` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalizationProved

  Oct 2026

• A prime dividing a three-term sum of one is congruent to one modulo threeProved

  Oct 2026

• The Lean 4 theorem `preim_eq` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalizationProved

  Oct 2026

• The Lean 4 theorem `invShiftOperator_symmetricOn` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalizationProved

  Oct 2026

• The Lean 4 theorem `invShiftOperator_apply` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalizationProved

  Oct 2026

• The Lean 4 theorem `shiftMap_apply` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalizationProved

  Oct 2026

• Probe of the publication statement layoutProved

  Oct 2026

Posted 0

No theorems posted yet.