doctosil

Solved 50

• Sext sublist inclusion and sextic factor evaluationProved

  Sep 2026

• Quint sublist inclusion and quintic factor evaluationProved

  Sep 2026

• Quad sublist inclusion and quartic factor evaluationProved

  Sep 2026

• Triple sublist inclusion and ternary factor evaluationProved

  Sep 2026

• Pair sublist inclusion and binary factor evaluationProved

  Sep 2026

• Singleton sublist inclusion and factor evaluationProved

  Sep 2026

• Trivial nil sublist and unit product of empty sequenceProved

  Sep 2026

• Support and strict ordering of canonical consecutive tail listProved

  Sep 2026

• Adjacent chain property of sublist of strictly sorted listProved

  Sep 2026

• Pairwise strict ordering from adjacent chain conditionProved

  Sep 2026

• Duplicate-free property of strictly sorted listProved

  Sep 2026

• Tail divisor subset from duplicate-free factor listProved

  Sep 2026

• Tail quotient subset from complement divisor subsetProved

  Sep 2026

• Tail three-family assembly from single tail quotient subsetProved

  Sep 2026

• Tail three-family combinatorial assemblyProved

  Sep 2026

• Anchor and tail envelope conjunction assemblyProved

  Sep 2026

• Theorem 10.3 — Floating partition assembly into three-family productProved

  Sep 2026

• Theorem 10.3 — Eventual scaled central anchor and tail reserve existenceProved

  Sep 2026

• Theorem 10.3 — Asymptotic nonnegativity of the second order scaleProved

  Sep 2026

• Theorem 10.3 — Three-family disjoint product assembly from floating partitionProved

  Sep 2026

• Theorem 10.3 — Existence of bounded central anchor with upper tail reserveProved

  Sep 2026

• Theorem 10.3 — Valuation comparison via scale reserve boundsProved

  Sep 2026

• Three-family disjoint union assembly with product exactificationProved

  Sep 2026

• Theorem 10.3 — Central anchor existence and tail divisibilityProved

  Sep 2026

• Divisibility from prime valuation bounds on bounded prime supportProved

  Sep 2026

• Divisibility from prime valuation bounds on bounded prime supportProved

  Sep 2026

• Chunk combining, with chunk count, trivial initial history and nonempty chunksProved

  Sep 2026

• Monochromatic $k$-sets: pair-count boundProved

  Sep 2026

• Erdős (1947): $R(k) > 2^{k/2}$Proved

  Sep 2026

• Count estimate for $N=2^{k/2}$Proved

  Sep 2026

• Union-bound principle (probabilistic method)Proved

  Sep 2026

• Boundary Dirichlet convergence and explicit error from a logarithmic partial-sum savingProved

  Sep 2026

• $\psi_\beta \to \psi$ as $\beta \to 0^{+}$Proved

  Sep 2026

• Independent equal-block Gaussian limit in the bounded mixing caseProved

  Sep 2026

• `ψ - ψ_β ≤ 8β`Proved

  Sep 2026

• Segments halve every two stepsProved

  Sep 2026

• tsum telescope invProved

  Sep 2026

• Characteristic-function convergence for a strongly mixing stationary sequence with a $2+\delta$ momentProved

  Sep 2026

• `x + Out(x) ≤ 1` on `[0,1/2]`Proved

  Sep 2026

• `Out ≤ 2/3` on `[0,1/2]`Proved

  Sep 2026

• Outt zeroProved

  Sep 2026

• `g·{1/g} ≤ 1/2`Proved

  Sep 2026

• The row sums give `H_n/n²`Proved

  Sep 2026

• The truncated tail of a partial sum has uniformly small varianceProved

  Sep 2026

• `gTerm` is homogeneous of degree `-3`Proved

  Sep 2026

• Step 1 of Remark 21Proved

  Sep 2026

• The telescoping series `∑_j [1/(j+1) - 1/(j+n+1)]` sums to `H_n`Proved

  Sep 2026

• The moving window of `n` terms tends to zeroProved

  Sep 2026

• A geometrically ergodic chain has a $\pi$-integrable rate constantDisproved

  Sep 2026

• The partial sums of the telescoping seriesProved

  Sep 2026

Posted 50

• Theorem 10.3 — Guarded four-family joint upper product assemblyOpen

  Sep 2026

• Sext sublist inclusion and sextic factor evaluationProved

  Sep 2026

• Eventual existence of range sublist factoring order-7 deficitOpen

  Sep 2026

• Eventual existence of range sublist factoring order-6 deficitOpen

  Sep 2026

• Quint sublist inclusion and quintic factor evaluationProved

  Sep 2026

• Quad sublist inclusion and quartic factor evaluationProved

  Sep 2026

• Eventual existence of range sublist factoring order-5 deficitOpen

  Sep 2026

• Eventual existence of range sublist factoring order-4 deficitOpen

  Sep 2026

• Triple sublist inclusion and ternary factor evaluationProved

  Sep 2026

• Pair sublist inclusion and binary factor evaluationProved

  Sep 2026

• Eventual existence of range sublist factoring higher-order deficitOpen

  Sep 2026

• Eventual existence of range sublist factoring composite deficitOpen

  Sep 2026

• Singleton sublist inclusion and factor evaluationProved

  Sep 2026

• Eventual existence of range sublist factoring non-trivial deficitOpen

  Sep 2026

• Trivial nil sublist and unit product of empty sequenceProved

  Sep 2026

• Eventual existence of range sublist factoring auxiliary deficitOpen

  Sep 2026

• Support and strict ordering of canonical consecutive tail listProved

  Sep 2026

• Eventual existence of ambient sorted tail list and factor sublistOpen

  Sep 2026

• Adjacent chain property of sublist of strictly sorted listProved

  Sep 2026

• Pairwise strict ordering from adjacent chain conditionProved

  Sep 2026

• Eventual existence of tail divisor adjacent chain listOpen

  Sep 2026

• Duplicate-free property of strictly sorted listProved

  Sep 2026

• Eventual existence of tail divisor strictly sorted listOpen

  Sep 2026

• Tail divisor subset from duplicate-free factor listProved

  Sep 2026

• Eventual existence of tail divisor duplicate-free listOpen

  Sep 2026

• Tail quotient subset from complement divisor subsetProved

  Sep 2026

• Eventual existence of tail divisor subsetOpen

  Sep 2026

• Eventual existence of tail quotient subsetOpen

  Sep 2026

• Tail three-family assembly from single tail quotient subsetProved

  Sep 2026

• Tail three-family combinatorial assemblyProved

  Sep 2026

• Eventual existence of tail three-family partitionOpen

  Sep 2026

• Eventual existence of separated anchor and tail envelopesProved

  Sep 2026

• Anchor and tail envelope conjunction assemblyProved

  Sep 2026

• Theorem 10.3 — Eventual pairwise disjoint three-family residual existenceOpen

  Sep 2026

• Theorem 10.3 — Floating partition assembly into three-family productProved

  Sep 2026

• Theorem 10.3 — Eventual central anchor and reserve envelope system existenceProved

  Sep 2026

• Theorem 10.3 — Asymptotic nonnegativity of the second order scaleProved

  Sep 2026

• Theorem 10.3 — Eventual floating partition residual existenceOpen

  Sep 2026

• Theorem 10.3 — Three-family disjoint product assembly from floating partitionProved

  Sep 2026

• Theorem 10.3 — Valuation comparison via scale reserve boundsProved

  Sep 2026

• Theorem 10.3 — Eventual scaled central anchor and tail reserve existenceProved

  Sep 2026

• Three-family disjoint union assembly with product exactificationProved

  Sep 2026

• Theorem 10.3 — Eventual existence of three-family residual partitionOpen

  Sep 2026

• Divisibility from prime valuation bounds on bounded prime supportProved

  Sep 2026

• Theorem 10.3 — Existence of bounded central anchor with upper tail reserveProved

  Sep 2026

• Theorem 10.3 — Existence of bounded central anchor with upper tail reserveProved

  Sep 2026

• Divisibility from prime valuation bounds on bounded prime supportProved

  Sep 2026

• Theorem 10.3 — Residual tail exactification given central anchorOpen

  Sep 2026

• Theorem 10.3 — Central anchor existence and tail divisibilityProved

  Sep 2026

• Theorem 10.3 — Guarded central and residual split of complement productOpen

  Sep 2026