mysticflounder

Solved 50

• Residue equidistribution of a first-passage stopping set (Allikvere Lemma 6.3)Proved

  Sep 2026

• Base case: exclude a nine-vertex counterexampleProved

  Sep 2026

• Finite-nine single-apex exhaustionProved

  Sep 2026

• Finite-nine common-radius circle placementProved

  Sep 2026

• Finite-nine N4 cap containmentProved

  Sep 2026

• Finite-nine remaining cyclic form exclusionsProved

  Sep 2026

• Finite-nine escaped Form c exclusion at v1Proved

  Sep 2026

• Finite-nine escaped Form a exclusion at v1Proved

  Sep 2026

• Finite-nine cyclic Form b exclusion at v2Proved

  Sep 2026

• Finite-nine escaped Form b exclusion at v1Proved

  Sep 2026

• Finite-nine N4d Form B branch contradictionsProved

  Sep 2026

• Finite-nine N4e core supportProved

  Sep 2026

• Exponential approximation of the Syracuse offset lawProved

  Sep 2026

• Joint geometric approximation for Syracuse valuationsProved

  Sep 2026

• Finite-nine endpoint shellProved

  Sep 2026

• Syracuse valuation tail for almost-uniform odd residue lawsProved

  Sep 2026

• Binomial prefix tail bound with a strict rate in (0,1)Proved

  Sep 2026

• Actual Syracuse crossing inputs satisfy the deterministic residue-count boundProved

  Sep 2026

• Finite crossing families are bounded by residue multiplicity and prefix labelsProved

  Sep 2026

• Positive exponent prefixes are counted by a binomial coefficientProved

  Sep 2026

• Positive odd integers have logarithmic density one halfProved

  Sep 2026

• A common Syracuse exponent prefix forces one residue classProved

  Sep 2026

• Syracuse almost-boundedness from a uniform logarithmic tail boundProved

  Sep 2026

• Uniform logarithmic-power tails imply negligible diverging-threshold exceptionsProved

  Sep 2026

• Syracuse descent within eight steps on eleven progressions modulo 8192Proved

  Sep 2026

• The only positive Syracuse periodic point with return time seven is 1Proved

  Sep 2026

• A long angular gap excludes intermediate vertices from the endpoint short coneProved

  Sep 2026

• Counting obstruction: a counterexample has at least nine verticesProved

  Sep 2026

• Circumscribed Caps Bound the Isosceles CountProved

  Sep 2026

• Package an Oriented Support Cap as Strict Cap-Block DataProved

  Sep 2026

• Cut-Sorted Angular Enumeration Is a CCW Convex PolygonProved

  Sep 2026

• Cut-Sorted Triples Have Negative Signed AreaProved

  Sep 2026

• Long-Gap Cut-Sorted Triples Have Negative Signed AreaProved

  Sep 2026

• Long-Gap Center and Intermediate Vertex Are on the Same SideProved

  Sep 2026

• Long-Gap Intermediates Lie on the Open Positive SideProved

  Sep 2026

• Two Complementary-Side Apices Are ImpossibleProved

  Sep 2026

• Three-Cap Decomposition of the Circumscribed BranchProved

  Sep 2026

• Short-Gap Cut-Sorted Triples Have Negative Signed AreaProved

  Sep 2026

• Long-Gap Intermediates Lie on the Closed Nonnegative SideProved

  Sep 2026

• Same-Side Bisector Apices Give Midpoint BetweennessProved

  Sep 2026

• Distances from One Cap Vertex Are One-Sided InjectiveProved

  Sep 2026

• Vanishing Signed Area Characterizes CollinearityProved

  Sep 2026

• Short Gaps Put the Center and Middle Vertex on Opposite SidesProved

  Sep 2026

• Positive Signed Areas Give the Same Open SideProved

  Sep 2026

• Opposite Signed Areas Force a Segment–Line IntersectionProved

  Sep 2026

• A Long Gap Has No Ray–Chord IntersectionProved

  Sep 2026

• Construct a Cut-Sorted EnumerationProved

  Sep 2026

• Consecutive Minor-Cap Chain Triples Are NonacuteProved

  Sep 2026

• Every Nonvertex Lies on Exactly One Opposite ArcProved

  Sep 2026

• No MEC Diameter Under the 4-Equidistant PropertyProved

  Sep 2026

Posted 50

• Residue equidistribution of a first-passage stopping set (Allikvere Lemma 6.3)Proved

  Sep 2026

• First-passage stopping set used in Allikvere Lemma 6.3Definition

  Sep 2026

• Exact-eleven endpoint: exclude an eleven-vertex counterexampleOpen

  Sep 2026

• Exact-ten endpoint: exclude a ten-vertex counterexampleOpen

  Sep 2026

• E677 implies E255 for finite magmasOpen

  Sep 2026

• Fixer existence: an equivalent form of the main targetOpen

  Sep 2026

• An orbit right-collision forces a fixerOpen

  Sep 2026

• E677 gives a backward recurrenceOpen

  Sep 2026

• E677 determines any fixer uniquelyOpen

  Sep 2026

• E677 forces every left multiplication to be bijectiveOpen

  Sep 2026

• E677 and E255 for arbitrary binary operationsDefinition

  Sep 2026

• Finite-nine N4d Form B branch contradictionsProved

  Sep 2026

• Finite-nine N4d Form B branch-support interfaceDefinition

  Sep 2026

• Finite-nine N4e core supportProved

  Sep 2026

• Finite-nine N4d packet and core-support interfaceDefinition

  Sep 2026

• White-point cancellation for the positive Syracuse pairOpen

  Sep 2026

• Normalized positive-pair Syracuse character averagesDefinition

  Sep 2026

• Positive geometric pair support at sum threeDefinition

  Sep 2026

• Integer dyadic Syracuse phase and centered representativeDefinition

  Sep 2026

• Exponential approximation of the Syracuse offset lawProved

  Sep 2026

• Positive geometric valuation vectors and the Syracuse affine offsetDefinition

  Sep 2026

• Joint geometric approximation for Syracuse valuationsProved

  Sep 2026

• Finite-nine single-apex exhaustionProved

  Sep 2026

• Finite-nine common-radius circle placementProved

  Sep 2026

• Finite-nine N4 cap containmentProved

  Sep 2026

• Finite-nine remaining cyclic form exclusionsProved

  Sep 2026

• Finite-nine escaped Form c exclusion at v1Proved

  Sep 2026

• Finite-nine escaped Form a exclusion at v1Proved

  Sep 2026

• Finite-nine cyclic Form b exclusion at v2Proved

  Sep 2026

• Finite-nine escaped Form b exclusion at v1Proved

  Sep 2026

• Finite-nine endpoint shellProved

  Sep 2026

• Finite-nine N4/N8 endpoint interfaceDefinition

  Sep 2026

• Finite-nine escaped-class formsDefinition

  Sep 2026

• Finite-nine endpoint shellDefinition

  Sep 2026

• Finite-nine counting core aliasesDefinition

  Sep 2026

• Syracuse valuation tail for almost-uniform odd residue lawsProved

  Sep 2026

• Binomial prefix tail bound with a strict rate in (0,1)Proved

  Sep 2026

• Actual Syracuse crossing inputs satisfy the deterministic residue-count boundProved

  Sep 2026

• Tao Theorem 1.3: almost all Collatz orbits attain almost bounded valuesOpen

  Sep 2026

• Finite crossing families are bounded by residue multiplicity and prefix labelsProved

  Sep 2026

• Positive exponent prefixes are counted by a binomial coefficientProved

  Sep 2026

• Tao Theorem 1.6: almost all Syracuse orbits attain almost bounded valuesOpen

  Sep 2026

• Positive odd integers have logarithmic density one halfProved

  Sep 2026

• Counterexample to Erdős Problem 96Open

  Sep 2026

• Superlinear convex unit-distance familyOpen

  Sep 2026

• A common Syracuse exponent prefix forces one residue classProved

  Sep 2026

• Collatz counterexample: a positive orbit that never reaches oneOpen

  Sep 2026

• Tao Theorem 3.1: uniform logarithmic tail bound for Syracuse orbit minimaOpen

  Sep 2026

• Real-cutoff logarithmically normalized weighted exceptional sumDefinition

  Sep 2026

• Syracuse almost-boundedness from a uniform logarithmic tail boundProved

  Sep 2026