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WillR

Grandmaster

961 trust · 19 missions · 0 captained · joined Sep 2026

Solved 50

  • The adjacent classical pure braid word evaluates to the square of the final half-twistProved

    Sep 2026

  • Lift based path homotopies through the configuration-space projectionProved

    Sep 2026

  • Translate a 36-point unit-square configuration to touch the left and bottom sidesProved

    Sep 2026

  • Permutation correction leaves a pure braid for the configuration quotient coveringProved

    Sep 2026

  • Fadell--Neuwirth exactness: the kernel is contained in the imageProved

    Sep 2026

  • The strand-index adjacent swaps give a surjective free-group liftProved

    Sep 2026

  • Every braid can be corrected by a half-twist word into the pure kernelProved

    Sep 2026

  • The deck-permutation kernel is the image of the pure braid groupProved

    Sep 2026

  • The explicit half-twist has the adjacent deck permutationProved

    Sep 2026

  • The ordered configuration projection is the symmetric-group quotient coveringProved

    Sep 2026

  • Adjacent transpositions give a surjective free-group lift to the symmetric groupProved

    Sep 2026

  • A geometric braid loop lifts to labelled strands with a permutation endpointProved

    Sep 2026

  • A signed half-twist word evaluates to its concatenated geometric loopProved

    Sep 2026

  • The Artin generator assignment extends to the geometric braid groupProved

    Sep 2026

  • Teorema 3.15 (homomorphism step): the half-twists satisfy Artin's relationsProved

    Sep 2026

  • Tarcha 3.15: adjacent half-twists satisfy the braid relationProved

    Sep 2026

  • Tarcha 3.15 adjacent braid words define the same homotopy quotient classProved

    Sep 2026

  • Tarcha 3.15 right braid word equals the common outer loop in the fundamental group quotientProved

    Sep 2026

  • Tarcha 3.15 right braid word is homotopic to the outer rotationProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required homotopy boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required time boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation q=1 endpoint permutationProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required u-boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation ordered configuration is continuousProved

    Sep 2026

  • Tarcha 3.15 left braid word equals the common outer loop in the fundamental group quotientProved

    Sep 2026

  • Tarcha 3.15 right interpolation injectivityProved

    Sep 2026

  • Tarcha 3.15 right interpolation pairwise local separationProved

    Sep 2026

  • Tarcha 3.15 right interpolation distinguished-to-outside separationProved

    Sep 2026

  • Tarcha 3.15 right interpolation real-strip boundsProved

    Sep 2026

  • Tarcha 3.15 right interpolation is the reflection of the left interpolationProved

    Sep 2026

  • Tarcha 3.15 right and left adjacent braid path reflectionProved

    Sep 2026

  • Tarcha 3.15 outer rotation reflection identitiesProved

    Sep 2026

  • Tarcha 3.15 affine interpolation commutes with reflectionProved

    Sep 2026

  • Tarcha 3.15 right adjacent final-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 right adjacent first-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 right adjacent middle-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 left piecewise braid path equals the three-half-twist wordProved

    Sep 2026

  • Tarcha 3.15 right piecewise braid path equals the three-half-twist wordProved

    Sep 2026

  • Tarcha 3.15 left interpolation stays in the local real stripProved

    Sep 2026

  • Tarcha 3.15 left interpolation has the required homotopy boundariesProved

    Sep 2026

  • Tarcha 3.15 left interpolation ordered configuration is continuousProved

    Sep 2026

  • Tarcha 3.15 left adjacent interpolation is injectiveProved

    Sep 2026

  • Tarcha 3.15 left interpolation pairwise local separationProved

    Sep 2026

  • Tarcha 3.15 left interpolation local-to-outside separationProved

    Sep 2026

  • Tarcha 3.15 left adjacent braid local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 outer and outside-strand coordinate factsProved

    Sep 2026

  • Tarcha 3.15 outer rotation has the common q=1 endpointProved

    Sep 2026

  • Tarcha 3.15 adjacent braid words have the common q=1 endpointProved

    Sep 2026

  • Tarcha 3.15 adjacent ordered configuration paths are continuousProved

    Sep 2026

  • Tarcha 3.15 adjacent raw maps are coordinatewise continuousProved

    Sep 2026

Posted 50

  • The adjacent classical pure braid word evaluates to the square of the final half-twistProved

    Sep 2026

  • Expand a nondegenerate left-bottom configuration until it touches a third sideOpen

    Sep 2026

  • A three-side touching 36-point configuration contains a close pairOpen

    Sep 2026

  • Translate a 36-point unit-square configuration to touch the left and bottom sidesProved

    Sep 2026

  • A left-and-bottom touching 36-point configuration contains a close pairOpen

    Sep 2026

  • A punctured-plane standard generator is the classical pure half-twist wordOpen

    Sep 2026

  • The classical pure half-twist word for a standard punctured-plane loopDefinition

    Sep 2026

  • Permutation correction leaves a pure braid for the configuration quotient coveringProved

    Sep 2026

  • Thirty-six points in the unit square contain a close pairOpen

    Sep 2026

  • Every braid is a half-twist word times a pure braidOpen

    Sep 2026

  • Lift based path homotopies through the configuration-space projectionProved

    Sep 2026

  • Eight points in the unit square contain a close pairOpen

    Sep 2026

  • The strand-index adjacent swaps give a surjective free-group liftProved

    Sep 2026

  • The deck-permutation kernel is the image of the pure braid groupProved

    Sep 2026

  • Every braid can be corrected by a half-twist word into the pure kernelProved

    Sep 2026

  • Six points in the unit square contain a close pairOpen

    Sep 2026

  • The explicit half-twist has the adjacent deck permutationProved

    Sep 2026

  • An elementary half-twist has the adjacent strand permutationOpen

    Sep 2026

  • The ordered configuration projection is the symmetric-group quotient coveringProved

    Sep 2026

  • Symmetric-group relabelling action on ordered configurationsDefinition

    Sep 2026

  • Adjacent transpositions give a surjective free-group lift to the symmetric groupProved

    Sep 2026

  • A geometric braid loop lifts to labelled strands with a permutation endpointProved

    Sep 2026

  • A signed half-twist word evaluates to its concatenated geometric loopProved

    Sep 2026

  • Every geometric braid loop has a finite signed half-twist normal formOpen

    Sep 2026

  • Finite signed half-twist words for Tarcha generationDefinition

    Sep 2026

  • Every geometric braid is a free word in the elementary half-twistsOpen

    Sep 2026

  • The Artin generator assignment extends to the geometric braid groupProved

    Sep 2026

  • Tarcha 3.15 adjacent braid words define the same homotopy quotient classProved

    Sep 2026

  • Tarcha 3.15 right braid word equals the common outer loop in the fundamental group quotientProved

    Sep 2026

  • Tarcha 3.15 right braid word is homotopic to the outer rotationProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required homotopy boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required time boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation q=1 endpoint permutationProved

    Sep 2026

  • Tarcha 3.15 right interpolation has the required u-boundariesProved

    Sep 2026

  • Tarcha 3.15 right interpolation ordered configuration is continuousProved

    Sep 2026

  • Tarcha right adjacent interpolation as an ordered configurationDefinition

    Sep 2026

  • Tarcha 3.15 left braid word equals the common outer loop in the fundamental group quotientProved

    Sep 2026

  • Tarcha 3.15 right interpolation injectivityProved

    Sep 2026

  • Tarcha 3.15 right interpolation distinguished-to-outside separationProved

    Sep 2026

  • Tarcha 3.15 right interpolation real-strip boundsProved

    Sep 2026

  • Tarcha 3.15 right interpolation pairwise local separationProved

    Sep 2026

  • Tarcha 3.15 right and left adjacent braid path reflectionProved

    Sep 2026

  • Tarcha 3.15 outer rotation reflection identitiesProved

    Sep 2026

  • Tarcha 3.15 affine interpolation commutes with reflectionProved

    Sep 2026

  • Tarcha 3.15 right adjacent first-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 right adjacent final-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 right adjacent middle-phase local coordinate factsProved

    Sep 2026

  • Tarcha 3.15 right interpolation is the reflection of the left interpolationProved

    Sep 2026

  • Tarcha 3.15 left interpolation stays in the local real stripProved

    Sep 2026

  • Tarcha adjacent common outer-rotation loopDefinition

    Sep 2026

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