Preprints
Our papers and data deposits in one place — 13 papers, 14 data deposits. Every item is permanently archived on Zenodo (CERN) with a DOI; this page is the reading room, Zenodo is the vault. Also on arXiv: 2 of the 13 papers, marked with their arXiv identifier. New items and new versions: Atom feed (one entry per deposit, dated by its newest version).
Papers are written articles with full text (PDF); data deposits hold data, code and computation logs, described in their README. Dates in the lists below are those of the first deposit; titles are shown as on Zenodo.
Papers
- Turk's head knots with at least three leads and three bights are not perfectly straight
Werner Alois Stanggassinger · 2026-10-26 · PDF · doi:10.5281/zenodo.23659578 · knot theory, Turk's head knots, weaving knots, straight number, semi-meander diagrams, flyping theorem - Positive amphichirality of Turk's head knots: the orders of the maps
Werner Alois Stanggassinger · 2026-10-26 · PDF · doi:10.5281/zenodo.23659958 · knot theory, Turk's head knots, amphichirality, strongly positive amphichiral, symmetry group, periodic maps - A certified census of spiral knots: no satellites and no coincidences in a finite range
Werner Alois Stanggassinger · 2026-10-26 · PDF · doi:10.5281/zenodo.23660571 · knot theory, spiral knots, weaving knots, hyperbolic knots, satellite knots, verified computation - Two of Jabłonowski's candidate inequalities hold for all prime knots with at most 18 crossings
Werner Alois Stanggassinger · 2026-10-22 · PDF · doi:10.5281/zenodo.23566264 · Rasmussen s invariant, HOMFLY polynomial, four-ball genus, knot tables, computer-assisted proof, knot theory - The symmetry group of the Turk's head knots Th(p,2)
Werner Alois Stanggassinger · 2026-10-22 · PDF · doi:10.5281/zenodo.23562743 · knot theory, Turk's head knots, two-bridge knots, amphicheiral knots, hyperbolic knots, symmetry group - Prime knots with twisted Alexander vanishing order 24 up to 19 crossings
Werner Alois Stanggassinger · 2026-10-22 · PDF · doi:10.5281/zenodo.23570037 · knot theory, twisted Alexander polynomial, twisted Alexander vanishing order, symmetric group, knot tables, computer census - The symmetry group of Turk's head knots
Werner Alois Stanggassinger · 2026-10-08 · PDF · doi:10.5281/zenodo.23234787 · arXiv:2610.16600 · knot theory, Turk's head knots, weaving knots, symmetry group, alternating knots, flyping theorem - Conway polynomials of Th(p,q) and Th(q,p): a proof of Takemura's conjecture
Werner Alois Stanggassinger · 2026-10-06 · PDF · doi:10.5281/zenodo.23183920 · arXiv:2610.32269 · knot theory, Conway polynomial, Alexander polynomial, Turk's head knots, Takemura's conjecture, reduced Burau representation - Vol-Det, Fox, Hoste and a conjecture of Hirasawa–Murasugi for all prime alternating knots with at most 19 crossings
Werner Alois Stanggassinger · 2026-10-05 · PDF · doi:10.5281/zenodo.23156040 · knot theory, alternating knots, Vol-Det conjecture, Fox's trapezoidal conjecture, Hoste's conjecture, Alexander polynomial - The degree of the Alexander polynomial of twisted torus knots for every s
Werner Alois Stanggassinger · 2026-10-05 · PDF · doi:10.5281/zenodo.23155383 · knot theory, Alexander polynomial, twisted torus knots, braids, Burau representation, degree - Hoste's condition for all Turk's head knots
Werner Alois Stanggassinger · 2026-10-05 · PDF · doi:10.5281/zenodo.23154788 · knot theory, Alexander polynomial, Turk's head knots, Hoste's conjecture, reduced Burau representation, weaving knots - The Alexander plateau of a two-bridge knot is carried by one coherent twist region
Werner Alois Stanggassinger · 2026-10-03 · PDF · doi:10.5281/zenodo.23117903 · knot theory, two-bridge knots, Alexander polynomial, Fox trapezoidal conjecture, Hirasawa-Murasugi conjecture, signature - The leading coefficient of the Alexander polynomial of twisted torus knots
Werner Alois Stanggassinger · 2026-09-15 · PDF · doi:10.5281/zenodo.22769534 · twisted torus knots, Alexander polynomial, leading coefficient, fibered knots, monic Alexander polynomial, convex hull
Data deposits
- The Apprentice Folder (workshop kit): a working procedure for an AI tool in an existing environment
Werner Alois Stanggassinger · 2026-11-06 · doi:10.5281/zenodo.24005142 · AI collaboration, working procedure, laboratory notebook, knowledge management, reproducibility, Claude Code - θ detects chirality for all prime knots up to 14 crossings — and first fails at 15: the chiral θ-trivial knots 15nh_048139 and 15nh_048140
Werner Alois Stanggassinger · 2026-11-01 · doi:10.5281/zenodo.23856098 · knot invariants, chirality, amphichiral knots, Bar-Natan–van der Veen Theta, two-loop polynomial, knot census - OEIS A343358 extended: a(14) = 17,831 and a(15) = 74,581 connected realizable circle graphs, with the graphs themselves
Werner Alois Stanggassinger · 2026-11-01 · doi:10.5281/zenodo.23855791 · OEIS A343358, circle graphs, Gauss diagrams, interlacement graphs, alternating knots, mutant knots - The positive 3-braid knots σ₁³σ₂³σ₁⁶σ₂⁶ and σ₁³σ₂⁵σ₁³σ₂⁷ are not concordant
Werner Alois Stanggassinger · 2026-10-30 · doi:10.5281/zenodo.23808250 · knot concordance, positive braids, 3-braids, Casson–Gordon invariants, twisted Alexander polynomial, SnapPy - knot-identification-pipeline: knot type of closed space curves from their geometry
Werner Alois Stanggassinger · 2026-10-29 · doi:10.5281/zenodo.23766950 · source code · knot theory, knot identification, space curves, Fourier knots, knot invariants, GPU - Grid diagrams of nontrivial knots: a(9) and a(10) of OEIS A163566
Werner Alois Stanggassinger · 2026-10-26 · doi:10.5281/zenodo.23660288 · knot theory, grid diagrams, Alexander polynomial, arc index, OEIS, GPU enumeration - Boninger's Conjectures 1.1, 1.6 and 1.7 hold for all prime alternating knots with at most 19 crossings: a computer check
Werner Alois Stanggassinger · 2026-10-03 · doi:10.5281/zenodo.23118923 · knot theory, alternating knots, Alexander polynomial, Boninger polynomial, M-convexity, log-concavity - The Andersen–Kashaev volume conjecture for 220 knots beyond the 14-crossing census of Ben Aribi, Guilloux and Wong
Werner Alois Stanggassinger · 2026-09-26 · doi:10.5281/zenodo.22975395 · knot theory, Andersen-Kashaev volume conjecture, Teichmüller TQFT, FAMED triangulation, ideal triangulation, hyperbolic knot - Symmetric ribbon numbers: r_s(12n706) = 4, a candidate for 12n504, and a computed subset of R^s_5
Werner Alois Stanggassinger · 2026-09-22 · doi:10.5281/zenodo.22893039 · knot theory, symmetric ribbon number, symmetric union, ribbon knot, labeled knotoid diagram, Alexander polynomial - Theta on constructed Conway-mutant pairs: thirty separated, one not
Werner Alois Stanggassinger · 2026-08-15 · doi:10.5281/zenodo.21946255 · knot theory, Conway mutation, mutant knots, pretzel knots, Theta invariant, Bar-Natan - Lower bounds for the unknotting number over a corpus of built curves
Werner Alois Stanggassinger · 2026-08-14 · doi:10.5281/zenodo.21933898 · unknotting number, lower bounds, Nakanishi index, Rasmussen s-invariant, tau invariant, signature - Congruences on the Conway polynomial forced by Conant's Corollary 7.3: an answer to the first half of Question 9.2
Werner Alois Stanggassinger · 2026-07-26 · doi:10.5281/zenodo.21596227 · knot theory, Conway polynomial, amphicheiral knots, Kawauchi conjecture, congruences modulo powers of two, Conant Corollary 7.3 - Priority deposit v5: 338 positive amphicheiral hyperbolic knots whose Conway polynomial does not split -- Part III, order 16 and a discrepancy in the rotation parameter
Werner Alois Stanggassinger · 2026-07-25 · doi:10.5281/zenodo.21590760 · knot theory, amphicheiral knots, Conway polynomial, Kawauchi conjecture, rotary reflection, Fourier knots - Priority deposit: c7 inequality at 14/15 crossings, Knot 15331 bounds, and a blind Farey/precessing-ellipse knot atlas
Werner Alois Stanggassinger · 2026-07-15 · doi:10.5281/zenodo.21389680 · knot theory, Kauffman polynomial, HOMFLY polynomial, a-spread, torus knots, Farey sequence