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Primary-source notes

Li 2026

Shana Yunsheng Li, The complete 10-tetrahedra census of orientable cusped hyperbolic 3-manifolds, arXiv:2512.02142v2, 4 March 2026.

  • Page 1, Theorem 1 certifies the complete census of orientable cusped hyperbolic manifolds with minimal 10-tetrahedron triangulations.
  • Page 2, Table 1 identifies the naming interval o10_000000 through o10_150729.
  • Page 9 states that representatives were given shortest peripheral curves, ordered, named, published, and included with SnapPy 3.3.
  • Pages 10--11, Theorem 14 and its proof certify the exceptional census. Relevant short quotation: “we cut M(alpha) into connected sum summands”.
  • Official dataset version 2.0: https://doi.org/10.7910/DVN/BFEXZA.

The official rows for this example are preserved in relevant_official_rows.txt; the complete source files are authenticated by official_manifest.json and checked by reproduce.py.

Dunfield 2020

Nathan M. Dunfield, A census of exceptional Dehn fillings, arXiv:1812.11940v2 (published 2020).

  • Section 1.1 defines slopes modulo sign and their fillings.
  • Page 8, Section 3.5 asks whether both connected-sum fillings must have a small lens-space summand. Relevant short quotation: “must both have at least one summand”.

Formalisation of the question used here:

For every relevant M and distinct slopes alpha,beta,
if M(alpha) and M(beta) are connected sums,
then each of M(alpha), M(beta) contains a prime summand in
{L(2,1), L(3,1), L(4,1)}.

Its logical negation only requires one of the two connected-sum fillings to lack every listed summand. The (1,0) filling supplies that witness.

Hoffman--Matignon 2003

James A. Hoffman and Daniel Matignon, Examples of bireducible Dehn fillings, Pacific Journal of Mathematics 209 (2003), 67--83, DOI: 10.2140/pjm.2003.209.67.

That is stronger than the negation of Dunfield's “must both” formulation. o10_069684 retains small summands in one filling and therefore does not settle the 2003 question.