Metadata
bibkey: cfmp2026degree10star
authors: trureturing contributors
year: 2026
title: An explicit degree-ten high edge in a three-star packet
doi: null
url: https://github.com/the-omega-institute/trureturing/pull/11568
claim: Paper proof of one explicit orientable three-star degree-eight packet triangulation with high degrees 10 and 38, realized by a heterogeneous shared-edge co-volume box.
license: citation-only
triage: anchor
strata_touched: []
The proof and pairing table are in docs/develop/theory/CFMP_DEGREE10_STAR.md.
This is outside the previous three-edge degree-eight/high-at-least-twelve
result: six degree-eight global classes remain a three-star in every
16-tetrahedron, while the other classes have degrees ten and 38.
The global cosh box is [11/8,2] on degree-eight edges, [11/10,71/50] on the degree-ten edge, and [1009/1000,21/20] on degree-38 edges. Exact endpoint squares are checked by verify_degree10_star.py and audit_degree10_bounds.py. Degree-eight cosine bounds are 143/200 below and 35941/50941 above. Degree-ten upper endpoint is 19195sqrt(880915135)/704732108, whose square is 1842240125/2818928432 < cos(pi/5)^2. For degree 38, the two actual high/low coordinate patterns have the same relaxed upper endpoint 4489sqrt(8216635)/13146616, with square 100755605/105172928 < cos(pi/19)^2; the lower endpoint uses 1982/2009 > cos(pi/19) via rational Taylor bounds.
The generalized incidence condition is: every degree-ten occurrence has at least one high neighbour of degree at least 38; its other high neighbour may have degree 10 or at least 38. The explicit example has six degree-ten occurrences with two degree-38 neighbours and four with one degree-10 and one degree-38 neighbour.
The finite topology verifier checks coherent orientation, one circular edge link per edge class, no reversed edge, six degree-eight classes, the degree ten incidence placement, and vertex links (16,6,-2),(48,10,-14). The endpoint verifier enumerates all formula-coordinate stabilizers exactly with rational squares.
This is a restricted explicit realization theorem, not arbitrary minimum-eight CFMP, and does not claim a general degree-ten packet criterion.