Joint-support analysis on (γ=6, T_1=(m_1=3, antipodal, SP), T_2=(k_2=3, no chord, SP)):
T_1's σ_D space = 18 elements (half of Latin set's 36; saturation-
threshold violated by m_1=3 < γ=6). T_2's σ_U space = 84 elements.
The two are intrinsically disjoint on γ, AND S_3-closure of T_1's
outer-ring colorings is already saturated (all 6 permutations
realised) — so abstract Kempe modification on the outside cannot
enlarge T_1's γ-support. The failure is A-IRREDUCIBLE in the
strict Birkhoff sense.
Significance: the SP failure cases aren't 4CT-relevant obstructions
but modeling artifacts. SP treats non-triangular O-faces as single
G-faces, which is incompatible with maximal-planar G. A faithful
maximal-planar G further triangulates these faces, changing the
face-connector and enlarging σ-supports.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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