Promotes the orbit_decomposition finding (rainbow orbit appears in 3
different (T_1, T_2) pairs, all with T_1 = (6, (0,3), SP)) into an
explicit conjecture:
Conjecture (Obs:antipodal-rainbow-conjecture):
For T = (m, (0, m/2), SP) (an antipodal-chord SP tire with m even),
π_D(C(T)) always contains the combined orbit of
(a, b, c, b, c, ..., b, c, a) under S_3 × C_m, with the a-positions
at the chord endpoints and b/c alternating elsewhere.
If true, this gives a uniform structural property of antipodal-chord
SP tires: chain pigeonhole on |γ| = m shared cycles reduces to
"π_U of the other tire meets this fixed orbit." Tested at m = 6 in
3 pairs; the m = 4 direct test (24-element conjectured orbit ⊂
36-element support) is mechanical.
Also adds a forward-pointer paragraph at the end of Obs:rainbow in
tire_fiber_step2.tex referencing orbit_decomposition.tex.
orbit_decomposition.tex: 3 pages -> 3 pages (added Conjecture section
and a "why antipodal?" paragraph).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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