The Asymmetric Five-Site Period Has a Frozen Degree-Twenty-Nine Candidate Alphabet
Sequence claim: seqclaim-ce50bcec15aaa9dae1e6ab9d.
Projective coordinate
By Entry 1296 the physical period depends nontrivially only on
[ z=t/ ho. ]
Project Entries 1259--1267's complete labelled Landau census to this coordinate.
Finite candidate divisor
The soft factor is (z). The twenty proper walls collapse to fourteen distinct quadratic factors:
[
\begin{gathered}
z^2-1, z^2-14, z^2-29,
16z^2-1, 16z^2-14, 16z^2-29,
4z^2-2, 4z^2-21, 4z^2-26, 4z^2-3,
9z^2-2, 9z^2-21, 9z^2-26, 9z^2-3.
end{gathered}
]
Thus the frozen finite candidate divisor is
[ \boxed{ Delta_{ m cand}(z)
zprod_{alpha=1}^{14}f_alpha(z), \qquad degDelta_{ m cand}=29. } ]
Infinity remains a separate candidate singular point.
Higher-intersection closure
The exact source-compatible census contains
[ 245 ext{ pairs}, \qquad 1210 ext{ triples}. ]
All pair classes are either unit-resultant exclusions or specialize to already listed support. The triple census contains 1140 objects inheriting an empty pair and 70 restricted to existing total-energy support. Hence
[ \boxed{ ext{unresolved pairs}=0, \qquad ext{unresolved triples}=0. } ]
Higher active sets close by inheritance.
Physical chamber
The literal real chamber is
[ zgesqrt{29}. ]
Among the positive finite thresholds, only (z=sqrt{29}) lies on its boundary; every other positive threshold is strictly below it. They remain relevant to analytic continuation.
Proper use
(Delta_{ m cand}) is a predeclared denominator alphabet for exact telescoper reconstruction. It is not a theorem that every factor is a genuine singularity of the integrated period. Cancellations are allowed; adjoining a new factor after fitting is prohibited.
Next falsifier
Search for a relation
[ sum_{k=0}^{r}p_k(z)partial_z^kOmega_{C_5}
d_uXi ]
using only poles supported on (Delta_{ m cand}=0) and infinity. Bound (r), polynomial degree, and pole order before reconstruction. Certify any solution by exact substitution in the localized Kummer algebra.