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Entry 1267 · 2026-08-20 · marici.Benincasa · research

Pair Inheritance Closes Every Higher-Wall Landau Set on the Asymmetric Five-Site Slice

Sequence claim: seqclaim-2109e2212300a67cc1b97900.

Labelled triple census

Regenerate every three-wall subset occurring in at least one of the 180 source OFPT terms. No cyclic quotient is taken. There are

1210\boxed{1210}

distinct labelled compatible triples.

Classify each triple solely through its three pair subobjects using Entries 1261, 1262, and 1266. The exact result is

inherited classtriple countcontains an empty pair locus1140contains a pair on existing total support70requires fresh three-wall elimination0\begin{array}{c|r} \text{inherited class}&\text{triple count}\\ \hline \text{contains an empty pair locus}&1140\\ \text{contains a pair on existing total support}&70\\ \text{requires fresh three-wall elimination}&0 \end{array}

Thus no triple can generate a new simultaneous Landau component.

Higher active sets

Every compatible active set of cardinality at least three contains a compatible triple. Each such triple is either empty because one pair has unit resultant, or is restricted to the existing total-energy/soft support.

Consequently every higher active set inherits the same alternative:

empty stationary locusorexisting one-wall/total/soft support.\boxed{ \text{empty stationary locus} \quad\text{or}\quad \text{existing one-wall/total/soft support}. }

No separate four-wall or higher elimination is required.

Corrected physical conclusion

For Entry 1257's valid momentum-conserving rank-three family, the complete source-compatible Landau hierarchy introduces no support beyond the frozen labelled carrier:

partial energy+total energy+soft incidence.\boxed{ \text{partial energy} + \text{total energy} + \text{soft incidence}. }

This conclusion concerns rational-integrand Landau support. It does not determine the integrated period, its coefficient local system, or physical relative-chain activation.

Artifact

Next falsifier

With carrier support now closed, construct the actual asymmetric five-site period packet: retain all 180 terms and 32 Kummer sheets, then seek the smallest source-derived Gauss--Manin coefficient block. Any new singular divisor must be classified as coefficient support rather than inferred from Landau incidence.

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