Primitive period comparison and smaller skew Schur probes

We exclude primitive least-common-multiple comparisons of source-minimal nonline inners in empty-mark skew Schur compositions with ribbon outers. The proof treats both orientations and recovers literal motifs in the parallel case, without lower-area induction. Under strict discrete-interior entry hypotheses, we also construct equal proper ribbon-outer probes of strictly smaller area from positive ordinary comparison charts with a nonribbon source inner and uniform ribbon candidate inventory. Complete signed high identities give primitive polynomial rays, and a two-window calculation recognizes actual ribbons after the required endpoint words have been identified. Lower rooted transport converts these constructions into a conditional period obstruction. Residue grading, Hall tails, and an imported original-determinant theorem give further scoped comparison consequences. Chart restoration and equal-period marked-key recognition remain separate obligations.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23665232
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Primitive period comparison and smaller skew Schur probes

John Shields
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Primitive period comparison and smaller skew Schur probes

John Shields
preprint en

Abstract

We exclude primitive least-common-multiple comparisons of source-minimal nonline inners in empty-mark skew Schur compositions with ribbon outers. The proof treats both orientations and recovers literal motifs in the parallel case, without lower-area induction. Under strict discrete-interior entry hypotheses, we also construct equal proper ribbon-outer probes of strictly smaller area from positive ordinary comparison charts with a nonribbon source inner and uniform ribbon candidate inventory. Complete signed high identities give primitive polynomial rays, and a two-window calculation recognizes actual ribbons after the required endpoint words have been identified. Lower rooted transport converts these constructions into a conditional period obstruction. Residue grading, Hall tails, and an imported original-determinant theorem give further scoped comparison consequences. Chart restoration and equal-period marked-key recognition remain separate obligations.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
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