The Canonical Local Singular Series on Primorial Lattices: Strict Decrease, Crossing Structure, and the Plateau Conjecture

v1.0.3 (2026-09-15): new Section 7.5 certifies the previously open k=5000 case (two-segment pipeline, 306/306 locking points now all certified; O-9 numerical layer closed). New Section 7.6 / Theorem 21 gives an explicit crossing-point constancy bound |s_exact - s_model| <= (E_1w+E_3w+A_pert,w)(1+eta)(1+eps_Q^max) = 0.33906 x 1.2730 = 0.43160694 < 0.5 for k in [100, 2e7], with a five-constant table and PROVEN error-propagation skeleton. Zero renumbering of Theorems 1-20; zero grade upgrades (Plateau Conjecture remains OPEN). Full manuscript, 45+ scripts, frozen claims registers and stage ledgers S0-S7 included. Authors: Chen, Shiqiang.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22788563
Primary Topic
Polynomial and algebraic computation
Type
preprint
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preprint

The Canonical Local Singular Series on Primorial Lattices: Strict Decrease, Crossing Structure, and the Plateau Conjecture

Shiqiang Chen
Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
preprint

The Canonical Local Singular Series on Primorial Lattices: Strict Decrease, Crossing Structure, and the Plateau Conjecture

Shiqiang Chen
preprint en

Abstract

v1.0.3 (2026-09-15): new Section 7.5 certifies the previously open k=5000 case (two-segment pipeline, 306/306 locking points now all certified; O-9 numerical layer closed). New Section 7.6 / Theorem 21 gives an explicit crossing-point constancy bound |s_exact - s_model| <= (E_1w+E_3w+A_pert,w)(1+eta)(1+eps_Q^max) = 0.33906 x 1.2730 = 0.43160694 < 0.5 for k in [100, 2e7], with a five-constant table and PROVEN error-propagation skeleton. Zero renumbering of Theorems 1-20; zero grade upgrades (Plateau Conjecture remains OPEN). Full manuscript, 45+ scripts, frozen claims registers and stage ledgers S0-S7 included. Authors: Chen, Shiqiang.

Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
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