LOGOS-44 / Axis Hodge Research Publication Bundle

This independent research collection brings together the Hodge Detection Filtration framework, three explicit singular-section detection benchmarks, the Q4 minimal nodal complexity preprint, and historical working versions. The central new manuscript, Hodge Detection Filtrations by Singular Sections v0.2, introduces a restriction-defined, complexity-indexed filtration on the primitive rational middle Hodge space of a smooth projective variety. The filtration records which primitive Hodge directions become detectable by restriction to singular divisors below a prescribed complexity threshold, and its graded pieces admit an equivariant representation-theoretic interpretation. The collection contains three principal benchmark calculations: Q^4 with O_Q(2), where Hodge detection is separated from ordinary nodal defect; (P^1)^4 with O(1,1,1,1), where a two-dimensional primitive Hodge sector is detected at node complexity two; (P^1)^4 with O(1,1,2,3), where the detection filtration is genuinely multistep and separates the symmetric and antisymmetric eigenspaces. The Hodge Detection Filtration is defined intrinsically through restriction kernels. Vanishing-cycle theory enters only as a secondary interpretation in the setting of the Thomas–Saito framework. The included benchmark theorems have undergone an internal line-by-line proof audit but should be regarded as proof candidates pending independent mathematical verification. This collection does not claim a proof of the Hodge conjecture. This Zenodo record is a new independent deposit and is not a new version of the earlier Q4 record. Earlier Q4 DOI identifiers are retained only as provenance. Record DOI: 10.5281/zenodo.22785894Concept DOI: 10.5281/zenodo.22785893