HLV-LAYER-ORIGIN-004–006: Locked Numerical Gates for Native Plaquette Structure, Common-Origin Compatibility, and Antiunitary Hodge Symmetry

HLV-LAYER-ORIGIN-004–006 contains the locked computational notebooks and complete numerical result archives for Gates 004–006 of the HLV Layer-Origin programme. These gates continue the pre-specified investigation of whether a layered geometric construction derived from the HLV host can generate progressively stronger structures relevant to an intrinsic geometric origin of gauge and spin-like degrees of freedom. The archive contains the locked Colab notebook and corresponding result package for each gate: Gate 004: tests native plaquette/local geometric structure required for subsequent holonomy constructions. Gate 005: investigates whether the surviving native structures provide the stronger common-origin compatibility required by the programme rather than merely imposed geometric organization. Gate 006: tests a native Hodge/antiunitary route based on the oriented local two-dimensional structure, including the candidate �, the condition �, compatibility of the native local operator with the Hodge complex structure, doublet degeneracy, robustness controls, and a Golden-Carrier no-rescue identity. Gate 006 returns the locked verdict: NO_NATIVE_ANTIUNITARY_COMPATIBILITY Although the geometric complex structure � and the Golden-Carrier no-rescue identity are supported numerically, the native local operator does not exhibit the required robust Hodge/antiunitary compatibility or corresponding doublet degeneracy. The HLV branch is not distinguished from the tested controls at the required level. Accordingly, these results do not establish fermions, spin-�, �, Standard-Model gauge structure, or a continuum quantum field theory. In particular, the Gate-006 result constitutes a negative result for the specific tested route from oriented native plaquettes to an automatically emergent Kramers-like rank-two structure. The package is released to preserve the locked numerical tests, negative results, controls, and reproducibility record without post-result modification of the gate criteria. Contents: three locked Jupyter/Google Colab notebooks and three corresponding result archives for HLV-LAYER-ORIGIN-004, -005, and -006.