Hybrid HLV Cell Architecture: Native 6D Parent-Lattice Backbones, Dual Boundary Loops, ICE-Triangle Fibres, and Non-Exact Holonomy Channels

Simulation datasets, create by Elias de Jesus Ordered Projection-Loss Memory in the HLV/HICE Cut-and-Project Carrier A Three-Build Adversarial Audit of the Native–Projected Two-History Reformulation Elias De Jesús Independent Researcher ORCID: 0009-0007-0190-9143 Collaborative working note with M. Krüger (HLV / RFP) June 2026 The consolidated HICE path-memory audit established that ordered memory is relational: it lives in the comparison of two histories, and every single-history magnitude or spectrum is order-blind. This note tests Krüger’s reformulation of HICE memory as ordered projection loss between the native parent-lattice history P6 and its projected physical shadow P∥. Four adversarial builds are reported, all reusing the existing HICE-MEM comparator operator unchanged. Build I (exact, T1): the level-2 increment record splits into a Hermitian, order-free symmetric companion Ssym = ( Ai)2 − A2 i and the anti-Hermitian order carrier Santi = i<j[Ai,Aj]; these are orthogonal under the real Hilbert–Schmidt product the comparator uses (normalised overlap ∼5 × 10−19). Symmetric-invariant matching therefore isolates the antisymmetric order residual as an algebraic identity, not a statistical procedure. Build II (T2): the single-path native–projected comparator C(6,∥) is degenerate when the connection is geometry-blind (i.i.d. per edge); under a step-keyed geometric connection projection is lossless at full resolution and degrades the ordered area only as projected resolution coarsens, order-first and beyond generic averaging. Build III (T2): when the connection is driven by the internal acceptance-window coordinate y = P⊥n, memory is preferentially lost under a projection that retains the visible coordinate, and two internal histories sharing one 3D shadow are cleanly separable natively yet confused under projection—the relational two-history signature. Order-specificity is constructiondependent and is recorded as a caveat. Build IV (T2): genuine path-level shadow-twins (distinct native paths realised as lattice translates sharing a 3D shadow) are separated natively yet confused under projection only under a geometric E⊥-coupled connection (native−projected gap +0.77); under the operator’s i.i.d. connection the path-level test is degenerate (+0.00). The consolidated claim-state is unchanged: path-memory realisable; U3-localisation bridge not established. And simulation by Pasquale Kaboth