Unified Geometry Engine
Three geometric structures, three machine-checkable invariants. The math is established; the engineering benefit is a proposal we intend to test honestly.
The Lo Shu grid (294/753/618): all eight rows, columns and diagonals sum to 15. Complement pairs sum to 10; transpose pairs mirror across the main diagonal. Balance here is arithmetic — its use as a control/sense grid is a proposal.
An order-4 Hilbert path fills a 16×16 grid, visiting every cell once, with a verified locality property: cells close along the curve stay physically close. The curve math is established; its use as a ground-plane backbone is a proposal under test.
A closed circular ring of twelve harmonic spokes, centered on the board, with exact 12-fold rotational symmetry. The symmetry is arithmetic; ‘stability’ is a hypothesis until boards are measured.
Each structure is enforced by a gate script. Every gate was demonstrated to FAIL on corrupted input before it was trusted to PASS. Run log and scripts are public.
| Gate | Checks | Verified | Script |
|---|---|---|---|
| MS-Balance | 8 line sums equal; values 1..9 used once | Lo Shu PASS; corrupted grid FAIL | ms_balance_gate.py |
| Hilbert-Locality | coverage 256/256; unit steps; locality d ≤ 2√k+3 | order-4 PASS; corrupted curve FAIL | hilbert_locality_gate.py |
| Toroid-Symmetry | centering; closed ring; 12×30° symmetry; radial spokes | GTP geometry PASS; 31° spoke FAIL | toroid_symmetry_gate.py |
This page describes geometry and the scripts that check it. It does not claim measured impedance, EMI, transient or stability improvements — no boards have been fabricated yet. The GTP-FPGA-v1.0 integrated board is a blueprint awaiting pinout verification, not a product. The store sells the GTP-v3.3 Fabrication Package and the Same-Lot Measurement Kit pre-order; the Unified Geometry Engine adds no new deliverable and no new price.