Geometric Acoustics
A geometric-topology framework that maps the vibration modes of a square plate onto the Lo Shu grid, so mirror positions sing the same pitch and a detuned element announces itself.
Physics is established. The diagnostic is the proposal. Every claim on this page carries its status.
Chladni plate physics: sand patterns reveal nodal modes.
On an ideal simply-supported square plate, transpose mode pairs (m,n)<->(n,m) are exactly frequency-degenerate (f ∝ m²+n²).
Verified model result: uniform shifts cause zero mirror drift — the check does not false-alarm on global drift.
The Lo Shu allocation as a diagnostic grid: mirror pairs matched, center = fundamental (1,1).
Detection: mirror drift beyond a per-plate CALIBRATED tolerance flags a detuned or dead element.
Localization: the drift signature narrows the fault to a symmetry class (up to 8 positions); both plate diagonals are covered by a calibrated absolute-frequency companion check; unique pinpointing requires an asymmetric driver/sensor layout or a scan — state this plainly, it is a feature of our honesty, not a weakness.
Hilbert-ordered transducer layout (locality, shorter analog traces) and a toroid ring array (360° steering, acoustic vortices) reuse the same geometric backbone as our FPGA power topology.
Detectable detune: ~3.6% mass at 0.5% frequency noise; ~0.15% at 0.02%.
Class-localization: 93-100% of seeded runs at 4x the detection floor.
Blind spots: both plate diagonals (x=y and x+y=1) — companion required.
Real plates split degeneracies; the tolerance is calibrated per plate.
Every correction public, every model reproducible. Read the one-pager amendment and the verification log.