A Candidate Transformation-Stable Signature for Touch Written by Sound

This is a proposal, not a discovery. Mid-air ultrasound haptics writes a touch onto the skin by modulating a 40 kHz carrier; thefelt signal is the modulation envelope, delivered by amplitude (AM), lateral or spatiotemporal (STM) modulation, and the mapfrom waveform to felt percept is many-to-one. We ask, within the Watabe-Claude Method (WCM) used as atransformation-invariant reader, what quantity is stable across the family of waveforms intended to be percept-equivalent. Weare explicit about what is and is not observed: we measure waveform -> toy mechanoreceptor responses -> 24-cell occupancygeometry, and we do NOT measure human perception. Accordingly we do not claim a perceptual invariant; we propose acandidate transformation-stable mechanoreceptor-geometry signature and a program to test whether it corresponds toperception. In a how-possibly simulation, four percept-equivalence families are read three ways: an occupancy cosine vector, aB4 multicomponent decomposition, and a plain four-channel energy fraction (a differentiation control). The plain readerseparates the families entirely marginally (unchanged by a phase-randomization that preserves each channel's spectrum butdestroys cross-channel structure). The 24-cell readers are not marginal, and the stable part is carried by the B4 sign_balancecomponent -- the signed pattern of receptor co-activation. Under a label-shuffle outer-null it is significant in all threenormalizations (p = 0.0005, 0.0010, 0.0005) and loses significance when cross-channel structure is destroyed (p = 0.067, 0.712,0.236). Critically, we test the reader's own gauge: the signature survives the 24-cell's symmetry group (axis permutation andsign flip) but collapses under arbitrary orthogonal rotation and receptor mixing (p rising to 0.12), so it is a property of thereceptor-anchored frame the geometry is built for, not of an arbitrary coordinate choice. It is also robust to ablation of theleast-established (Ruffini/SA2) axis. We state plainly that the central missing link is human psychophysics, and we preregisterthe experiments -- perceptual equivalence, coordinate-gauge, family-transfer, and surrogate-hierarchy tests -- that wouldpromote this candidate to, or refute it as, a perceptual invariant. ※ The license for codes is AGPL3.0-or-later