Dancing on the Sun: A loop count that reads through holonomy, and the current it finds flowing in both polarities

We read winding numbers of the horizontal magnetic field on SDO/HMI SHARP vector magnetograms (hmi.sharp_cea_720s) and ask what such a count can see and what the instrument does to it. Round 2,941 loops on strong rims followed through two X-class flares (NOAA 11166 and 11158), not one count changed. Near disk centre,
the vertical electric current in strong field has a component of the same sign in both magnetic polarities, which the Sun’s own physics cannot make: a polarity-even “offset” beside the polarity-odd twist. It was predicted and found blind twice (24 of 26 and 45 of 50 regions) and is reproduced by a small azimuth rotation of the reported transverse field, about 3 degrees, of opposite sense in the two polarities, made in the instrument’s frame: about 4 degrees about the line of sight and about none about the local vertical, which is why it fades toward the limb. The loop count reads through that rotation (31 of 154,267 counts move, all at near-reversal steps), while every current takes it in full; a director-field count that ignores the 180-degree disambiguation has the opposite blind spot, and its half-integer residues come in nearest-neighbour pairs of opposite sign. Three further blind tests on fifteen regions followed day by day across the disk, from 2011 to 2024, found the rotation’s sign the same in both solar cycles but its size not one number (one number, one map and three maps each fail to fix it), two large regions of 2024 changing its sign across the meridian, and one region of 2015 turning the other way by tens of degrees; all are left as open walls with their numbers. SHARP’s published MEANJZD reproduces our mean current to a ratio of 1.000 on maps of 2011 to 2024 and carries the rotation’s upward part; TOTUSJZ does not; SAVNCPP carried it on 82 regions and not on six others. Fitting HMI’s own Stokes I, Q, U and V with a textbook Milne-Eddington inversion, the reported azimuths differ from ours by an S-shaped few degrees flipping with polarity; a mis-modelled magneto-optical (Faraday) term gives the rotation’s size and sign flip but not its shape, and the pipeline’s Stokes weights and eta0 regularisation move nothing. Every number is printed by a tool that ships with the paper, with every prediction fixed and fingerprinted before its maps were fetched. A companion to The Latch Atlas. Preprint, not peer reviewed; the literature pass is limited and stated.

Keywords: SDO/HMI; SHARP; vector magnetogram; winding number; loop count; holonomy; phase unwrapping; residues; 180-degree ambiguity; azimuth; vertical electric current; current neutralization; MEANJZD; SAVNCPP; TOTUSJZ; Milne- Eddington inversion; VFISV; magneto-optical effects; Faraday rotation; Stokes parameters; systematic error; blind test; preregistered prediction; solar active regions; sunspots; X-class flare; NOAA 11158; NOAA 11166; solar cycle 25; NOAA 13664; NOAA 13842; NOAA 12297; half-integer defects; director field