The Arrow Has Two Branches: Magnetism and Gravity as the Priced and the Reversible Registration of One Arrow

Physics has used one arrow twice without naming it. The arrow of registration, the direction in which an existent is read into a record, appears once with a record kept and once with none. Magnetism keeps the record: a nanomagnet swept through its hysteresis loop sits, at zero applied field, in one of two remanent states with the same record, the two-worlds theorem in iron, and it pays for every switch; the loop constructed here has remanence 0.996 on both branches, a switching field of 0.767 against the Stoner-Wohlfarth astroid's 0.766, and a loop area that prices a thermally stable bit at 5.0 x 10^-19 J per switch, 175 times Landauer's floor. Gravity keeps none: its sources have one sign, no source stands off its locus, and a Kepler orbit integrated here returns its energy to three parts in ten million over ten revolutions and, run backwards, retraces its start to 1.5 x 10^-12. Magnetism is the priced branch and the barrier of every open row; gravity is the reversible branch and the fold of every crossed row; the two differ in cost by theorem. At structural grade the typing gives a reading of why one field was always quantized and the other has resisted: quantization is the priced registration of a bit, and a field with no off-locus point has no bit to register. No field theory is written or implied.

Version 1.4.0, single-column Math Journal edition. The Lean engines and Fortran twins are printed in the appendices with the compiler's transcript; the Markdown source is in git, 1000sapients/Trisduction, protocols/RH One Bit/Nothing Escapes Twenty Three Rows/Witnesses/.