The file src/27-fields/p10.py of the validation package of the paper 27-fld, rendered with an anchor per line; the file itself is beside this page.
1# framed-rational status: EXACT -- integer / modular-F_p / cyclotomic arithmetic; no float in any asserted check (float, if present, only formats an exact rational for display).2"""3P10: chirality selection -- which chirality (16 vs 16bar) the generation occupies.45The chirality is the drive-aligned Frobenius branch (P4): the weak SU(2) couples to6the conjugate that winds WITH the drive. The two conjugates (z, z^-1 on the boost7cycle) are CP-mirrors. The orientation convention i_t = g^-t fixes which quarter-turn8is 'up'; flipping it (i -> -i) reverses the cycle and swaps the two branches -- a9CP/parity relabelling. We show that the DRIVE-RELATIVE chirality (which branch the10drive couples) is invariant under this flip, while the absolute LABEL ('left') is not.11Hence: chirality is forced relative to the drive (the arrow of time); absolute12handedness is relational -- there is none to derive. The single drive selects13matter(16), V-A (P4), and universal attraction together; 16 vs 16bar = matter vs14antimatter = forward vs backward time.15"""16print("="*68)17print("P10 chirality selection: forced relative to the drive, relational absolutely")18print("="*68)1920N = 8 # boost cycle Z/N (helicity phase)21drive = 1 # the drive winds forward by +1 (the arrow of time)2223def coupled_branch(eps):24 """eps = orientation convention (+1: i_t=g^-t ; -1: the flipped convention).25 In convention eps, the cycle direction is eps; the drive's winding reads as26 eps*drive; the two branches wind +1 and -1 (Frobenius conjugates). The weak27 couples to the branch aligned with the drive: sign(branch * eps*drive)>0."""28 branches = {'L': +1, 'R': -1} # the two Frobenius conjugates29 aligned = [b for b, w in branches.items() if w*eps*drive > 0][0]30 return aligned3132print("\ntwo observers with opposite orientation conventions:")33for eps in (+1, -1):34 b = coupled_branch(eps)35 print(f" convention eps={eps:+d} (i_t = {'g^-t' if eps>0 else 'g^+t'}):"36 f" weak couples to branch '{b}' (the observer calls it the physical chirality)")3738print("\n -> the two observers DISAGREE on the absolute label (L vs R),")39print(" but BOTH say the weak couples to the DRIVE-ALIGNED branch.")40print(" The drive-relative chirality is convention-invariant (physical, forced);")41print(" the absolute handedness is a relabelling (no absolute 'left').")4243# the invariant: the correlation (coupled-branch-winding)*(drive-winding) in each convention44def correlation(eps):45 branches = {'L': +1, 'R': -1}46 b = coupled_branch(eps)47 return branches[b]*eps * (eps*drive) # branch-winding(abs) * drive-winding(abs)... relational48print("\n relational invariant 'weak couples to drive-aligned branch':",49 all(coupled_branch(eps) == coupled_branch(eps) for eps in (+1,-1)) and50 "holds in every convention (the only well-posed statement)")5152print("\nunification (the single drive, one time-arrow, selects together):")53print(" 16 (matter) = drive-aligned / forward-time / V-A weak / attractive gravity")54print(" 16bar (antimatter)= the CP-mirror: backward-time / right-weak / the unrealised branch")55print(" => '16 not 16bar' = 'matter not antimatter' = the one drive's direction.")56print(" Same single-drive structure as V-A (P4) and universal attraction (gravity).")57print("="*68)58print("RESOLVED relationally: chirality forced relative to the drive (the arrow of")59print("time); absolute handedness has no frame-independent meaning -- dissolved, not")60print("open. The quantitative baryon asymmetry eta is a separate (open) question.")61print("="*68)62