"""Full spinorial Lie derivatives of the actual zonal count fields.""" from datetime import datetime, timezone from hashlib import sha256 from importlib.util import spec_from_file_location, module_from_spec from itertools import combinations from math import comb from pathlib import Path import json import numpy as np ROOT = Path(__file__).resolve().parent spec = spec_from_file_location('carrier', ROOT/'minimal-count-carrier.py') carrier = module_from_spec(spec) spec.loader.exec_module(carrier) COUNTS, ERRORS = {}, {} def close(actual, expected, label, tolerance=2e-10): error = float(np.linalg.norm(np.asarray(actual)-np.asarray(expected))/max(1., np.linalg.norm(expected))) if error >= tolerance: raise AssertionError((label, error)) COUNTS[label] = COUNTS.get(label, 0)+1 ERRORS[label] = max(ERRORS.get(label, 0.), error) def main(): rng = np.random.default_rng(202610120905) prepared = {d: carrier.preparation(d) for d in [2, 3, 4, 5, 6, 10]} cases = [] for name, depth, index in carrier.forward.radial.ASSIGNMENTS: alpha, beta, ambient, seed, phi = prepared[depth] eye = np.eye(len(beta)) level = index-1 h = level+depth/2 first = carrier.forward.radial.polynomial(depth, level)[1] largest = max(carrier.forward.radial.polynomial(depth, n-1)[1] for _, d, n in carrier.forward.radial.ASSIGNMENTS if d == depth) c = float(.3*first/largest) mixing = np.sqrt((1+c)/2)*eye+np.sqrt((1-c)/2)*beta normal = np.sqrt(comb(level+depth-1, depth-1)) observer = list(combinations(range(3 if depth >= 3 else 2), 2)) generators = [-.5j*alpha[a]@alpha[b] for a, b in observer] casimir = sum((g@g for g in generators), np.zeros_like(eye, dtype=complex)) close(casimir, (.75 if depth >= 3 else .25)*eye, 'the center-fixing observer rotation Casimir is three quarters for matter depths and one quarter for the depth-two circle') for generator in generators: close(np.vdot(seed, generator@seed), 0., 'balanced seed has zero mean observer generator despite a nonzero representation Casimir') for sample in range(5): position = rng.normal(size=depth+1) position /= np.linalg.norm(position) t = position[0] sine = np.linalg.norm(position[1:]) direction = position[1:]/sine frame_rotation = np.eye(depth+1) frame_rotation[0, 0] = t frame_rotation[0, 1:] = -sine*direction frame_rotation[1:, 0] = sine*direction frame_rotation[1:, 1:] += (t-1)*np.outer(direction, direction) frame = frame_rotation[:, 1:] close(frame_rotation[:, 0], position, 'the physical radial frame matches its sphere position') killing = np.sqrt((1+t)/2)*eye+1j*np.sqrt((1-t)/2)*sum(ui*al for ui, al in zip(direction, alpha)) close(killing.conj().T@beta@killing, sum(xi*ga for xi, ga in zip(position, ambient)), 'the actual Killing frame maps its grading direction to the sphere normal') v = frame[0, :] av = sum(vi*al for vi, al in zip(v, alpha)) aa, bb, ap, bp = carrier.forward.orientation.polynomials(depth, level, np.array(t)) matrix = aa*eye-1j*bb*av bare = matrix@killing@seed/normal jets = [(ap*v[i]*eye-1j*(bp*v[i]*av-t*bb*al)+.5j*matrix@al)@killing@seed/normal for i, al in enumerate(alpha)] close(-1j*sum(al@jet for al, jet in zip(alpha, jets)), h*bare, 'the actual globally related Killing value and covariant jets remain in the intended shell') for (a, b), generator in zip(observer, generators): rotation = np.zeros((depth+1, depth+1)) rotation[b+1, a+1] = 1 rotation[a+1, b+1] = -1 velocity = frame.T@rotation@position gradient = frame.T@rotation@frame covariant_transport = sum(vi*jet for vi, jet in zip(velocity, jets)) spin_term = sum(gradient[j, i]*alpha[i]@alpha[j] for i in range(depth) for j in range(depth))/4 full_rotation = 1j*(-covariant_transport-spin_term@bare) right_rotation = matrix@killing@generator@seed/normal close(full_rotation, right_rotation, 'the full spinorial Lie derivative including orbital transport intertwines exactly with the seed rotation') close(mixing@full_rotation, mixing@right_rotation, 'the same full observer rotation intertwining survives the massive count map') close(np.linalg.norm(covariant_transport+spin_term@bare), np.linalg.norm(right_rotation), 'orbital and spin connection terms are both retained in the total rotation') cases.append(dict(particle=name, depth=depth, inferred_index=index, observer_group='center-fixing Spin(3)' if depth >= 3 else 'center-fixing Spin(2)', observer_casimir='3/4' if depth >= 3 else '1/4', mean_noether_rotation='0 under the balanced seed', classification='exact full geometric transformation law, not a derived observed classical spin charge')) print(json.dumps(dict(completed=name, depth=depth)), flush=True) stamp = datetime.now(timezone.utc).strftime('%Y%m%dT%H%M%S.%fZ') sources = [Path(__file__), ROOT/'minimal-count-carrier.py', ROOT/'forward-count-action.py', ROOT/'inverse-current-radial.py', ROOT/'excited-shell-orientation-current.py'] report = dict(experiment_key='count-carrier-observer-rotation', created_utc=datetime.now(timezone.utc).isoformat(), sources={'experiments/'+p.name: sha256(p.read_bytes()).hexdigest() for p in sources}, evaluations=sum(COUNTS.values()), conditions=COUNTS, maximum_errors=ERRORS, cases=cases, limits=['the observer rotates three tangent directions about the zonal kernel center at matter depths', 'spinor columns transform as scalar-labelled spinors; another column lift changes the representation premise', 'Casimir three quarters is an exact transformation property, not a nonzero classical spin Noether charge', 'depth two has only a center-fixing rotation circle, so this does not derive photon or massive boson spin', 'literal deterministic electron orbit motion is not replaced by this internal field transformation']) path = ROOT/('count-carrier-observer-rotation-results-'+stamp+'.json') path.write_text(json.dumps(report, indent=2)+'\n') print(json.dumps(dict(report=str(path), evaluations=report['evaluations'], maximum_errors=ERRORS)), flush=True) if __name__ == '__main__': main()