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#!/usr/bin/env python3
"""Retain a dynamical pair phase in zero-moment color reduction and audit its lift."""
from pathlib import Path
import argparse
import hashlib
import importlib.util
import json
import math
import numpy as np
from scipy.linalg import expm
CHECKS = 0
CASES = []
DEPTHS = (2, 3, 4, 5, 6, 10)
def check(condition, message):
global CHECKS
CHECKS += 1
if not condition:
raise AssertionError(message)
def close(actual, expected, message, atol=3e-10):
check(np.allclose(actual, expected, atol=atol, rtol=3e-10), message)
def unit(v):
return v/np.linalg.norm(v)
def su_generators(k):
result = []
for i in range(k):
for j in range(i+1, k):
t = np.zeros((k, k), complex); t[i, j] = t[j, i] = .5; result.append(t)
t = np.zeros((k, k), complex); t[i, j] = -.5j; t[j, i] = .5j; result.append(t)
for j in range(1, k):
diagonal = np.zeros(k); diagonal[:j] = 1; diagonal[j] = -j
result.append(np.diag(diagonal)/math.sqrt(2*j*(j+1)))
return result
def quotient_controls(rng):
generators = su_generators(3)
for sample in range(8):
r = rng.uniform(.2, 2.)
phi = rng.uniform(-3., 3.)
u = unit(rng.normal(size=3)+1j*rng.normal(size=3))
z = r*np.exp(.5j*phi)*u
w = r*np.exp(.5j*phi)*u.conj()
pair = np.r_[z, w]
density = np.array([np.vdot(z, t@z)-np.vdot(w, t.T@w) for t in generators])
close(density, 0, 'actual direct-sum color moment vanishes')
close(np.outer(z, z.conj())-np.outer(w.conj(), w), 0,
'zero-moment rank-one Hermitian density equality')
invariant = w @ z
close(invariant, r*r*np.exp(1j*phi), 'bilinear invariant retains the independent pair phase')
dr = pair/r
dphi = .5j*pair
close(np.vdot(dr, dr).real, 2, 'reduced radial metric')
close(np.vdot(dphi, dphi).real, r*r/2, 'reduced angular metric')
close(np.vdot(dr, dphi).real, 0, 'radial and angular coordinates are metric orthogonal')
close(2*np.vdot(dr, dphi).imag, 2*r, 'nonzero canonical symplectic pairing survives the free pair phase')
close(-np.vdot(pair, dphi).imag, -r*r, 'first-order canonical one-form is minus R dphi')
for t in generators:
gauge = np.r_[1j*t@z, -1j*t.T@w]
close(2*np.vdot(dr, gauge).imag, 0, 'gauge direction is symplectically null on radial tangent')
close(2*np.vdot(dphi, gauge).imag, 0, 'gauge direction is symplectically null on phase tangent')
close(np.vdot(dr, gauge).real, 0, 'radial representative is metric horizontal')
close(np.vdot(dphi, gauge).real, 0, 'symmetric pair-phase representative is metric horizontal')
rotation = expm(1j*sum(rng.normal()*t for t in generators))
close((rotation.conj()@w) @ (rotation@z), invariant, 'non-Abelian gauge orbit preserves the invariant bilinear')
charge_cases = []
for label, weights in [('exterior', (1., 2.)), ('spin-lift', (-.5, .5)),
('common-inverse-determinant', (-2., -1.)),
('mixed-determinant-branches', (1., -1.))]:
theta = .37
rotated_invariant = (np.exp(1j*weights[1]*theta)*w) @ (np.exp(1j*weights[0]*theta)*z)
total = sum(weights)
close(rotated_invariant, np.exp(1j*total*theta)*invariant, 'pair central character uses the actual specified lift')
close((weights[0]*np.vdot(z, z)+weights[1]*np.vdot(w, w))/3,
total*r*r/3, 'electric moment agrees with the reduced phase generator')
central_velocity = np.r_[1j*weights[0]*z, 1j*weights[1]*w]
difference = (weights[0]-weights[1])/2
gauge_generator = difference/(1-1/3)*(np.outer(u, u.conj())-np.eye(3)/3)
gauge_velocity = np.r_[1j*gauge_generator@z, -1j*gauge_generator.T@w]
close(central_velocity, total*dphi+gauge_velocity,
'central action splits into the measured quotient phase plus a true SU3 gauge motion')
charge_cases.append({'lift': label, 'component_weights': list(weights),
'bilinear_weight': total, 'determinant_normalized_weight': total/3})
omega = .83
time = .51
evolved_z = np.exp(-1j*omega*time)*z
evolved_w = np.exp(-1j*omega*time)*w
close(evolved_w@evolved_z, np.exp(-2j*omega*time)*invariant,
'bilinear frequency is twice the constituent field frequency under the common linear clock')
CASES.append({'case': f'normal-SU3-phase-quotient-{sample}', 'radius_r': r, 'pair_phase': phi,
'quotient_coordinate': 'B = w^T z = R exp(i phi), R = r^2',
'canonical_one_form': '-R dphi', 'canonical_two_form': '-dR wedge dphi',
'reduced_metric': '(dR^2 + R^2 dphi^2)/(2R)',
'central_characters': charge_cases,
'common_clock_bilinear_frequency_factor': 2,
'fixed_absolute_electric_charge_derived': False})
def sector_current_controls(geometry, rng):
gamma, color, residual, number = geometry.build_geometry()
parity4 = np.diag([1., -1., -1., 1.])
epsilon2 = np.array([[0., 1.], [-1., 0.]])
for d in DEPTHS:
hodge = geometry.hodge(d if d % 2 == 0 else d+1)
active = bool(np.linalg.norm(hodge)>1e-10)
check(active == (d in (3, 4)), 'phase quotient audit retains the same all-sector Hodge gate')
if d <= 4:
r = .9
phi = .4
normal = np.zeros(8, complex)
normal[4] = normal[3] = r*np.exp(.5j*phi)
spin = unit(rng.normal(size=4)+1j*rng.normal(size=4))
psi = np.kron(spin, normal)
q = np.array([np.vdot(psi, t@psi) for t in color])
j = np.array([[np.vdot(psi, g@t@psi) for t in color] for g in gamma[:d]])
close(q, 0, 'normal pair phase permits zero SU3 density on every base spinor')
close(j, 0, 'normal pair phase permits every full base spatial current to vanish')
available = True
residual_norm = None
elif d <= 6:
r = .9
z = r*unit(rng.normal(size=2)+1j*rng.normal(size=2))
w = np.exp(.4j)*epsilon2@z.conj()
normal = np.zeros(8, complex)
normal[[2, 1]] = z
normal[[6, 5]] = w
spin = unit(rng.normal(size=4)+1j*rng.normal(size=4))
psi = np.kron(spin, normal)
q = np.array([np.vdot(psi, t@psi) for t in residual])
j = np.array([[np.vdot(psi, g@t@psi).real for t in residual] for g in gamma[:d]])
close(q, 0, 'a residual SU2 density quotient exists in the actual exterior carrier')
close(j[:4], 0, 'base directions retain zero color current')
chirality = np.vdot(spin, parity4@spin).real
close(j[4]@j[4], chirality**2*r**4,
'added fifth spatial direction has an exact residual current obstruction')
if d == 6:
close(j[5]@j[5], chirality**2*r**4,
'sixth direction independently retains the residual current obstruction')
check(np.linalg.norm(j[4:])>1e-4, 'zero density alone does not satisfy the full inactive source constraints')
available = False
residual_norm = float(np.sum(j[4:]**2))
else:
available = False
residual_norm = None
CASES.append({'case': f'actual-sector-phase-quotient-depth-{d}', 'real_depth': d,
'hodge_coefficient_active': active, 'normal_algebra_dimension': 8 if d<=4 else 3 if d<=6 else 0,
'normal_SU3_pair_reduction_retains_arbitrary_base_spinor': available,
'residual_added_direction_current_norm': residual_norm,
'all_particle_charges_or_occupations_selected': False})
def main():
parser = argparse.ArgumentParser()
parser.add_argument('--geometry-source', type=Path, required=True)
parser.add_argument('--report', type=Path, required=True)
args = parser.parse_args()
spec = importlib.util.spec_from_file_location('gauss_geometry', args.geometry_source)
geometry = importlib.util.module_from_spec(spec)
spec.loader.exec_module(geometry)
rng = np.random.default_rng(2026101023)
quotient_controls(rng)
sector_current_controls(geometry, rng)
report = {'title': 'A Dynamical Zero-Color Pair Phase and Its Actual Central Character',
'sources': {'experiments/color-phase-quotient-checks.py': hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),
'experiments/hodge-gated-gauss-checks.py': hashlib.sha256(args.geometry_source.read_bytes()).hexdigest()},
'checks_passed': CHECKS, 'dependency_checks_passed': geometry.CHECKS,
'case_count': len(CASES), 'occupied_depths': list(DEPTHS),
'scope': 'explicit local commuting-amplitude zero-moment reduction and full spatial-current audit; not physical charge quantization or a particle identification',
'cases': CASES}
args.report.write_text(json.dumps(report, indent=2)+'\n')
print(f'{CHECKS} quotient and current checks plus {geometry.CHECKS} geometry checks passed across {len(CASES)} cases')
if __name__ == '__main__':
main()