PASS: first tetrahedron equation
PASS: second tetrahedron equation
PASS: first moment equation
PASS: second moment equation
PASS: mixed orientation is strict
PASS: no zero or forbidden shapes
PASS: folded tangent identity
PASS: exact imaginary-part identity at G(re=Fraction(1, 2), im=Fraction(3, 8))
PASS: exact imaginary-part identity at G(re=Fraction(32, 25), im=Fraction(-24, 25))
PASS: isotropic moment rows
PASS: full moment row rank
PASS: mixed tangent rank drops
PASS: joint Jacobian has rank three
PASS: universal folded syzygy f2=-x1^2 f1
PASS: outgoing triangle branch factor
PASS: incoming triangle branch factor
PASS: face bigon branch factor
PASS: Euler tetrahedron half-face product
PASS: opposite-root signs (0, 1)
PASS: opposite-root signs (0, 2)
PASS: opposite-root signs (0, 3)
PASS: vertex central branch factor 0
PASS: vertex central branch factor 1
PASS: vertex central branch factor 2
PASS: vertex central branch factor 3
PASS: Lagrangian squares unchanged
PASS: two self-glued face pairs: every vertex has two arrivals/departures
PASS: two self-glued face pairs: half-face product at 0
PASS: four parallel faces: every vertex has two arrivals/departures
PASS: four parallel faces: half-face product at 0
PASS: four parallel faces: half-face product at 1
PASS: loops with parallel faces: every vertex has two arrivals/departures
PASS: loops with parallel faces: half-face product at 0
PASS: loops with parallel faces: half-face product at 1
PASS: original PP common scalar takes c_B=-i to 1
PASS: shape factor for original-to-default vertex

All exact checks passed.
The rank lemma, signed geometric lift, and quotient conclusions are proved in the note.
No test count is used as a measure of mathematical significance.
