3829 — The Literal G12 Residue Chain Meets Exactly Two Marked Walls
Source geometry
The exact tetrahedral Cayley–Menger matrix has loop-to-vertex lengths
(a,b,c) and opposite external edges (x,y,z). Its determinant is -2K.
After the ordered q_G12 residue, the measure depends on c^2=E^2, so the
literal Euclidean chamber uses the positive length
c=E=x+y+z.
Assume strict positive external-triangle kinematics:
x,y,z>0,
x<y+z, y<x+z, z<x+y.
Wall incidence
The signed-minor inequalities give exactly two nonempty marked-wall segments:
g1: b=y+z, x+z <= a <= y+2z,
g2: a=x+z, y+z <= b <= x+2z.
The other three marks have no literal real incidence:
g3: a+b+z=0 has no positive solution,
g23: b=x would require x>=y+z,
g31: a=y would require y>=x+z.
Sheet sequence
On the g1 interval, R1 is strictly decreasing. Its endpoint values factor
with opposite signs under the strict triangle inequalities, so it has exactly
one switch:
D_plus -> D_minus,
with residue orientation -da.
On the g2 interval, R2 is strictly increasing and likewise has exactly one
switch:
D_minus -> D_plus,
with residue orientation +db.
At (x,y,z)=(2,3,4), the switch points are
a=3 sqrt(46)/2,
b=sqrt(94).
Narrow conclusion
The literal real residue-chain incidence is now completely selected: two
oriented intervals, each split once. The algebraic five-wall Čech cocycle of
Entry 3824 remains necessary for coefficient descent, but only its g1 and
g2 walls meet the literal real chain.
This does not assign winding to the three nonincident pole walls under a further complex continuation. Such winding is a separate relative-homology datum and cannot be inferred from algebraic wall residues.
Artifacts
research/benincasa/checkers/check_rank26_literal_residue_chain_wall_segments.pyresearch/benincasa/results/rank26-literal-residue-chain-wall-segments.json
Allocator claim: seqclaim-6de630cc2f458a3a5520ab8a.