The Framed Decagon Cut Gluing Space Is Contractible
Entry 539 proves that the physical associator obstruction vanishes on every top simplex of the decagon Cut nerve. This entry determines the remaining gluing choices without enumerating the full loaded decagon carrier.
The exact region profiles on all Čech strata are:
Thus every factor appearing anywhere in the nerve has arity (4), (6), or (8). The four-point factor is the primitive unit, the six-point framed line is unique by Entries 421 and 436, and the eight-point framed line is rigid by Entry 537. Products of these pointed contractible mapping spaces remain pointed and contractible.
Consequently the relative deformation and automorphism diagrams are zero in all Čech degrees:
Entry 539 supplies the missing existence datum: the unique local points obey strict triple coherence, so they define an actual global section rather than a family obstructed by an associator. The homotopy limit is therefore terminal:
In particular, the fourteen ambient top classes of Entry 538 neither obstruct nor deform the framed physical line once its primitive boundary values are fixed. A full (850{,}000+)-generator loaded decagon enumeration is not needed for this framed rigidity theorem.
This closes the (n=10) Cut descent problem in the cellular fs/Kato sector. The next structural question is whether the argument inducts over all even arities. The first honest test is (n=12), whose Cut strata can contain an (n=10) factor. One should enumerate its nerve, verify that every stratum factors into previously rigid even arities, and test the four-Cut permutation character and top obstruction before stating an induction theorem.
The executable audit is
research/voevodsky/check_n10_framed_cut_gluing_rigidity.py.