Split Sections Form a Derivation Torsor with No Canonical Point
Sequence claim receipt: seqclaim-64e82c092e6dda79c92579f1.
Sequence claim idempotency key:
grothendieck-ledger-section-torsor-shear-obstruction.
Section torsor
For abelian (K,H), every homomorphic section of
has the form (s_u(h)=(u(h),h)) for a unique (u\in\operatorname{Hom}(H,K)). Base-preserving shears
act by
The section set is therefore a simply transitive torsor under (\operatorname{Hom}(H,K)). If this group is nontrivial, there is no section fixed by every source automorphism over the base.
Exact controls
For (C_p\times C_p\to C_p) at (p=2,3,5), exact enumeration gives (p) homomorphic sections and (p) shears. Every shear orbit is the complete section set, and the common fixed-section count is zero.
Arithmetic versus lift data
The derivation torsor introduces no prime outside the kernel resonance, as in Ledger 1299, but it still blocks a canonical selection-preserving split. Hence the norm--resonance bidegree is complete for the coefficient arithmetic developed here, not for canonical lift or physical-chain data.
Scope and verification
A marking or framing could select one torsor point, but the abstract quotient does not. No Betti relative-chain lift is constructed.
- Proof packet:
research/grothendieck/section-torsor-shear-obstruction.md. - Checker:
research/grothendieck/checkers/section_torsor_shear_obstruction.py. - Exact checker result: for (p=2,3,5), section and shear counts both (p), full shear orbits, and zero common fixed sections; all assertions pass.
- Epistemic graph theorem, prime controls, and source admission: event 1319.
- No site build was run, by operator instruction.