3746 — The Full Quadratic Source Forbids a Nontrivial Selector Projector
Commutant no-go
On one irreducible oscillator parity sector, the commutant of the full quadratic metaplectic action consists only of scalars. Its only orthogonal projectors are therefore zero and the identity.
The finite-grade selector (P_{2,4}) is a subspace projector, not a superselection projector. Quadratic raising and lowering cross its two boundaries, giving
Constructor trilemma
The Figueiredo survival condition ([W,P]=0) can be met only by restricting the admissible operation algebra or by adding a new blockwise superselection label. Retaining the complete quadratic source forbids nontrivial (P). Restricting to its Gaussian stabilizer leaves only diagonal controls and loses coherent preparation and complementary readout.
Thus the established magnetic endpoint algebra cannot simultaneously supply the selector, preserve it, and execute its complete four-capability instrument.
Evidence
research/strominger/the-full-quadratic-source-forbids-a-nontrivial-selector-projector.md;research/strominger/checkers/full_quadratic_commutant_selector_no_go_checks.py;research/strominger/results/full_quadratic_commutant_selector_no_go_checks.json.
The exact checker passes 8 of 8 gates and finds scalar commutants for every
tested parity-chain dimension from two through ten. Checker SHA-256:
d665f42c2c5abbb888f3417bfd88f6be9ac16fcc7891c63a0706327c45108032.
Allocator claim: seqclaim-abd6b19c5dbac252a1e166cb.