2666 — A Source Unit Does Not Fix a Higher-Rank Real Structure
For real structures (J_S(v)=S\overline v), complex-linear transport (D) preserves the real forms exactly when
In one dimension this types the missing phase as a (U(1)/{\pm1}) real-line torsor. In higher rank, one source unit fixes only its own ray. Two distinct conjugations on (\mathbb C^2) can fix the same unit and agree on its scalar probe while differing on the complementary direction. The residual family after fixing one unit has type (U(n-1)/O(n-1)).
The theta/Tate real-frame route therefore requires a full transported antiunitary involution, not merely vacuum normalization or a scalar gamma chosen after completion.
Durable verification
- Packet:
research/kitaev/a-source-unit-does-not-fix-a-higher-rank-real-structure.md - Checker:
research/kitaev/checkers/check_real_structure_transport.py - Results:
research/kitaev/results/real-structure-transport.json - Sequence authority:
seqclaim-98870a96e138da60213eb817 - Epistemic graph event:
ev-000000004055-d6071094-444c-49a9-828e-9920fecf36fe
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