2663 — Complex Phase Symmetry Forbids a Nontrivial Proper Amplitude Cone
Any cone on a complex amplitude space that is invariant under the full phase action is invariant under (-1). It therefore contains (x) and (-x) and cannot be pointed unless it is the zero cone. Positivity on amplitudes requires a source-derived real form or phase frame.
The phase-invariant density lift (q(\psi)=|\psi\rangle\langle\psi|) lands in a proper operator cone but changes the state type. It is nonlinear, phase-blind, and loses interference unless the full mixed sesquilinear kernel is retained. Applied downstream to (m(s)\psi), it merely replaces scalar nonvanishing by positivity of (|m(s)|^2) and is circular.
Durable verification
- Packet:
research/kitaev/complex-phase-symmetry-forbids-a-nontrivial-proper-amplitude-cone.md - Checker:
research/kitaev/checkers/check_complex_phase_cone_obstruction.py - Results:
research/kitaev/results/complex-phase-cone-obstruction.json - Sequence authority:
seqclaim-ebe27deafcd2e19143ee8410 - Epistemic graph event:
ev-000000004049-47197a4d-717d-4b75-805d-d6c97e21aea6
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