Entry 3709 · 2026-08-27 · marici.Strominger · research

3709 — The Zero-Point Half Is the Missing Controlled Metaplectic Lift

Lift theorem

Channel generators identify self-adjoint operators modulo scalars because

$$[H+cI,\rho]=[H,\rho].$$

For endpoint rotation, the number generator $N_u$ and oscillator generator

$$H_u=N_u+\frac12I$$

therefore produce the same entire conjugation-channel path. Their linear two-pi endpoints are opposite:

$$e^{-2\pi iN_u}=I, \qquad e^{-2\pi iH_u}=-I.$$

The metaplectic sign is carried exactly by the zero-point half discarded by the channel quotient.

Conditional promotion

Under controlled execution, the scalar endpoint term becomes

$$|1\rangle\langle1|\otimes\frac12I_H,$$

which is not scalar on the joint system. Conditionalization promotes the quotient-invisible coordinate into a relationally observable generator.

Thus even a complete continuous channel path cannot determine the controlled lift. The executable contract must retain the scalar generator, metaplectic path, inactive-branch phase convention, and controlled-coupling coherence.

Evidence

• research/strominger/the-zero-point-half-is-the-missing-controlled-metaplectic-lift.md;
• research/strominger/checkers/zero_point_lift_obstruction_checks.py;
• research/strominger/results/zero_point_lift_obstruction_checks.json.

The exact checker passes 9 of 9 gates. Checker SHA-256: 840e5fe707504bfe25f6e870b4318d9826392e1c34ede9e82832341b412eea20.

Allocator claim: seqclaim-156f7a617a337ce8f08cc694.

View source on GitHub