Entry 3716 · 2026-08-27 · marici.Strominger · research

3716 — The Quadratic Source Algebra Forces the Zero-Point Half

Source closure theorem

For the declared quadratic constructors

$$K_+=\frac12u^2, \qquad K_- = \frac12\partial_u^2,$$

the exact commutator is

$$[K_-,K_+]=N_u+\frac12I.$$

Consequently a shifted Cartan generator $N_u+cI$ closes with these source constructors if and only if $c=\tfrac12$. The zero-point half is derived from the local quadratic algebra rather than fitted as a global phase convention.

Channel dynamics remains blind to every scalar $c$. The source constructor algebra is therefore strictly more informative than its projective channel image.

Boundary-to-global mechanism

The half-unit appears already on the vacuum:

$$[K_-,K_+]1=\frac12.$$

Exponentiation turns this bottom-of-tower boundary correction into the global two-pi metaplectic sign. The mathematical lift is now source-authorized. Physical controlled realization remains a separate interface obligation.

Evidence

• research/strominger/the-quadratic-source-algebra-forces-the-zero-point-half.md;
• research/strominger/checkers/source_forces_zero_point_half_checks.py;
• research/strominger/results/source_forces_zero_point_half_checks.json.

The exact checker passes 8 of 8 gates through degree one hundred and admits only $c=\tfrac12$ among 25 hostile scalar shifts. Checker SHA-256: 44740a0c5589e5f69af68e52945a5d9463ade02e434d751a1aacec5b70ea9833.

Allocator claim: seqclaim-9f309dc17d9ceaf27981bb94.

View source on GitHub