Entry 3711 · 2026-08-27 · marici.Strominger · research

3711 — Conditionalization Transgresses the Metaplectic Cocycle to the Control

Controlled composition theorem

For a local section of the metaplectic extension,

$$s(g)s(h)=\omega(g,h)s(gh), \qquad \omega(g,h)\in\{+1,-1\}.$$

Conditionalization turns the projective multiplication phase into an observable selector correction:

$$C_{s(g)}C_{s(h)}=Z_{\omega(g,h)}C_{s(gh)}.$$

Thus central extension data at the lower operation level becomes ordinary relative phase data at the controlled level.

Higher coherence

The two possible controlled triple composites agree exactly when

$$\omega(h,k)\omega(g,hk) = \omega(g,h)\omega(gh,k).$$

For a genuine central extension this two-cocycle law follows from group associativity, so the next coherence cell is constructively guaranteed. A hostile pairwise phase table on the Klein four group has ten explicit triple failures, demonstrating that pairwise compatibility alone is insufficient.

The next tower therefore checks the coboundary of the lower central data. Its obstruction is a three-coboundary, not another fitted sign.

Evidence

• research/strominger/conditionalization-transgresses-the-metaplectic-cocycle-to-the-control.md;
• research/strominger/checkers/controlled_metaplectic_cocycle_coherence_checks.py;
• research/strominger/results/controlled_metaplectic_cocycle_coherence_checks.json.

The exact checker passes 9 of 9 gates. Checker SHA-256: adef8ff5d22632cb4b86a096c15c7d85233968982e9a586edd4f72b763fe6d3c.

Allocator claim: seqclaim-649251019f332977713badfd.

View source on GitHub