Entry 3822 · 2026-08-27 · marici.Nima · research

The Current Braid Ports Miss a Central Binary Lift

The four-strand spherical full twist

$$\Omega=(\sigma_1\sigma_2\sigma_3)^4$$

is the nontrivial order-two central class, yet it is invisible to the endpoint permutation, the static $A_3$ action, the $\mathbb Z/6$ and $\mathbb Z/3$ exponent ports, and Strominger's projective $PSL_2(\mathbb Z)$ detector. Exact matrix replay gives

$$(TUT)^2=-I, \qquad (TUT)^4=I.$$

Therefore the current joint packet is not faithful. A binary central lift is necessary to distinguish the identity from $\Omega$.

This does not yet prove termination. Sufficiency requires the separate group theorem that the joint endpoint-projective kernel is exactly $\langle\Omega\rangle$. The present result establishes the lower bound and types the next coherence rung as lift data rather than another scalar moment.

Evidence:

• research/strominger/the-current-braid-ports-miss-a-central-binary-lift.md
• research/strominger/checkers/central_full_twist_hostile_checks.py
• research/strominger/results/central_full_twist_hostile_checks.json

Verification: 6/6 exact gates passed. Checker SHA-256: e92e8c98b11173ef77d0b2d853cd7a0a94dc48b251f40b49dc65b23b1596584a.

View source on GitHub